CN104679991A - Ordered proposition-oriented novel method of information fusion - Google Patents

Abstract

The invention discloses an ordered proposition-oriented novel method of information fusion. Focusing on problems of ordered propositions, concepts, such as convexity and extensional ignorance of basic support functions, information center and entropy of basic (or quasi-basic) support functions Lambada*, and compatibility of basic support functions. A novel method of calculating the information center of the basic support functions Lambada*, different from a solving of the center of mass, is provided. Solving the information center of the basic support functions Lambada* is related to only a great trust value of the basic support functions Lambada*; the effect of the method is highlighted; the fact that the great trust value is imparted higher weight is understandable. A modified calculating method of information entropy is provided for the basic support functions Lambada* having multiple maximum trust values and/or 'approximately maximum' trust values, and effectiveness of the method is verified. Finally, the novel method of fusing basic support functions, integrating information center and entropy calculation, compatibility measurement, non-positive integer information center processing, extensional ignorance, convexity and the like, is provided; the problems in information fusion of the problems of ordered propositions are effectively solved.

Description

A kind of information fusion new method towards ordered proposition

Technical field

The present invention relates to a kind of information fusion new method, particularly a kind of information fusion new method towards ordered proposition.

Background technology

Much information is merged, higher-quality information can be obtained, the validity of decision-making can be significantly improved.Information fusion research has very important theory significance and using value, and, Main Countries competitively carries out information fusion research from 20 century 70s so far.Along with the arrival of large data age, information fusion research more becomes the focus of people's common concern.

Ordered proposition class problem has its singularity, and such problem presents the numerous and complicated of application problem.Ordered proposition class problem is the very important problem of a class, evaluates the Typical Representative that class problem is ordered proposition class problem.Evaluate class problem in daily life to be seen everywhere.Such as: the fertility evaluation in arable land, Cultivated-land Fertility can be divided into " high fertility, in upper fertility, middle fertility, in lower fertility, low fertility "; School grade is evaluated, and school grade can be divided into " outstanding, well, to pass, fail "; Fund project is evaluated, the fund project of application is divided into " special excellent, excellent, good, in, poor "; Etc..Although the evidence theory of classics is the Theory of Information Fusion of a kind of " general ", it can not solve ordered proposition class problem.

Someone once proposed the ordered proposition fusion method of physically based deformation barycenter, was the method that uniquely more effectively can process the fusion of ordered proposition class problem so far, better solved ordered proposition class problem, significant to information fusion area research.This fusion method comprises two steps, and one is that to obtain in fusion results be most possibly the sequence number g of true proposition, two be according to process after the uncertainty value of g to proposition redistribute.But there are problems in this fusion method.For easy meter, the fusion method of this physically based deformation barycenter is claimed to be out-of-date methods.

The problems that out-of-date methods exist can be found out by following example.

Example 1.

Substantially function is supported, μ for two: (0.65,0.2,0.1,0.05), ν: (0.7,0.15,0.1,0.05), its weight is respectively, Ω _μ=0.5 and Ω _νthe original fusion result ω ' of=0.5. μ and ν is (0.675,0.175,0.1,0.05).Out-of-date methods first adopt physics to ask the method for barycenter to calculate the barycenter G of ω ' ^old(ω ')=1.525, then construct final fusion results ω.

Press respectively with calculate corresponding ω ^floor, ω ^ceiling:

1., corresponding

ω ^Floor＝(0.8083333333333,0.1333333333333,0.04583333333333,0.0125)

②、

ω ^Ceiling＝(0.3375,0.5791666666667,0.06666666666667,0.01666666666667)

3., ω is combined ^floor, ω ^ceilingobtain

ω＝(0.5611458333333,0.3673958333333,0.0567708333333,0.014687500000)

From both μ, ν compatible (consistance is fine), and value feature is known: point illustrated of the net result ω of fusion should be significantly enhanced, i.e. the maximal value ω (s of ω ₁)=ω ₁obviously should be greater than max{0.65,0.7}; But the maximal value obtained by out-of-date methods but be less than max{0.65,0.7}, this almost runs counter to completely with the intuition of people.Its main cause has two: the first, and centroid calculation is inaccurate; It two is merge and do not link up with the compatibility between μ, ν.

Example 2.

Substantially support function for two, μ=(0.25,0.25,0.25,0.25), ν=(0.25,0.25,0.25,0.25), its weight is respectively Ω _μand Ω _ν, and Ω _μ=Ω _ν=0.5. out-of-date methods: the barycenter calculated is G ^old(ω ^old)=2.5 are ω=ω to the fusion results of μ, ν structure ^old=(0.104166,0.395833,0.395833,0.104166).

Ordered proposition class problem is a classification problem, and basic support function clearly should express the classification being classified object and should being subordinate to usually, allows the proposition adjacent to subscript to give identical trust value at the most.Inherently see, μ=(0.25,0.25,0.25,0.25) and ν=(0.25,0.25,0.25,0.25) be all express ignorant, so two ignorants are through merging, how could become to have and to know? no matter be μ, or ν does not know being investigated object O ' should belong to which kind of actually, just learn that O ' is under the jurisdiction of Equations of The Second Kind or the 3rd class with equally likely possibility 0.395833 once fusion, this is blankety-blank.In other words, out-of-date methods cannot explain why two " ignorants " become " have and know " through merging, and namely increase the foundation of proposition 2,3 true value at all.

If can not from " only have (and 0,0 ..., 0) be that ignorant supports function substantially " jump out in this wrong views, so situation can become very serious.In fact, the basic support function of expressing ignorant has infinite many.Represent that all ignorant and approximate ignorant support the set of function substantially with Δ, namely expand the set that ignorant supports function substantially.Represent all with Θ the set of basic support function. ν ∈ Δ and with the huge of number of combinations is infered, and out-of-date methods, because it is to the erroneous cognition of ignorant concept, cause it to the combination of enormous quantity all to the fusion results made mistake.Meanwhile, expand ignorant and substantially support that the concept of function also can make important expansion to uncertainty knowledge transaction module.As can be seen here, ignorant is differentiated and approximate ignorant supports that how important the concept of function is substantially.

Example 3.

Substantially function is supported for two, μ=(0.1,0.6,0.3), ν=(0.6,0.3,0.1), Ω _μ=Ω _ν=0.5. original fusion result is ω '=(0.35,0.45,0.2).Out-of-date methods draw G ^old(ω ')=1.85, its fusion results is as shown in the table:

	ω old(s 1)	ω old(s 2)	ω old(s 3)
				ω′	0.35	0.45	0.2
ω Floor	0.641666667	0.291666667	0.066666667
				ω Ceiling	0.175	0.725	0.1
ω＝ωold	0.24500000005	0.66000000005	0.09500000005

The subject matter of out-of-date methods is: on the one hand, fails fusion process to associate with there being certain conflict between μ, ν, and the barycenter calculated on the other hand is also bigger than normal, thus result in ω ^old(s ₁) value is on the low side, proposition ω ^old(s ₂) value is bigger than normal, entropy is less than normal.

Example 4.

Basic support function, μ=(0.1,0.2,0.2,0.5), ν=(0.1,0.15,0.15,0.6), Ω _μ=Ω _ν=0.5.

Out-of-date methods: original fusion result ω '=(0.1,0.175,0.175,0.55), G ^old(ω ')=3.175, final fusion results ω=(0.0333333,0.120833,0.570833,0.275).The compatibility of both μ, ν is fairly good, and also easily show that the true value of proposition 4 should be maximum from its value feature, this and ω (s ₃)=ω ^old(s ₃)=max{0.0333333,0.120833,0.570833,0.275} has larger difference.

Example 5.

Basic support function, μ=(0.05,0.1,0.15,0.7), ν=(0.05,0.1,0.15,0.7), Ω _μ=Ω _ν=0.5.

Out-of-date methods:

Original fusion result ω '=(0.05,0.1,0.15,0.7), G ^old(ω ')=3.5;

Final fusion results is ω=ω ^old=(0.0145833,0.05625,0.34375,0.585417);

μ, ν are completely compatible, and the true value of proposition 4 should be maximum, and should be greater than 0.7, visible G ^old(ω ')=3.5 are irrational, simultaneously ω ^oldclearly demarcated degree be starkly lower than μ, ν, ω ', i.e. ω ^oldentropy E (ω ^old) bigger than normal, be also irrational.

To sum up, the problem of out-of-date methods can be summarized as follows:

1. fail to make full use of basic some value features supporting function, the quantity etc. of trust value average, convexity, entropy, maximum trust value;

2. do not consider the compatibility degree between two basic support functions to be fused, fail, according to the Adjusted Option of compatibility degree determination trust value, not provide the basic quantization method supporting function degree of uncertainty of tolerance.This tolerance supports that the effect of the method for function has three substantially: accurately can portray the basic degree of uncertainty supporting function, can be used for the adjusting range of control trust value, can be used as the end condition of adjustment process;

3. for determining the position G of the maximum true value of ω ^old(ω '), simple employing is physical asks centroid method, and its result of calculation has relatively large deviation;

4. G is worked as ^oldwhen (ω ') is for non-integer, to round simply or with respectively corresponding two substantially support that the method for combination of function is very undesirable;

5. G is asked ^old(ω '), calculating original fusion result and trust value set-up procedure are failed clear separating;

6. fail to differentiate the concept that ignorant supports function substantially.

The problems referred to above, the final fusion results that out-of-date methods are obtained and the judgement of people have relatively large deviation.

Summary of the invention

The object of the invention is to propose a kind of information fusion new method towards ordered proposition, to solve the problems that the existing ordered proposition fusion method based on barycenter exists.

The information fusion new method towards ordered proposition that the present invention proposes, specifically describes as follows:

Before expansion specifically describes, do 3 agreements.

