CN1645358A - Evidence theory information blending decision method based on state vector distance - Google Patents

Abstract

The invention is an evidence theory information fusion decision-making method based on state vector distance for decision-making on multi-source heterogeneous information fusion results. Steps: determine the information fusion result based on D-S evidence theory; determine the support degree of the focal element attribute, and use each focal element in the power set of the identification framework as a candidate decision; determine the candidate decision vector, considering the BPA distribution of the candidate decision And the focal element support obtained from the attribute level, normalize the candidate decision vector; determine the ideal state vector of the candidate decision. The decision-making focal element that 100% meets the decision-maker's requirements is regarded as an ideal focal element; the distance between state vectors is determined; the decision-making method. First determine the total support of the candidate decision A _i (i=1, 2, Λ, m), and then select the largest A ^* , which is the result of DS evidence fusion decision based on the state vector distance. Advantages: This method combines the attributes of decision-making primitives and non-primitives, fully considers the degree of correlation between focal elements, reduces the loss of opportunities, and is objective and effective.

Description

Evidence theory information blending decision method based on state vector distance

Technical field

What the present invention relates to is a kind of evidence theory information blending decision method based on state vector distance that multi-source heterogeneous information fusion results is made a strategic decision.Belong to technical field of information processing.

Background technology

At present, carry out decision methods according to D-S (Dempster-Shafer) evidence theory Multi-source Information Fusion result and mainly contain two kinds of forms: one is based on decision-making primitive (element that can not divide again among the framework of identification Θ) attribute; Another kind is the attribute in conjunction with decision-making primitive and non-primitive.There are defectives such as subjectivity is strong, versatility is poor, connotation is not obvious, decision-making results is undesirable in these two class methods.

Summary of the invention

The objective of the invention is to defective, designed a kind of D-S evidence information blending decision method based on state vector distance at above-mentioned existence.This method is in conjunction with the attribute of decision-making primitive and non-primitive, taken into full account the degree of correlation between the burnt unit, reduced the loss of chance (be meant obtain correct state estimation and the chance of recognition objective), and this method has characteristics such as objective, effective, technical solution of the present invention: based on the evidence theory information blending decision method of state vector distance, its steps in sequence is divided into:

(1) definite information fusion result based on the D-S evidence theory.According to the difference that merges background, select framework of identification Θ={ θ ₁, θ ₂, Λ, θ _nAnd power set P (Θ)={ A ₁, A ₂, Λ, A _m, and multi-source information is carried out fusion treatment based on the D-S evidence theory.

(2) determine burnt meta-attribute support.Each burnt unit among the power set P (Θ) of framework of identification Θ is all made a strategic decision burnt first A as the candidate _iAttribute is to the candidate A that makes a strategic decision _jThe attribute level support, just become first A for Jiao _i(i=1,2, Λ, m) support between the attribute.This support is $s(i,j)=\frac{\left|A_{i}I{A}_j\right|}{\left|A_{i}Y{A}_j\right|}$ (i，j＝1，2，Λ，m)，

Wherein || represent the number of the primitive that burnt meta-attribute comprises.

(3) candidate's decision vector determines.If ∏ _{P (Θ)}The space of being made up of the element among the P (Θ) is if ∏ _{P (Θ)}In element carry out linear combination after, still at ∏ _{P (Θ)}In, ∏ then _{P (Θ)}Be the burnt first vector space of evidence, its base is the element { A among the P (Θ) ₁, A ₂, Λ, A _m.If T (V) ∈ ∏ _{P (Θ)}, then can be expressed as T (V)=[α ₁A ₁, α ₂A ₂, Λ, α _mA _m] or $T\left(V\right)=\underset{i=1}{\overset{m}{\mathrm{\Σ}}}{\mathrm{\α}}_i{A}_i,$ α wherein _i∈ R, (i=1,2, Λ, m).Consider burnt first support that BPA distributes and the dependency aspect obtains that the candidate makes a strategic decision, candidate's decision vector is expressed as T (A _iT)=[(i, 1), t (i, 2), Λ, t (i, m)], wherein t (i, j)=s (i, j) * m (A _j), (i, j=1,2, Λ, m).Candidate's decision vector is carried out normalization, get T _n(A _iT ')=[(i, 1), t ' (i, 2), Λ, t ' (i, m)], wherein $t^{\′}(i,j)=\frac{t(i,j)}{\underset{j=1}{\overset{m}{\mathrm{\Σ}}}t(i,j)},$ (i，j＝1，2，Λ，m)。