1., by " // " as starting character, or use "/* " respectively, explanation or comment section that passage that " */" makes starting character and end mark is step (or sub-step);

2., " BEGIN " and " END ", " { " and " } " and " [" with "] " is statement bracket;

3., μ=(μ ₁, μ ₂..., μ _n), ν=(ν ₁, ν ₂..., ν _n) be any two n units to be fused-substantially support function, " μ average ", " ν average " represents the trust value average of μ, ν respectively, and the weight of μ, ν is respectively Ω _μ, Ω _ν. Δ G represents the compatibility degree between μ, ν, and Α *, Β * represent that ignorant and approximate ignorant support the set of function substantially respectively, Δ=Α * ∪ Β *, γ *=(γ * ₁, γ * ₂..., γ * _n) ∈ Α *, γ * ₁=γ * ₂=...=γ * _n=0. ω ' expression μ, the original fusion result of ν, ω represents μ, the final fusion results of ν.

Step one, [expansion ignorant, the approximate ignorant of expansion support the fusion of function substantially]

Substantially support the concept of function according to expansion ignorant, the approximate ignorant of expansion, to there being one or all to belong to Δ in μ, ν, namely expression formula [μ, ν ∈ Δ or (μ ∈ Δ and ) or ( and ν ∈ Δ)] be genuine situation, provide μ, the corresponding fusion results of ν.

In // following steps, have and

Step 2, [calculating initial fusion results ω ' and the information mind thereof of μ, ν]

1). ${\mathrm{\ω}}^{\′}\left(s_i\right)\←{\mathrm{\Ω}}_{\mathrm{\μ}}\×\mathrm{\μ}\left(s_i\right)\×[1+\mathrm{\μ}\left(\stackrel{\‾}{S}\right)]+{\mathrm{\Ω}}_v\×v\left(s_i\right)\×[1+v\left(\stackrel{\‾}{S}\right)],$ To i=1,2,3,4.

// ω '=(ω ' (s ₁), ω ' (s ₂) ..., ω ' (s _n)), brief note ω ' be (ω ' ₁, ω ' ₂..., ω ' _n)

2). press basic support function and accurate-basic computing method supporting the information mind of function, ask ω '.

/ * G (ω ') represents the information mind of ω ', and the quality of information mind computing method is the key of fusion method, in fusion results, information mind mean the sequence number of the proposition that true value is maximum, position or subscript */

In the following statement of/*, ω ' (s _i)=ω ' _i, 1≤ρ≤1.5, ω ' ^averagethe average of the trust value represented.In the method asking information mind, trust value is more large more important, is less than ω ' ^averagetrust value be excluded */

Step 3, [fusion that G (ω ') is positive integer]

/ * by compatibility tolerance with towards fundamental sum accurate-basic support the information entropy computing method of function to combine to realize to merge */

If G (ω ') non-positive integer, then GOTO step 4.

1). according to definition and the measure thereof of compatibility, ask the compatibility degree of μ and ν.

/ * G (μ), G (ν) they are μ respectively, if the information mind of ν. μ, ν are compatible, then point illustrated of fusion results should obviously strengthen; If μ, ν conflict, then point illustrated of fusion results should obviously weaken */

/ *, when constructing fusion results, selects three to adjust intensity according to compatibility degree, namely forward Adjusted Option respectively with first term be 1, tolerance ζ ₁the arithmetic progression (referring to the sub-step 2 of step 3) of=0.2,0.1 and 0,3), 4)).These forward Adjusted Option provable can guarantee that fusion results has convexity matter, and entropy is diminished.Tolerance by experiment determine */

ΔG←|G(μ)-G(ν)|/(n-1).

2).[0≤ΔG≤1/6？]

The compatibility of/* μ and ν is better, and namely all trust values of compatibility ∈ [completely compatible, compatibility is better], ω ' are maximum to the convergence intensity of information mind; Forward Adjusted Option adopts that first term is 1, tolerance ζ ₁the arithmetic progression * of=0.2/

If 0≤Δ G≤1/6, be then the arithmetic progression forward adjustment ω ' of 0.2 by tolerance.

3).[1/6≤ΔG≤1/3？]

Compatibility between/* μ and ν is placed in the middle, i.e. compatibility ∈ [compatibility is better, and compatibility is poor], and all trust values of ω ' are placed in the middle to the convergence intensity of information mind; Forward Adjusted Option adopts that first term is 1, tolerance ζ ₂the arithmetic progression * of=0.1/

If 1/6≤Δ G≤1/3, be then the arithmetic progression forward adjustment ω ' of 0.1 by tolerance.

4).[1/3＜ΔG？]

Compatibility between/* μ and ν is poor, namely compatibility ∈ (compatibility is poor, completely incompatible], all trust values of ω ' are minimum to the convergence intensity of information mind; Forward Adjusted Option adopts that first term is 1, tolerance ζ ₃the arithmetic progression * of=0/

/ * because of the compatibility between μ, ν poor, need first do forward adjustment, then make reverse adjustment; Reverse adjustment, usual circulation performs reverse adjustment sub-step, and each execution all generates one and substantially supports function, when reverse adjustment sub-step is performed certain, the entropy of its basic support function generated and E (ω ') approximately equal, then circulation executive termination */

The sub-step 2 of the comprehensive above-mentioned steps of/* three), 3), 4) known, first according to compatibility measurement results, select the arithmetic progression of proper tolerances to carry out forward adjustment to ω ', obtain ω ^f. only work as μ, when the compatibility between ν is poor, just need to ω ^fcarry out reverse adjustment, however reverse adjustment need mating surface to fundamental sum accurate-basic support the information entropy computing method of function just can complete */

Although/* is μ, the compatibility between ν is poor, and it is less to the convergence intensity of information mind that forward adjusts all true value, but still may make entropy E (ω ^f) be significantly less than entropy E (ω '). thus, multiple exercise reverse adjustment sub-step may be needed, make E (ω ^f) finally level off to E (ω ') */

If 1/3 < Δ G, then

BEGIN

[first time forward set-up procedure] is the arithmetic progression forward adjustment ω ' of zero by tolerance.

// forward method of adjustment makes entropy reduce, and forward adjustment result is stored in ω ^f

[second time reverse adjustment step]

The main thought of/* second time reverse adjustment step: support function trust value envelope along negative Y direction extruding is basic, make envelope milder, under maintenance package winding thread, trust value histogram area is constant, makes the entropy of entropy close to ω ' of final fusion results ω.Second time reverse adjustment step, is made up of multiple reverse adjustment sub-step usually.Reverse adjustment sub-step makes entropy increase.Generation one is supported the sequence of function by multiple reverse adjustment sub-step substantially: ω ^f-1..., ω ^f-i, ω ^f-(i+1)..., ω=ω ^f-k; E (ω is had in sequence ^f-i) <E (ω ^f-(i+1)), with ω ^f-(i+1)corresponding envelope ratio and ω ^f-icorresponding envelope is milder; And have $E\left({\mathrm{\&omega;}}^{\&prime;}\right)\&cong;E\left(\mathrm{\&omega;}\right)=E\left({\mathrm{\&omega;}}^{F-k}\right)*/$

END.

5). [method ends] method ends.

Step 4, [pre-service is carried out to ω ']

/ *, when G (ω ') is for non-positive integer, by the maximum and secondary large trust value of structure fusion results, needs to carry out pre-service to ω ' for this reason under certain situation (summary). concrete operations slightly */

Step 5, [fusion of G (ω ') non-positive integer]

/ * according to compatibility tolerance and towards fundamental sum accurate-basic support the information entropy computing method of function realize merging */

1). [asking the compatibility between μ and ν]

ΔG←|G(μ)-G(ν)|/(n-1).

2).[0≤ΔG≤1/6？]

The sub-step 2 of/* Adjusted Option and step 3) different, in subscript two places are divided into obtain two parts, itself and be δ */

If/* or then exist punish ? punish if then in subscript with place all get δ/2*/

The compatibility of/* μ and ν is better, i.e. compatibility ∈ [completely compatible, compatibility is better]; All trust values of ω ' are maximum to the convergence intensity of information mind.Forward Adjusted Option adopts that first term is 1, tolerance ζ ₁the arithmetic progression * of=0.2/

If 0≤Δ G≤1/6, then employing tolerance is the arithmetic progression forward adjustment ω ' of 0.2.

3).[1/6≤ΔG≤1/3？]

Compatibility between/* μ and ν is placed in the middle, i.e. compatibility ∈ [compatibility is better, and compatibility is poor], and all trust values of ω ' are placed in the middle to the convergence intensity of information mind.Adjusted Option adopts that first term is 1, tolerance ζ ₂the arithmetic progression * of=0.1/

If 1/6≤Δ G≤1/3, then employing tolerance is the arithmetic progression forward adjustment ω ' of 0.1.

4).[1/3＜ΔG？]

If 1/3 < Δ G, the then sub-step 6 of GOTO step 5).

5). [treatment on special problems]

// sub-step 2 to step 5), 3) ω that obtains, process when there are special circumstances

6).[1/3＜ΔG？]

Compatibility between/* μ and ν is poor, i.e. compatibility ∈ [compatibility is poor, completely incompatible], and all trust values of ω ' are minimum to the convergence intensity of information mind; Adjusted Option adopts that first term is 1, the arithmetic progression * of tolerance ζ 3=0/

If 1/3 < Δ G, then // with the sub-step 4 of step 3).

BEGIN

[first time forward adjustment]

Employing tolerance is the arithmetic progression forward adjustment ω ' of zero.

Treatment on special problems.

If // ω ^fthere are special circumstances, then it is processed, use ω ^fsubstitute ω.

[second time reverse adjustment]

The main thought of/* second time reverse adjustment: along negative Y direction, function trust value envelope is supported in downward extruding substantially, make envelope milder, under maintenance package winding thread, the histogrammic area of trust value is constant, make the entropy of final fusion results ω close to ω ' entropy .*/

/ * reverse adjustment step, be usually made up of multiple sub-reverse adjustment step, reverse adjustment sub-step makes entropy increase. reverse adjustment need to use information entropy New calculating method .*/

/ * reverse adjustment sub-step is recycled execution, generates basic support sequence of function ω ^f-1..., ω ^f-i, ω ^f-(i+1)..., ω=ω ^f-k, in sequence, have E (ω ^f-i) <E (ω ^f-(i+1)), with ω ^f-(i+1)corresponding envelope ratio and ω ^f-icorresponding envelope is milder; When time, above-mentioned loop termination .*/▌

Basic definition in said method and principle as described below:

1, expand ignorant and substantially support function

Basic support letter α *=(α * ₁, α * ₂..., α * _n), if to k=1...n, there is 0≤α * _k≤ 1/n and α * ₁=α * ₂=...=α * _n, then claim α * to be that ignorant supports function substantially, all α * form the set Α * that ignorant supports function substantially.Basic support letter β *=(β * ₁, β * ₂..., β * _n), if to k=1...n, there is 0≤β * _k≤ 1/n and k≤n, has again | β * _j-β * _k|≤ε (ε > 0, very little arithmetic number), then think claim β * to be that approximate ignorant supports function substantially, all β * form the set Β * that approximate ignorant supports function substantially. with all that expansion ignorant supports function substantially.Δ=Α * ∪ Β * is the set that all expansion ignorant supports function substantially, and the radix of Δ is ∞. for convenience of meter, be also called for short expansion ignorant and substantially support that function is that ignorant supports function substantially.

γ *=(γ * ₁, γ * ₂..., γ * _n) ∈ Α *, γ * ₁=γ * ₂=...=γ * _n=0, substantially support that function gamma * expresses ignorant by ignorant more natural.

Expansion ignorant supports function substantially, can further expand the concept of ignorant, be of great significance uncertainty knowledge process tool.Its reason has two:

1., with combination, and with combination, the huge of quantity can be infered, and except to except extremely special combination, out-of-date methods are all to the fusion results made mistake;

2. it is believed that for all uncertain inference models to only have one " uncertain value " to express ignorant, so far.As: certainty factor is theoretical, and 0 expresses ignorant; Evidence theory, [0,0] expresses ignorant; Convex Evidence Theory, γ *=(γ * ₁, γ * ₂..., γ * _n), γ * ₁=γ * ₂=...=γ * _n=0, express ignorant; Etc..Visible expansion ignorant concept is the important expansion to uncertain inference model.

2, basic support function and accurate-basic computing method supporting the information mind of function

λ=(λ ₁, λ ₂..., λ _n) be arbitrary basic support function.If arbitrary function lambda *, except convexity matter, its meets basic all character supporting function, then claim λ * be as the criterion-substantially support function.λ or λ * is represented with λ λ.With reference to physical barycenter formula, obtain the primary Calculation formula of the information mind of λ λ:

CI ^tentatively(λ λ)=(Σ _i=1...nλ λ (s _i) × i)/Σ _i=1...nλ λ (s _i) (#)

But when we are from the visual angle of λ λ, after thinking over the factor relevant to information mind, can find must do important modification to formula (#).Reason has three: the information mind of one, λ λ means the acting in conjunction of all larger trust values (true value), but not information mind is relevant to all trust values; Two, the maximum true value of λ λ is extremely important, in most of the cases maximum trust value subscript determines by the classification investigating object, maximum trust value is larger, and it is larger on the impact of information mind, as the convexity >=γ of λ λ, the information mind G (λ λ) of λ λ gets the subscript of the maximum trust value of λ λ, γ is undetermined constant, and γ=0.55 is determined in experiment; Three, when trust value is less than normal (particularly, when can compare with trust value error range), allow those little trust values being distributed in both ends or one end (because of convexity matter) participate in the calculating of information mind, will relatively large deviation be caused.

Calculate basic support function and accurate-basic method CCI supporting the information mind CI (λ λ) of function:

Method CCI:

In/* step CCI2, the definition of β highlights the effect of the trust value of ">=λ λ average " (also referred to as ">=average "), and the distribution of the trust value of>=average generally levels off to the subscript of maximum trust value; θ ₁, θ ₂for undetermined parameter, θ is determined in experiment ₁=0.55, θ ₂=0.5*/

CCI1. [convexity>=the θ of λ λ ₁]

IF NC (λ λ)>=θ ₁the maximum trust value subscript of THEN{CI (λ λ) ← λ λ. method ends .}.

CCI2. [CI (λ λ) is asked]

// step 2, from scheme (I), (II), (III), selects one

// scheme (I): removing is less than the trust value of 0.5 × λ λ average, the outstanding trust value being more than or equal to λ λ average

// scheme (II): only consider the trust value being more than or equal to λ λ average

// scheme (III): only consider the trust value being more than or equal to τ × λ λ average

// connected applications domain knowledge and experimental result, select θ ₃=0.2 (step CCI3, CCI44)

CCI3. [CI (λ λ) is close ]

IF CI tHEN method ends .).

CCI4. [CI (λ λ) is close ]

IF ₃THEN CI ▌

Such as λ=(0.65,0.2,0.1,0.03,0.02), according to out-of-date methods, the barycenter calculated by formula (#) is 1.57, but all can show that the proposition subscript of decision objects classification should very close to 1. from intuition or experience

By new method, because of NC (λ)=(0.65-0.2)/(1-0.2)=0.5625 > 0.55, therefore have CI (λ)=1, namely information mind is 1.

3, basic concept and the measure thereof supporting compatibility between function

If two basic support functions to be fused are identical, such as μ=(0.1,0.2,0.4,0.2,0.1), ν=(0.1,0.2,0.4,0.2,0.1), consistance (compatibility) is between the two best, the viewpoint so expressed by fusion results, should than the original fusion result (0.1 of μ, ν, 0.2,0.4,0.2,0.1) clearly more demarcated, its information entropy (information entropy will the 5th elaboration) should much smaller than (0.1,0.2,0.4,0.2,0.1) information entropy.

Thus, reply original fusion result adjusts, and the result for example adjusted is (0.033,0.133,0.667,0.133,0.033), (or uncertain reduce) is strengthened from point illustrated of the viewpoint representated by it, its adjustment result is obviously than original fusion result (0.1,0.2,0.4,0.2,0.1) to get well.

Obviously, here a problem needing to solve is had, namely to the original fusion result of any two basic support functions to be fused, make its point of illustrated strengthen (corresponding forward adjustment) or weaken (corresponding reverse adjustment) to what degree by adjusting its trust value actually? a solution is: propose two basic compatibility measures supported between function to be fused, and then provide the true value Adjusted Option according to compatibility degree.

Basic or accurate-basic measure supporting compatibility between function

Might as well suppose 2≤n≤10 (in application, the situation of n > 10 is rare), G (μ), G (ν) represent the information mind position of two basic support function mu to be fused, ν respectively, μ ^average, ν ^averagerepresent the average of the trust value of μ, ν respectively.Compatibility between μ, ν is defined as Δ G=|G (μ)-G (ν) | and/(n-1), wherein n is basic or accurate-basic first number supporting function.

If Δ G=1, then say that μ, ν are incompatible; If Δ G=0, then say that μ, ν are compatible; If 0 < Δ G < 1, then say μ, ν partially compatible.According to the value of Δ G, also by the compatibility degree between μ and ν, following quantitative classification can be done:

1., as 0≤Δ g≤δ ₁, the compatibility between μ and ν is better;

2., δ is worked as ₁< Δ g≤δ ₂, the compatibility between μ and ν is general;

3., δ is worked as ₂< Δ g, the compatibility between μ and ν is poor.

By testing determine δ ₁=1/6, δ ₂=1/3, δ in application ₁, δ ₂value can be provided by expert or professional.

When to two substantially support function mu, ν merge time, by their original fusion result (basic support function or standard-substantially support function) both sides (or) trust value (true value) be rational to information mind convergence to form maximum true value (or maximum and secondary large true value), convergence intensity depends on the compatibility degree between μ, ν, and the better convergence intensity of compatibility is larger.

4, accurate-basic information entropy concept and the computing method thereof supporting function of fundamental sum

For portraying fundamental sum standard-basic uncertainty (the clearly demarcated degree of viewpoint namely) supporting function better, and the fusion difficult problem solving and substantially supports function that to combine with concept of compatibility, compatibility measure, propose basic and accurate-basic information entropy concept and the computing method thereof supporting function.

Information entropy

Be provided with a discrete random variable X, have the value that n possible, a ₁, a ₂..., a _n, the probability that each value occurs is respectively p ₁=P (a ₁), p ₂=P (a ₂) ..., p _n=P (a _n) and Σ _i=1...np _i=1

Also density available matrix description X, $\left(\begin{array}{c}X\\ P\left(x\right)\end{array}\right)=\left[\begin{array}{cccc}{a}_1& a_2& ...& a_n\\ p_1& p_2& ...& p_n\end{array}\right]$

Example 1 evaluates class problem for school grade, the school grade of student is divided into outstanding, good, pass, four classes such as to fail.Here will substantially support that function is considered as stochastic variable, different basic support functions, its degree of uncertainty is not quite similar.For example, substantially support that the density matrix of function (i.e. three stochastic variables) P, S, Z is respectively for three:

$\left(\begin{array}{c}P\\ P\left(p\right)\end{array}\right)=\left[\begin{array}{cccc}1& 2& 3& 4\\ 0& 1& 0& 0\end{array}\right],$

$\left(\begin{array}{c}T\\ P\left(t\right)\end{array}\right)=\left[\begin{array}{cccc}1& 2& 3& 4\\ 0.15& 0.7& 0.1& 0.05\end{array}\right],$

$\left(\begin{array}{c}Z\\ P\left(z\right)\end{array}\right)=\left[\begin{array}{cccc}1& 2& 3& 4\\ 0.25& 0.25& 0.25& 0.25\end{array}\right],$

Substantially support that the degree of uncertainty of function (or saying three stochastic variables) is obviously different, be explained as follows: the degree of uncertainty of P is minimum, and in fact P determines, be i.e. proposition " school grade of student S is well determine " for these three; The degree of uncertainty of T is placed in the middle, and T determines substantially in other words, i.e. proposition " school grade of student S is essentially good "; The degree of uncertainty of Z is maximum, and Z is completely uncertain in other words, does not provide any information of the quality of student S school grade.