(4) determine the perfect condition vector that the candidate makes a strategic decision.The 100% burnt unit of decision-making that satisfies decision maker's requirement is regarded as desirable burnt unit, and its satisfaction degree can be represented with following state vector: T ^*(A _i)=[t ^*(i, 1), t ^*(i, 2), Λ, t ^*(i, m)], wherein $t^{*}(i,j)=\left\{\begin{array}{cc}1& i=j\\ 0& i\≠j\end{array}\right.,$ (i，j＝1，2，Λ，m)。Claim T ^*(A _i) be the perfect condition vector of candidate decision-making.

(5) determine distance between the state vector.If T is (V ₁), T (V ₂) ∈ ∏ _{P (Θ)}, and T (V ₁)=[α ₁, α ₂, Λ, α _m], T (V ₂)=[β ₁, β ₂, Λ, β _m], α _i, β _i∈ R, (i=1,2, Λ, m), T (V then ₁) and T (V ₂) between distance may be defined as: $\mathrm{Dis}[T\left(V_1\right),T\left(V_2\right)]=\frac{1}{m}\underset{i=1}{\overset{m}{\mathrm{\Σ}}}|{\mathrm{\α}}_i-{\mathrm{\β}}_i|.$ Correspondingly, the candidate A that makes a strategic decision _iNormalized vector T _n(A _i) with the perfect condition vector T of this candidate decision-making ^*(A _i) between distance: $\mathrm{Dis}[T_n\left(A_i\right),T^{*}\left(A_i\right)]=\frac{1}{m}\underset{j=1}{\overset{m}{\mathrm{\Σ}}}|t^{\′}(i,j)-t^{*}(i,j)|$ (i＝1，2，Λ，m)。

(6) decision-making technique.At first determine the candidate A that makes a strategic decision _i(i=1,2, Λ, m) total support:

TSD (A _i)=1-Dis[T _n(A _i), T ^*(A _i)], select wherein maximum then $A^{*}(A^{*}=\underset{A_i}{\max }[\mathrm{TSD}\left(A_i\right)\left]\right),$ The D-S evidence that is based on state vector distance merges the result of decision.

Advantage of the present invention: each the burnt unit among the power set P (Θ) of framework of identification Θ all as candidate's decision-making, has been avoided the improper loss that may cause of choosing of candidate's decision-making.On attribute level, do not consider that the BPA of burnt unit distributes, only consider the degree of correlation between the burnt meta-attribute, i.e. support.The function of determining this support has unique, the univocal advantage of form.On the evidence aspect, according to burnt first support that BPA distributes and the dependency aspect obtains of candidate's decision-making, structure evidence aspect support.By the element of framework of identification power set, constitute a space, in conjunction with the evidence aspect support of candidate's decision-making, determine candidate's decision vector.Introduce the perfect condition vector of candidate's decision-making, the definition distance measure makes up decision model.This decision model is in conjunction with the attribute of decision-making primitive and non-primitive, taken into full account the degree of correlation between the burnt unit, reduced the loss of chance, and decision model is more objective, effective, introduces the subjectivity that the BUM function brings when having avoided in the evidence aspect, calculating evidence level support in the prior art.

Embodiment

Embodiment,

With a certain hydrometric station, entrance of Changjiang River 1-3 in 2002 month water monitoring data is information source, based on the D-S evidence theory it is carried out fusion treatment, and is object with its fusion results, and implementation step of the present invention is described.

(1) definite information fusion result based on the D-S evidence theory.The basic reliability distribution value of water monitoring data sees Table 1.According to the characteristics of water quality assessment, selecting framework of identification Θ is { I, II, III, IV} and power set P (Θ) thereof={ I, I II, II, II III, III, III IV, IV, Θ }, the corresponding respectively expression water quality of I, I II, II, II III, III, IIIIV, IV classification one class, one or two classes, two classes, two or three classes, three classes, three or four classes, four classes, the uncertain water quality classification of the corresponding expression of Θ.Based on the D-S evidence theory it is carried out fusion treatment, the results are shown in Table 2.