1948 is the uncertainty of metric, and Shannon publishes thesis on Bell System Technical Journal " A Mathematical Theory of Communication ", the concept of entropy is introduced message area, and provides the analytical expression of entropy

H(p ₁,p ₂,…,p _n)＝-Σ _i＝1...np _iln p _i＝Σ _i＝1...np _iln(1/p _i) (1)

" entropy " of formula that people claim (1) definition is Shannon entropy, or says information entropy.Entropy is nonnegative number, and the minimum value of entropy is zero.When entropy is zero, corresponding stochastic variable is determined.

Below, with the basic support function (x of (1) formula calculated example 1 ₁, x ₂, x ₃, x ₄) entropy, will can substantially support that function regards stochastic variable as, wherein Σ _i=1...nx _i≤ 1, do not consider the entropy substantially supporting function (0,0,0,0) here.

Definition 1, the basic entropy supporting function

If Θ is one comprise removing (x ₁=0, x ₂=0 ..., x _n=0) all n units-basic space supporting function outside, n>=2; Assuming that during x=0, x ln (1/x)=0.

1., λ=(x ₁, x ₂..., x _n) entropy of ∈ Θ is defined as E (λ)=Σ _i=1...nx _iln (1/x _i);

(2)

2., λ ^mA=(x ₁=1/n, x ₂=1/n ..., xn=1/n) and ∈ Θ has maximum entropy,

E(λ ^MA)＝Σ _i＝1...n(1/n)lnn＝lnn；

3., λ ^mI=(x ₁, x ₂..., x _n) ∈ Θ, right x _k=1, x _j=0, then λ ^mIentropy E (λ ^mI)=0;

4., in Θ, minimum entropy is zero;

5., specification entropy be: NE (λ)=Σ _i=1...nx _iln (1/x _i)/lnn.

Table 1 example 1 represents the entropy of the basic support function of Students ' Learning achievement

Title	Basic support function	Entropy	Proposition	Uncertainty is retouched
					P	(0，1，0，0)	0	Students ' Learning achievement is good	Determine
Q	(0.04,0.9,0.03,	≈0.4339729709
					R	(0.1,0.8,0.1,0)	≈0.6390318597
S	(0.5,0.5,0.0,	≈0.6931471806
					T	(0.15,0.7,0.1,	≈0.9142855815	Students ' Learning achievement is good	Substantially determine
U	(0.2,0.6,0.1,	≈1.0888999753
					U*	(1/3，1/3，1/3，0)	≈1.0986122887
U″	(0.15,0.6,0.15,	≈1.1058898790
					V	(0.4,0.4,0.15,	≈1.1673871969
W	(0.25,0.5,0.15,	≈1.2079736876
					X	(0.25,0.4,0.2,	≈1.3195454632
Y	(0.25,0.3,0.25,	≈1.3762266043
					Z	(0.25,0.25,0.25,	≈1.3862943611	Do not provide appointing of school grade quality	Uncertain

Found out by table 1, the basic support function unique to maximum true value, " entropy " goodishly can portray its uncertainty, and its uncertainty of the larger explanation of entropy is larger.

Basic support function S=(0.5,0.5,0.0,0.0) and V=(0.4,0.4,0.15,0.05) two maximum true value (abbreviation maximal value) are had, actually degree of uncertainty not ideal enough .S, V of describing S, V with entropy are to the school grade " outstanding " of student " or well " can not clearly be distinguished, the uncertainty of S, V is larger in other words, but the entropy of S, V is smaller.As: the viewpoint of T=(0.15,0.7,0.1,0.05) is clearly demarcated more than S, but its entropy is obviously greater than S; The viewpoint of W=(0.25,0.5,0.15,0.1) is also clearly demarcated more than V, but its entropy is greater than V. U for another example, the entropy of ", V, W and X etc., its viewpoint is all clearly demarcated more than U*=(1/3,1/3,1/3; 0), but U ", V, W and X etc. is all greater than U*, and U* has 3 maximal values.

Visible, describing the uncertainty having the basic support function of multiple maximum true value, is the first problem that information entropy faces.Substantially support that the original fusion the possibility of result of function does not meet convexity matter for two, measuring its uncertainty by information entropy is the Second Problem that information entropy faces.For this reason, standard-basic definition supporting function is first provided.

Ω is the set substantially supporting all character of function, meets the function of all character in Ω '=Ω-{ convexity matter }, is called as standard-substantially support function.

Substantially support that the original fusion the possibility of result of functions is standards-substantially support function for two.As, α=(0.86,0.05,0.04,0.03,0.02), β=(0.02,0.03,0.04,0.05,0.86) is two basic support functions to be fused, and their authority is Ω respectively _α=0.5, Ω _β=0.5, easily see that α, β represent two conflicting viewpoints, original fusion result is ω '=(0.415,0.065,0.04,0.065,0.415), ω ' does not meet convexity matter, but it is a standard-substantially support function, so how measure the information entropy of ω '? on the one hand, ω ' has 2 maximal value ω ' (s ₁)=ω ' (s ₅)=0.415=max{ ω ' (s ₁), ω ' (s ₂) ..., ω ' (s ₅); On the other hand, ω ' inherits again conflicting feature between α, β.Sn is made to be a function asking the sequence number of proposition, sn (ρ (s _k))=k, ρ be arbitrary basic or accurate-substantially support function.Aim at-substantially support function, portray the absolute value of the sequence number difference of the maximum two propositions of true value, than portraying, maximal value number is more meaningful.To ω ', should consider | sn (ω ' (s ₅))-sn (ω ' (s ₁)) |/n.To sum up provide as given a definition.

Definition 2, accurate-basic information entropy supporting function of fundamental sum

If to be all n unit basic supports accurate-basic set supporting function of function ∈ Θ (identical with the Θ implication in definition 1) and n unit, n>=2 for Θ *, right there is Σ _i=1...ny _i=1, y _k=max{y ₁, y ₂..., y _n, if there is β × y in 1≤k≤n _k≤ y _j≤ y _k, 1≤j ≠ k≤n (β>=0.9 is determined in experiment), claims y _jbe as the criterion-maximum trust value, and the new computing formula of the information entropy of y is:

Wherein: α is undetermined constant, α=0.1 is determined in experiment; N ' is sum that is maximum and standard-maximum trust value; In formula (3.4), k ', j ' ∈ { maximum true value subscript, secondary large true value subscript }, and make | k '-j ' | maximum; E (y) is identical with the formula (2) in definition 1.Demonstrate by experiment, new information entropy computing method (definition 2) effectively can portray basic or accurate-basic uncertainty supporting function of multiple maximum true value.

Explanation about definition 2:

1. function (x is substantially supported ₁=1/n, x ₂=1/n ..., x ₂=1/n) ∈ Θ has maximum entropy ln n, represents that certain object belongs to n class with equally likely possibility, in other words have expressed and investigated object and belong to actually which kind of ignorant viewpoint, meaningless in actual applications.

2. for the basic function and accurate-substantially support function supported, illustrate k ', j ' ∈ { maximum trust value subscript, secondary large trust value subscript } respectively, and make | k '-j ' | maximum implication:

2.-1 substantially function is supported

A), θ=(0.25,0.25,0.25,0.25,0.0), the entropy of θ:

θ has 4 maximal values, and viewpoint is fuzzy very: do not know by investigated object assign to the 1st, 2,3, which kind of in 4 classes.

E(θ)≈1.58776631147,n′＝4,α＝0.1,E′(θ)＝E(θ)+(ln5-E(θ))×0.8 ^0.1≈1.604513752039097.

B), θ '=(0.24,0.29,0.24,0.23,0), the entropy of θ ': E ' (θ ')=E (θ ') ≈ 1.382024887061296

C), the entropy of θ "=(0.395,0.395,0.07,0.07,0.07), θ ": n '=2, E (θ ") ≈ 1.292251523879885;

α＝0.1，E′(θ″)＝E(θ″)+(ln5-E(θ″))×0.4 ^0.1≈1.581666193999554

2.-2 is accurate-substantially support function

A), ρ=(0.395,0.07,0.07,0.07,0.395), the entropy of ρ: E (ρ) ≈ 1.292251523879885;

α＝0.1,(|k′-j′|/n) ^α＝0.8 ^0.1,E′(ρ)＝E(ρ)+(ln5-E(ρ))×0.8 ^0.1≈1.602438486982842

B), ρ '=(0.395,0.07,0.07,0.395,0.07), the entropy of ρ ':

α＝0.1,E′(ρ′)＝E(ρ′)+(ln5-E(ρ′))×0.6 ^0.1≈1.593642098956754

C), the entropy of ρ "=(0.395,0.07,0.395,0.07,0.07), ρ ":

α＝0.1,E′(ρ″)＝E(ρ″)+(ln5-E(ρ″))×0.4 ^0.1≈1.581666193999554

D), ρ " '=(0.395,0.395,0.07,0.07,0.07), ρ " ' substantially supports function, for carrying out the comparison of ρ " ', ρ ", ρ ' and ρ, by ρ " ' be put in this.E (ρ " ')=E (ρ ")=E (ρ ')=E (ρ), ρ " ' entropy:

α＝0.1,E′(ρ″′)＝E(ρ″′)+(ln5-E(ρ″′))×0.2 ^0.1≈1.562284959336278.

Example 2U*=(1/3,1/3,1/3,0); E (U*) ≈ 1.09861228866811, ln (4)-E (U*) ≈ 0.287682072451781

α＝0.1,(n′/n) ^α＝0.75 ^0.1，E′(U*)≈1.378136174482643

Example 3S=(0.5,0.5,0.0,0.0); E (S) ≈ 0.693147180559945, ln (4)-E (S) ≈ 0.693147180559945

α＝0.1，(n′/n) ^α＝0.5 ^0.1，E′(S)≈1.339876368013095

Example 4V=(0.4,0.4,0.15,0.05), E (V) ≈ 1.167387196909906, ln (4)-E (V) ≈ 0.218907164209985

α＝0.1，(n′/n) ^α＝0.5 ^0.1，E′(V)≈1.371634803201587

Table 2 entropy of the multiple basic support function in new method reckoner 1

Easily see: the entropy of basic support function S, V, U* in table 2, than table 1 in the entropy of basic support function S, V, U* more reasonable.And then explain that point illustrated (or entropy) of U " entropy be greater than the entropy of U: U, U " is very close, the reason of " remain two and three respectively, this entropy that can be used as U is slightly less than U " if but ignore the trust value being less than 0.5 × average, then U, U.For U, the principle of object is divided into Equations of The Second Kind, considers the first kind more at the most; And for U ", the principle of object is divided into Equations of The Second Kind, sometimes perhaps also needs consideration first and the 3rd liang of class, although possibility is very little.

In table 3 (videing infra), for n=5, line number is 2,3,4,5, the basic support function (be expert at and added grey shading) of 6, adopt new formula (4.4.3) to calculate entropy, and press entropy descending (degree of uncertainty is descending) to its sequence, obtain: (0.3,0.3,0.3,0.1,0), (0.32,0.32,0.32,0.04,0), (1/3,1/3,1/3,0,0), (0.4,0.4,0.1,0.1,0), (0.45,0.45,0.1,0,0)

Substantially support that the evaluation result of function is asserted by two tuple < evaluation results for one, evaluation result asserts that confidence level > forms.Being called for short " line number is the basic support function of k " is below " investigate in the principle of object and can not exceed one, two, three classes " for k*. supports the evaluation result of function 2* to assert substantially; The evaluation result of 3*, 4* is asserted basic identical with 2*, be evaluation result assert that confidence level is different, thus, the > 2*'s of the > 3* of 4*.For 4*, the true value at its subscript 4,5 place is zero, and its evaluation result is asserted as " can not exceed first, second and third class ", and this is asserted and determines.The evaluation result of 5* is asserted as " substantially can not exceed first and second class ", and investigation scope narrows down to two classes from three classes, and the entropy of 5* is all less than the entropy of 2*, 3*, 4*.Easily see, it is identical that the evaluation result of 6* is asserted with 5*, just 6* assert Reliability ratio 5* outline higher (entropy is slightly smaller).

See two examples of table 3 again:

1. observe n=5, line number is the basic support function of 12,13, with regard to maximum true value, 13* than 12* add 1,000,000/, the entropy of 13* decreases about 1,000,000 five than the entropy of 12*; 2. observe n=5 again, line number is the basic support function of 6,7, all has two maximum true value therefore need to use the new calculation method of entropy because of the two.The maximum true value of 7* than the maximum true value of 6* add 1,000,000/, the entropy of 7* decreases about 2/1000000ths than the entropy of 6*.It serves to show that it is quite effective for portraying degree of uncertainty by new entropy computing method.

Table 3 couple n=3,4,5, calculates entropy by new method

Theorem 1.

Θ does not comprise μ ₀=(x ₁=0, x ₂=0 ..., x _n=0) substantially function space is supported, μ=(x for one ₁, x ₂..., x _n) be first number n>=2 and have the arbitrary basic support function of unique maximum true value in Θ.Make x=0, have x ln (1/x). assuming that: x _k=max{x ₁, x ₂..., x _nmaximum true value in μ, x _l< x _k; x _k< 1; 0 < Δ _k< 1; Δ _k=Δ ₁+ Δ ₂+ ...+Δ _k-1+ Δ _k+1+ ...+Δ _n, 0≤Δ ₁, Δ ₂..., Δ _k-1, Δ _k+1..., Δ _n≤ Δ _k; μ '=(x ₁-Δ ₁..., x _k-1-Δ _k-1, x _k+ Δ _k, x _k+1-Δ _k+1..., x _n-Δ _n) ∈ Θ;

To μ, perseverance has { Σ _j=1...nx _jln (1/x _j)-{ (x _k+ Δ _k) ln [1/ (x _k+ Δ _k)]+Σ _{j=1...n and j ≠ k}(x _j-Δ _j) ln [1/ (x _j-Δ _j)] > 0 sets up.

The implication of theorem 1 is further illustrated with the basic support function of two in table 3

Line number in table 3	Basic support function	Entropy
			8	λ＝(0.15,0.4,0.2,0.15,0.1)	1.4877983800016510600073553985869
9	λ′＝(0.15,0.400005,0.199995,0.15,	1.4877949141719978696484840021219

λ ' divides little by little clear slightly than the viewpoint representated by λ, its maximum true value adds 5/1000000ths, and the entropy being namely increased to 0.400005, λ ' from 0.4 just decreases about 0.000003465829653 (about 3/1000000ths) than the entropy of λ.The meaning of theorem 1 is, it demonstrates: when one is substantially supported the viewpoint expressed by function overstepping the bounds of propriety bright (or distincter, determinacy degree is higher), then its entropy is just bound to less.

Substantially the situation that the compatibility between function is poor is supported for be fused two, generation one is supported the sequence of function by new fusion method substantially, first element of sequence is original fusion result ω ', and second element is to ω ' the result ω that forward adjustment obtains with the arithmetic progression that tolerance is zero ^f, then may perform repeatedly reverse adjustment sub-step, each reverse adjustment sub-step generates the basic support function that an entropy increases to some extent, and the 3rd is ω to the sequence of last element ^f-1, ω ^f-2..., ω ^f-k, final fusion results ω=ω ^f-k, it is loop termination condition.Visible, concerning fusion new method, information entropy new calculation method is indispensable.

Theorem 1 not only demonstrates portrays the basic validity supporting function by information entropy, and it is provable based on theorem 1: in the step 3,5 of the information fusion new method towards ordered proposition class problem, performing forward set-up procedure necessarily makes entropy reduce, and performs reverse adjustment step and necessarily makes entropy increase.

Beneficial effect of the present invention:

Have on the basis of fusion method in ordered proposition class problem, towards substantially supporting function, giving average, convexity, expansion ignorant, basic supporting function and standard-basic to support " information mind " of function, basic new ideas and the new calculation method such as compatibility, information entropy supported between function.

When from classification angle, observe one when substantially supporting function or standard-basic support function lambda * *, the position of its maximum trust value is extremely important.Out-of-date methods consider that all trust values are to the effect determining maximum trust value position without distinction, therefore have employed physical " barycenter concept " and computing method thereof completely.New method then thinks that each trust value of λ * * is when determining maximum trust value position, there is different importance, trust value is more large more important, and does not go to consider very little trust value, uses " information mind concept " to describe maximum trust value position obviously more reasonable, the nature of λ * * thus.New method, when calculating " information mind ", eliminates and is less than " θ ₂× average " (θ is determined in experiment ₂=0.5) trust value, highlights the trust value being more than or equal to " average ", and special convexity of working as is more than or equal to θ ₁(θ is determined in experiment ₁=0.55), time, " information mind " is assigned the subscript of the proposition with maximum trust value.Visible, ask the method for information mind from ask the method for barycenter have essence different.

Substantially support function to portray from many aspects, introduce information entropy.To only there being the basic support function information entropy of a maximum trust value can describe the basic uncertainty supporting function well, or say a point illustrated.For have multiple maximum trust value basic support function and accurate-substantially support function, propose new information entropy computing method.Demonstrate theorem 1: when to the basic maximum trust value λ supporting function lambda _k< 1 is with positive increment δ _k> 0, λ _k← λ _k+ δ _k≤ 1, simultaneously to j=1...n and j ≠ k, put λ _j← λ _j-δ _j(to j=1 ... n and j ≠ k, have δ _j>=0 and Σ _{j=1 ... n and j ≠ k}δ _j=δ _k), λ is become λ ' by this conversion, and λ ' is still and substantially supports function, then the entropy of λ ' is necessarily less than the entropy of λ.Theorem 1 demonstrates information entropy energy meticulous depiction and has unique uncertainty increasing the basic support function of trust value.Meanwhile, necessarily make the entropy substantially supporting function reduce based on the provable forward set-up procedure of theorem 1, reverse adjustment step must be substantially support that the entropy of function increases.Experimental verification, new information entropy computing method can effectively describe has accurate-basic uncertainty supporting function of multiple fundamental sum that is maximum and/or " approximate maximum " trust value.

The basic measure supporting compatibility between function is proposed, according to the intensity that the trust value of the compatibility degree determination original fusion result between basic support function to be fused converges to information mind, the fusion results of two compatible basic support functions, point illustrated should be enhanced considerably, correspond to high convergence intensity, the fusion results of the basic support function of two conflicts, point illustrated should obviously be weakened, and correspond to low convergence intensity.When compatibility when between two Fused basic support function mu, ν is poor, the problem that could solve between μ, ν that the compatibility between basic support function is measured and fresh information entropy computing method cooperatively interact.

In a word, exactly because the basic support function proposing organic combination " information mind calculating ", " information entropy calculating ", " compatibility tolerance ", " process of the anon-normal integer information heart " and " expansion ignorant " etc. merges new method, just efficiently solve the basic fusion difficult problem supporting function.

Accompanying drawing explanation

Fig. 1 is the schematic diagram of the ordered proposition fusion method that the present invention relates to.

Embodiment

Refer to shown in Fig. 1:

The information fusion new method towards ordered proposition class problem that the present invention proposes, specifically describes as follows:

Before expansion specifically describes, do 3 agreements.

1., by " // " as starting character, or use "/* " respectively, explanation or comment section that passage that " */" makes starting character and end mark is step (or sub-step);

2., " BEGIN " and " END ", " { " and " } " and " [" with "] " is statement bracket;

3., μ=(μ ₁, μ ₂..., μ _n), ν=(ν ₁, ν ₂..., ν _n) be any two n units to be fused-substantially support function, " μ average ", " ν average " represents the trust value average of μ, ν respectively, and the weight of μ, ν is respectively Ω _μ, Ω _ν. Δ G represents the compatibility degree between μ, ν, and Α *, Β * represent that ignorant and approximate ignorant support the set of function substantially respectively, Δ=Α * ∪ Β *, γ *=(γ * ₁, γ * ₂..., γ * _n) ∈ Α *, γ * ₁=γ * ₂=...=γ * _n=0. ω ' expression μ, the original fusion result of ν, ω represents μ, the final fusion results of ν.

Step 1, [μ, ν ∈ Δ or (μ ∈ Δ and ) or ( and ν ∈ Δ)? ]

// foundation expansion ignorant supports the concept of function substantially, provides the fusion results of μ, ν.

/ * supports letter α *=(α * substantially ₁, α * ₂..., α * _n), if to k=1...n, there is 0≤α * _k≤ 1/n and α * ₁=α * ₂=...=α * _n, then claim α * to be that ignorant supports function substantially, all α * form ignorant and substantially support function set Α *; Basic support letter β *=(β * ₁, β * ₂..., β * _n), if to k=1...n, there is 0≤β * _k≤ 1/n and then claim β * to be that approximate ignorant supports function substantially, all β * form approximate ignorant and substantially support function set Β *. γ *=(γ * ₁, γ * ₂..., γ * _n) ∈ Α *, γ * ₁=γ * ₂=...=γ * _n=0, substantially support that function gamma * expresses ignorant by ignorant more natural. with and with the huge of number of combinations can infer, except to except extremely special combination, out-of-date methods all to the fusion results * made mistake/

If μ, ν ∈ Δ, then put ω ← γ *.

If μ ∈ Δ and then put ω ← ν.

If and ν ∈ Δ, then put ω ← μ.

Stop this method.

// in following steps, have ( and )

Step 2, [calculating initial fusion results ω ' and the information mind thereof of μ, ν]

${\mathrm{\&omega;}}^{\&prime;}\left(s_i\right)\&LeftArrow;{\mathrm{\&Omega;}}_{\mathrm{\&mu;}}\&times;\mathrm{\&mu;}\left(s_i\right)\&times;[1+\mathrm{\&mu;}\left(\stackrel{\&OverBar;}{S}\right)]+{\mathrm{\&Omega;}}_v\&times;v\left(s_i\right)\&times;[1+v\left(\stackrel{\&OverBar;}{S}\right)]$ To i=1,2,3,4.

/ * G (ω ') represents the information mind of ω '.The basic support function using us to propose and accurate-basic computing method supporting the function information heart.Information mind is used for determining in fusion results, and trust value is the sequence number of maximum proposition, or says the position of maximum trust value.As can be seen here, for information fusion, the accuracy of the information mind calculated is extremely crucial.The barycenter deviation that out-of-date methods calculate is larger.The position of the information mind that new method calculates is accurate.*/

// in following statement, ω ' (s _i)=ω ' _i, 1 < ρ≤1.5, represent the trust value average of ω ';

Step 3, [fusion that G (ω ') is positive integer]

If G (ω ') non-positive integer, then GOTO step 4.

Step 3.1, [asking the compatibility of μ and ν]

/ * G _μ, G _νif be the information mind of μ, ν respectively. μ, ν are compatible, then point illustrated of fusion results should obviously strengthen, and namely the entropy of fusion results should obviously diminish; If μ, ν conflict, then point illustrated of fusion results should obviously weaken, and namely the entropy of fusion results should obviously become large.New method needs compatibility to measure to calculate with new information entropy to combine closely, and this is one of new method and out-of-date methods fundamental difference.*/

ΔG←|G _μ-G _ν|/(n-1).

Step 3.2, [0≤Δ G≤1/6? ]

The compatibility of // μ and ν is better, i.e. compatibility ∈ [completely compatible, compatibility is better], all trust values are maximum to the convergence intensity of information mind.

// Adjusted Option adopts that first term is 1, tolerance ζ ₁the arithmetic progression I. of=0.2

If 0≤Δ G≤1/6, then arithmetic progression I is adopted to carry out forward adjustment to ω '.

To i=1 ... n, has:

Wherein,

/ * example μ=(0.05,0.15,0.6,0.15,0.05), ν=(0.05,0.15,0.6,0.15,0.05), ω '=(0.05,0.15,0.6,0.15,0.05), G (ω ')=3, G (ω ') is positive integer, and carry out forward adjustment with arithmetic progression I to ω ', process is as follows:

*/

Step 3.3, [1/6≤Δ G≤1/3? ]

The compatibility of/* μ and ν is placed in the middle, i.e. compatibility ∈ [compatibility is better, and compatibility is poor], and all trust values of ω ' are placed in the middle to the convergence intensity of information mind.Adjusted Option adopts that first term is 1, tolerance ζ ₂the arithmetic progression II* of=0.1/

If 1/6≤Δ G≤1/3, then arithmetic progression II is adopted to carry out forward adjustment to ω '.

To i=1 ... n, has:

Wherein,

Step 3.4, [1/3 < Δ G? ]

The compatibility of/* μ and ν is poor, and compatibility ∈ (compatibility is poor, completely incompatible], all trust values of ω ' are minimum to the convergence intensity of information mind.Adjusted Option adopts that first term is 1, tolerance ζ ₃the arithmetic progression III* of=0/

If 1/3 < Δ G, then

// need twice adjustment be carried out, first time forward adjustment, second time reverse adjustment.Forward adjustment result is stored in ω ^f.

// forward method of adjustment makes entropy reduce, and reverse adjustment method makes entropy increase (proving slightly).

Although it is less to the convergence intensity of information mind that/* forward adjusts all true value, forward adjustment still may make E (ω ^f) be significantly less than E (ω ').Reverse adjustment, usually comprise multiple reverse adjustment sub-step */

BEGIN

[forward set-up procedure] adopts arithmetic progression III to carry out forward adjustment to ω '.

[reverse adjustment step]

The target of/* reverse adjustment step is: along the basic trust value envelope supporting function of Y direction extruding, make envelope milder, under maintenance package winding thread, the histogrammic area of trust value is constant, makes the entropy of entropy close to ω ' of final fusion results ω.Reverse adjustment step, is made up of multiple reverse adjustment sub-step usually. reverse adjustment sub-step makes entropy increase (proving slightly).Multiple reverse adjustment sub-step forms one and substantially supports the sequence of function: ω ^f-1..., ω ^f-i, ω ^f-(i+1)..., ω=ω ^f-k; E (ω is had in sequence ^f-i) <E (ω ^f-(i+1)), with ω ^f-(i+1)corresponding envelope necessarily than with ω ^f-icorresponding envelope is milder; And have

σ←1.

If ω ^fmaximum trust value under be designated as n,

Then BEGIN ³// with ω ^fmaximum trust value under be designated as the class of operation of 1 seemingly. concrete operation step slightly .END ³.

If 1 < ω ^fmaximum trust value subscript < n,

Then BEGIN ⁴// with ω ^fmaximum trust value under be designated as 1 operation substantially similar.Concrete operation step is omitted.END ⁴.

END ¹.

Step 3.5, [method ends] method ends.

Step 4, [pre-service is carried out to ω ']

// so far, G (ω ') is non-positive integer.Only when meeting following three conditions for the moment, just pre-service need be carried out to ω '.

If the maximum and secondary large true value subscript of ω is respectively with and

and then adjust ω '.

// adjustment only relates to with have after adjustment

If the maximum and secondary large true value subscript of ω is respectively with and

and then adjust ω '.

// adjustment only relates to with have after adjustment

If then

/ * is to G (ω ') non-positive integer, and new method is neither simply round G (ω '), and also non-combined is corresponding with two fusion results, but the maximum and secondary greatly true value that structure subscript is adjacent, only when time, the maximum and secondary large true value constructed is equal. step 5 complete this process */

Step 5, [fusion of G (ω ') non-positive integer]

Step 5.1, [asking the compatibility of μ and ν]

ΔG←|G(μ)-G(ν)|/(n-1).

Step 5.2, [0≤Δ G≤1/6? ]

// Adjusted Option is different from step 3.2, in subscript with place is divided into obtain two parts, if this two parts and be δ

If/* or then punish punish if then in subscript with place all get δ/2*/

The compatibility of/* μ and ν is better, refers to compatibility ∈ [completely compatible, compatibility is better], the maximum * of convergence intensity from all true value of ω ' to information mind/

The adjustment of // forward adopts that first term is 1, tolerance ζ ₁the arithmetic progression I of=0.2

If 0≤Δ G≤1/6, then // 1≤i≤n

BEGIN

Put

END.

/ * example: G (ω ')=3.4285714285714285714285714285714, Δ G=0,

E (ω ')=1.4144565592355187543815296306473, E (ω)=1.037860468140304529610490015664*/step 5.3, [1/6≤Δ G≤1/3? ]

Compatibility between/* μ and ν is placed in the middle, and compatibility ∈ [compatibility is better, and compatibility is poor], all trust values of ω ' are placed in the middle to the convergence intensity of information mind.Forward Adjusted Option adopts that first term is 1, tolerance ζ ₂the arithmetic progression II* of=0.1/

If 1/6≤Δ G≤1/3, then // 1≤i≤n

BEGIN

Put

END.

Step 5.4, [1/3 < Δ G? ]

If 1/3 < Δ G, then GOTO step 5.6.

The special circumstances that the ω of step 5.5, [treatment on special problems] // obtain step 5.2,5.3 occurs process

Step 5.6, [1/3 < Δ G? ]

The compatibility of/* μ and ν is poor, and compatibility ∈ [compatibility is poor, completely incompatible], all trust values of ω ' are minimum to the convergence intensity of information mind.Forward Adjusted Option adopts that first term is 1, tolerance ζ ₃the arithmetic progression III* of=0/

If 1/3 < Δ G, then // with step 3.4

BEGIN

END.

[treatment on special problems]

If // ω ^foccur special circumstances, then process it, concrete operations (use ω with step 5.5 ^fsubstitute ω)

[second time reverse adjustment]

The target of/* second time reverse adjustment is: along negative Y direction, the envelope of function trust value is supported in downward extruding substantially, make envelope milder, under maintenance package winding thread, the histogrammic area of trust value is constant, make the entropy of final fusion results ω close to ω ' entropy */

// second time reverse adjustment, is made up of multiple reverse adjustment sub-step usually. reverse adjustment sub-step makes entropy increase (proving slightly)

// reverse adjustment sub-step is recycled execution, forms basic support sequence of function ω ^f-1..., ω ^f-i, ω ^f-(i+1)..., ω=ω ^f-k,

E (ω is had in // sequence ^f-i) <E (ω ^f-(i+1)), with ω ^f-(i+1)corresponding envelope ratio and ω ^f-icorresponding envelope is milder;

// when time, above-mentioned circulation executive termination.

σ←1.

If ω ^fmaximum trust value under be designated as n,

Then BEGIN ³// with ω ^fmaximum trust value under be designated as the class of operation of 1 seemingly. concrete operation step slightly .END ³.

If 1 < ω ^fmaximum trust value subscript < n,

Then BEGIN ⁴// with ω ^fmaximum trust value under be designated as 1 operation substantially similar. concrete operation step is omitted END ⁴.

END ¹.

END.▌

Claims (5)

1., towards an information fusion new method for ordered proposition, it is characterized in that, comprise the steps:

/ * uses respectively "/* ", " */" makes starting character and end mark, or the passage making starting character by " // " be step or sub-step explanation part .*/

// " BEGIN ", " END ", " { ", " } " and " [", "] " is statement bracket.

/ * μ=(μ ₁, μ ₂..., μ _n), ν=(ν ₁, ν ₂..., ν _n) be any two n units to be fused-substantially support function, the trust value average of μ, ν is expressed as " μ average ", " ν average ", and the weight of μ, ν is respectively Ω _μ, Ω _ν. Δ G represents the compatibility degree between μ, ν, and Α *, Β * represent that ignorant supports that function and approximate ignorant support the set of function substantially substantially respectively, Δ=Α * ∪ Β *, γ *=(γ * ₁, γ * ₂..., γ * _n) ∈ Α *, γ * ₁=γ * ₂=...=γ * _n=0. ω ' expression μ, the original fusion result of ν, ω represents μ, the final fusion results .* of ν/

Step one, [μ, ν ∈ Δ or (μ ∈ Δ and ) or ( and ν ∈ Δ)]

Substantially the concept of function is supported according to expansion ignorant, the approximate ignorant of expansion, judge that two to be fused are supported function mu substantially, in ν, there is one or all to belong to ignorant and substantially support that function set and approximate ignorant support the union Δ of function set substantially, if then provide μ, the corresponding fusion results of ν;

// in following steps or sub-step, have ( and ).

Step 2, [calculating initial fusion results ω ' and the information mind thereof of μ, ν]

1). ${\mathrm{\&omega;}}^{\&prime;}\left(s_i\right)\&LeftArrow;{\mathrm{\&Omega;}}_{\mathrm{\&mu;}}\&times;\mathrm{\&mu;}\left(s_i\right)\&times;[1+\mathrm{\&mu;}\left(\stackrel{\&OverBar;}{S}\right)]+{\mathrm{\&Omega;}}_v\&times;v\left(s_i\right)\&times;[1+v\left(\stackrel{\&OverBar;}{S}\right)],$ To i=1,2,3,4,

// ω '=(ω ' (s ₁), ω ' (s ₂) ..., ω ' (s _n)), brief note ω ' be (ω ' ₁, ω ' ₂..., ω ' _n);

2). press basic support function and accurate-basic new calculation method supporting the information mind of function, ask ω '.

/ * G (ω ') represents the information mind of ω ', and the quality of information mind computing method is the key of fusion method, in fusion results, information mind mean the sequence number of the proposition that true value is maximum, position or subscript .*/

In the following statement of/*, ω ' (s _i)=ω ' _i, 1≤ρ≤1.5, ω ' ^averagethe trust value average represented. in " information mind method ", trust value is more large more important, is less than ω ^{' average}trust value be excluded .*/

Step 3, [fusion that G (ω ') is positive integer]

/ * according to the compatibility tolerance between μ and ν and towards fundamental sum accurate-basic support the information entropy new calculation method of function realize merging .*/

If G (ω ') non-positive integer, then GOTO step 4.

1). [asking compatibility degree]

According to definition and the measure thereof of compatibility, obtain the compatibility degree of μ and ν.

/ * G (μ), G (ν) they are μ respectively, if the information mind of ν. μ, ν are compatible, then point illustrated of fusion results should

Obvious enhancing; If μ, ν conflict, then point illustrated of fusion results should obviously weaken .*/

/ *, when constructing fusion results, is divided into three forwards adjustment intensity according to compatibility degree, namely Adjusted Option respectively with first term be 1, tolerance ζ ₁the arithmetic progression (referring to the sub-step 2 of step 3) of=0.2,0.1 and 0,3), 4)), these Adjusted Option provable can guarantee that fusion results has convexity matter, tolerance by experiment determine .*/

ΔG←|G(μ)-G(ν)|/(n-1).

2).[0≤ΔG≤1/6？]

The compatibility of/* μ and ν is better, i.e. compatibility ∈ [completely compatible, compatibility is better], and all trust values are maximum to the convergence intensity of information mind, and Adjusted Option adopts first term to be 1, tolerance ζ ₁the arithmetic progression .* of=0.2/

If 0≤Δ G≤1/6, be then the arithmetic progression forward adjustment ω ' of 0.2 by tolerance.

3).[1/6≤ΔG≤1/3？]

The adjustment of/* forward makes Entropy Changes little, and the compatibility between μ and ν is placed in the middle, namely compatibility ∈ [compatibility is better, and compatibility is poor], ω ' convergence intensity .* placed in the middle from all trust values to information mind/

// forward Adjusted Option adopts that first term is 1, tolerance ζ ₂the arithmetic progression of=0.1.

If 1/6≤Δ G≤1/3, be then the arithmetic progression forward adjustment ω ' of 0.1 by tolerance.

4).[1/3＜ΔG？]

Compatibility between/* μ and ν is poor, namely compatibility ∈ (compatibility is poor, completely incompatible], all trust values of ω ' are minimum to the convergence intensity of information mind; Adjusted Option adopts that first term is 1, tolerance ζ ₃the arithmetic progression .* of=0/

/ * because of the compatibility between μ, ν poor, need twice adjustment be carried out, first do forward adjustment, after do reverse adjustment; Reverse adjustment, usual circulation performs reverse adjustment sub-step, and each execution all generates one and substantially supports function, when reverse adjustment sub-step is performed certain, the entropy of the basic support function generated and E (ω ') approximately equal, then circulation executive termination .*/

The sub-step 2 of the comprehensive above-mentioned steps of/* three), 3), 4) known, first according to compatibility degree, i.e. compatibility measurement results, the arithmetic progression of proper tolerances is selected to carry out forward adjustment to ω ', only work as μ, when the compatibility between ν is poor, just need to ω ^fcarry out reverse adjustment, however reverse adjustment need mating surface to fundamental sum accurate-basic support the information entropy computing method of function just can complete .*/

Although/* is μ, the compatibility between ν is poor, and it is less to the convergence intensity of information mind that forward adjusts all true value, but still may make entropy E (ω ^f) be significantly less than entropy E (ω '). thus, may need to perform multiple reverse adjustment sub-step, make E (ω ^f) finally level off to E (ω ') .*/

If 1/3 < Δ G, then

BEGIN

[first time forward set-up procedure] is the arithmetic progression forward adjustment ω ' of zero by tolerance.

// forward method of adjustment makes entropy reduce, and forward adjustment result is stored in ω ^f.

Second time reverse adjustment step:

The main thought of/* second time reverse adjustment step: support function trust value envelope along negative Y direction extruding is basic, make envelope milder, under maintenance package winding thread, trust value histogram area is constant, make the entropy of entropy close to ω ' of final fusion results ω, second time reverse adjustment step, usually being made up of multiple reverse adjustment sub-step. reverse adjustment sub-step makes entropy increase, and generation one is supported the sequence of function by multiple reverse adjustment sub-step substantially: ω ^f-1..., ω ^f-i, ω ^f-(i+1)..., ω=ω ^f-k; E (ω is had in sequence ^f-i) <E (ω ^f-(i+1)), with ω ^f-(i+1)corresponding envelope ratio and ω ^f-icorresponding envelope is milder; And have

E(ω′)≌E(ω)＝E(ω ^F-k).*/

END；

5). [method ends]

Method ends.

Step 4, [pre-service is carried out to ω ']

/ *, when G (ω ') is for non-positive integer, by the maximum and secondary large trust value of structure fusion results, needs to carry out pre-service to ω ' for this reason under certain situation (summary). concrete operations slightly .*/

Step 5, [fusion of G (ω ') non-positive integer]

// calculate realize fusion according to compatibility tolerance and towards the fundamental sum standard-information entropy of basic support function.

1). [asking the compatibility between μ and ν]

ΔG←|G(μ)-G(ν)|/(n-1).

2).[0≤ΔG≤1/6？]

The sub-step 2 of/* Adjusted Option and step 3) different, in subscript two places are divided into obtain two parts, itself and be δ .*/

If/* or then exist punish ? punish if then in subscript with place all get δ/2.*/

The compatibility of/* μ and ν is better, means compatibility ∈ [completely compatible, compatibility is better]; The maximum .* of convergence intensity from all trust values of ω ' to information mind/

// Adjusted Option adopts that first term is 1, tolerance ζ ₁the arithmetic progression of=0.2.

If 0≤Δ G≤1/6, then employing tolerance is the arithmetic progression forward adjustment ω ' of 0.2.

3).[1/6≤ΔG≤1/3？]

Compatibility between/* μ and ν is placed in the middle, and namely all trust values of compatibility ∈ [compatibility is better, and compatibility is poor], ω ' are placed in the middle to the convergence intensity of information mind, and Adjusted Option adopts first term to be 1, tolerance ζ ₂the arithmetic progression .* of=0.1/

If 1/6≤Δ G≤1/3, then employing tolerance is the arithmetic progression forward adjustment ω ' of 0.1.

4).[1/3＜ΔG？]

If 1/3 < Δ G, the then sub-step 6 of GOTO step 5).

5). [treatment on special problems]

// sub-step 2 to step 5), 3) ω that obtains, process when there are special circumstances

6).[1/3＜ΔG？]

Compatibility between/* μ and ν is poor, i.e. compatibility ∈ [compatibility is poor, completely incompatible], and all trust values of ω ' are minimum to the convergence intensity of information mind; Adjusted Option adopts that first term is 1, the arithmetic progression * of tolerance ζ 3=0/

If 1/3 < Δ G, then // with the sub-step 4 of step 3).

BEGIN

[first time forward adjustment]

Employing tolerance is the arithmetic progression forward adjustment ω ' of zero.

Treatment on special problems.

If // ω ^fthere are special circumstances, then it is processed, use ω ^fsubstitute ω.

[second time reverse adjustment]

The main thought of/* second time reverse adjustment: along negative Y direction, function trust value envelope is supported in downward extruding substantially, make envelope milder, under maintenance package winding thread, the histogrammic area of trust value is constant, make the entropy of final fusion results ω close to ω ' entropy .*/

/ * reverse adjustment step, be usually made up of multiple sub-reverse adjustment step, reverse adjustment sub-step makes entropy increase. reverse adjustment need to use information entropy New calculating method .*/

/ * reverse adjustment sub-step is recycled execution, generates basic support sequence of function ω ^f-1..., ω ^f-i, ω ^f-(i+1)..., ω=ω ^f-k, in sequence, have E (ω ^f-i) <E (ω ^f-(i+1)), with ω ^f-(i+1)corresponding envelope ratio and ω ^f-icorresponding envelope is milder; As E (ω ') ≌ E (ω)=E (ω ^f-k) time, above-mentioned loop termination .*/.

2. the information fusion new method towards ordered proposition class problem according to claim 1, is characterized in that, the method adopts expansion ignorant concept solution as follows to relate to expansion ignorant and substantially supports the fusion problem of function: basic support letter α *=(α * ₁, α * ₂..., α * _n), if to k=1...n, there is 0≤α * _k≤ 1/n and α * ₁=α * ₂=...=α * _n, then claim α * to be that ignorant supports function substantially, composition ignorant supports the set Α * of function substantially. basic support letter β *=(β * ₁, β * ₂..., β * _n), if to k=1...n, there is 0≤β * _k≤ 1/n and β * ₁≌ β * ₂≌ ... ≌ β * _n, then claim β * to be that approximate ignorant supports function substantially, the approximate ignorant of composition supports the set Β * of function substantially, and expansion ignorant supports that the concept of function means substantially, and Δ=Α * ∪ Β * is the set that all ignorant supports function substantially, and the radix of Δ is ∞.

3. the information fusion new method towards ordered proposition class problem according to claim 1, is characterized in that, basic support function with accurate-substantially support that the computing method of the information mind of function are as follows:

λ=(λ ₁, λ ₂..., λ _n) be arbitrary basic support function, if arbitrary function lambda *, except convexity matter, it meets the basic all character supporting function, then claim λ * be as the criterion-substantially support function, represent λ or λ * with λ λ. the method calculating the information mind CI (λ λ) of λ λ is CCI:

// θ ₁, θ ₃for undetermined parameter, θ is determined in experiment ₁=0.55, θ ₃=0.2

CCI1. [convexity>=the θ of λ λ ₁] //NC (λ λ) represents the convexity of λ λ

IF NC (λ λ)>=θ ₁the maximum trust value subscript of THEN{CI (λ λ) ← λ λ. method ends .}.

CCI2. [CI (λ λ) is asked]

CCI3. [CI (λ λ) is close or it is close ]

4. the information fusion new method towards ordered proposition class problem according to claim 1, is characterized in that, in new method fundamental sum accurate-basic support the concept of compatibility between function and measure as follows:

Might as well suppose 2≤n≤10 (in application, the situation of n > 10 is rare), G (μ), G (ν) represent the information mind position of two basic support function mu to be fused, ν respectively, μ ^average, ν ^averagerepresent the average of μ, ν respectively, the compatibility between μ, ν is defined as Δ G=|G (μ)-G (ν) | and/(n-1), if Δ G=1, says that μ, ν are incompatible; If Δ G=0, say that μ, ν are compatible; If 0 < Δ G < 1, says μ, ν partially compatible;

According to the value of Δ G, also by the compatibility degree between μ and ν, following quantitative classification can be done:

1., as 0≤Δ g≤δ ₁, the compatibility between μ and ν is better; 2., δ is worked as ₁< Δ g≤δ ₂, the compatibility between μ and ν is general; 3., δ is worked as ₂< Δ g, the compatibility between μ and ν is poor, obtains δ by experiment ₁=1/6, δ ₂=1/3;

When μ, ν merge, by its original fusion result: basic or accurate-basic support function both sides or true value be rational to information mind convergence to form maximum or secondary large true value, convergence intensity depends on the compatibility degree between μ, ν, and the better convergence intensity of compatibility is larger.

5. the information fusion new method towards ordered proposition class problem according to claim 1, is characterized in that, information entropy concept and the New calculating method thereof of accurate-basic support function of fundamental sum are as follows:

The analytical expression of entropy

H(p ₁,p ₂,…,p _n)＝-∑ _i＝1…np _ilnp _i＝∑ _i＝1…np _iln(1/p _i)

(1)

Definition 1, the basic entropy supporting function

If Θ is removing (x ₁=0, x ₂=0 ..., x _n=0) one outside comprises all n unit-basic space supporting function, n>=2; Assuming that during x=0, x ln (1/x)=0.

1. λ=(x ₁, x ₂..., x _n) entropy of ∈ Θ is defined as E (λ)=∑ _{i=1 ... n}x _iln (1/x _i)

(2)

② ${\mathrm{\&lambda;}}^{\mathrm{MA}}=(x_1=\frac{1}{n},x_2=\frac{1}{n},...,x_n=\frac{1}{n})\&Element;\mathrm{\&Theta;}$ There is maximum entropy, $E\left({\mathrm{\&lambda;}}^{\mathrm{MA}}\right)=\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}\frac{1}{n}\ln n=\ln n$

3. λ ^mI=(x ₁, x ₂..., x _n) ∈ Θ, right all there is x _k=1, x _j=0, then λ ^mIentropy E (λ ^mI)=0;

4., in Θ, minimum entropy is zero;

5. specification entropy be: NE (λ)=∑ _{i=1 ... n}[x _iln (1/x _i)]/(lnn).

Ω is the set substantially supporting all character of function, meets the function of all character in Ω '=Ω-{ convexity matter }, is called as standard-substantially support function, substantially supports that the original fusion the possibility of result of functions is standards-substantially support function for two;

Definition 2, accurate-basic information entropy supporting function of fundamental sum

If to be all n unit basic supports accurate-basic set supporting function of function ∈ Θ (identical with the Θ implication in definition 1) and n unit for Θ * _,n>=2 _,right there is ∑ _{i=1 ... n}y _i=1, y _k=max{y ₁, y ₂..., y _n, if there is β × y in 1≤k≤n _k≤ y _j≤ y _k, 1≤j ≠ k≤n (β>=0.9 is determined in experiment), claims y _jbe as the criterion-maximum trust value, and the new computing formula of the information entropy of y is:

Wherein: α is undetermined constant, α=0.1 is determined in experiment; N ' is sum that is maximum and standard-maximum trust value; In formula (3.4), k ', j ' ∈ { maximum true value subscript, secondary large true value subscript }, and make | k '-j ' | maximum; E (y) is identical with the formula (2) in definition 1;

Theorem 1.

Θ does not comprise μ ₀=(x ₁=0, x ₂=0 ..., x _n=0) substantially function space is supported, μ=(x for one ₁, x ₂..., x _n) be first number n>=2 and have the arbitrary basic support function of unique maximum true value in Θ, make x=0, have x ln (1/x). assuming that: x _k=max{x ₁, x ₂..., x _nmaximum true value in μ, x _l< x _k; x _k< 1; 0 < Δ _k< 1; Δ _k=Δ ₁+ Δ ₂+ ...+Δ _k-1+ Δ _k+1+ ...+Δ _n, 0≤Δ ₁, Δ ₂..., Δ _k-1, Δ _k+1..., Δ _n≤ Δ _k; μ '=(x ₁-Δ ₁..., x _k-1-Δ _k-1, x _k+ Δ _k, x _k+1-Δ _k+1..., x _n-Δ _n) ∈ Θ;

To μ, perseverance has { ∑ _j=1...nx _jln (1/x _j)-{ (x _k+ Δ _k) ln [1/ (x _k+ Δ _k)]+∑ _{j=1...n and j ≠ k}(x _j-Δ _j) ln [1/ (x _j-Δ _j)] > 0 sets up.