The basic reliability distribution value of table 1 water monitoring data

I I?II II II?III III IIIIV IV Θ

BOD ₅ 0.64 0.11 0.08 0.06 0.03 0.02 0.01 0.05

Permanganate

0.12 0.56 0.1 0.08 0.04 0.02 0.01 0.07

Index

Table 2 BOD ₅Merge with the permanganate index achievement data

k＝0.239 I I?II II II?III III IIIIV IV Θ

BOD5 0.64 0.11 0.08 0.06 0.03 0.02 0.01 0.05

Permanganate

0.12 0.56 0.1 0.08 0.04 0.02 0.01 0.07

Index

Fusion results 0.656 0.1279 0.1698 0.0171 0.0164 0.0037 0.0022 0.0046

(2) determine burnt meta-attribute support.Each burnt unit among the power set P (Θ) of framework of identification Θ is all made a strategic decision burnt first A as the candidate _iAttribute is to the candidate A that makes a strategic decision _jThe attribute level support s of (i, j=1,2, Λ, 8) (i, j), $s(i,j)=\frac{\left|A_{i}I{A}_j\right|}{{|A}_{i}Y{A}_j|},$ See Table 3.

The make a strategic decision support of burnt meta-attribute of table 3 candidate

I I?II II II?III III IIIIV IV Θ

I 1 0.5 0 0 0 0 0 0.25

I?II 0.5 1 0.5 0.33 0 0 0 0.5

II 0 0.5 1 0.5 0 0 0 0.25

II?III 0 0.33 0.5 1 0.5 0.33 0 0.5

III 0 0 0 0.5 1 0.5 0 0.25

IIIIV 0 0 0 0.33 0.5 1 0.5 0.5

IV 0 0 0 0 0 0.5 1 0.25

Θ 0.25 0.5 0.25 0.5 0.25 0.5 0.25 1

(3) candidate's decision vector determines.According to burnt first support that BPA distributes and the dependency aspect obtains of candidate's decision-making, candidate's decision vector T (A _i) be expressed as T (A _iT)=[(i, 1), t (i, 2), Λ, t (i, 8)], wherein t (i, j)=s (i, j) * m (A _j), (i, j=1,2, Λ, 8), A ₁, A ₂, Λ, A ₈Correspondence, I II, II, II III, III, III IV, IV, Θ.With candidate's decision vector T (A _i) carry out normalization, get normalized candidate's decision vector T _n(A _iT ')=[(i, 1), t ' (i, 2), Λ, t ' (i, 8)], wherein $t^{\′}(i,j)=\frac{t(i,j)}{\underset{j=1}{\overset{m}{\mathrm{\Σ}}}t(i,j)},$ (i，j＝1，2，Λ，8)。

Candidate's decision vector T _n(I)=(0.9096,0.0887,0,0,0,0,0,0.0017)

Candidate's decision vector T _n(I II)=(0.5977,0.2331,0.1547,0.0104,0,0,0,0.0042)

Candidate's decision vector T _n(II)=(0,0.2627,0.6970,0.0353,0,0,0,0.0049)

Candidate's decision vector T _n(II III)=(0,0.2726,0.5432,0.1094,0.0525,0.0077,0,0.0147)

Candidate's decision vector T _n(III)=(0,0,0,0.3071,0.5857,0.0643,0,0.0429)

Candidate's decision vector T _n(III IV)=(0,0,0,0.2714,0.3905,0.1762,0.0524,0.1095)

Candidate's decision vector T _n(IV)=(0,0,0,0,0,0.3585,0.4151,0.2264)

Candidate's decision vector T _n(Θ)=(0.5649,0.2205,0.1464,0.0296,0.0141,0.0066,0.0021,0.0159)

(4) determine the perfect condition vector that the candidate makes a strategic decision.The 100% burnt unit of decision-making that satisfies decision maker's requirement is regarded as desirable burnt unit, and its satisfaction degree can be represented with following state vector: T ^*(A _i)=[t ^*(i, 1), t ^*(i, 2), Λ, t ^*(i, 8)], wherein $t^{*}(i,j)=\left\{\begin{array}{cc}1& i=j\\ 0& i\≠j\end{array}\right.,$ (i，j＝1，2，Λ，8)。Claim T ^*(A _i) be the perfect condition vector of candidate decision-making.

The perfect condition vector T of candidate's decision-making ^*(I)=(1,0,0,0,0,0,0,0);

The perfect condition vector T of candidate's decision-making ^*(I II)=(0,1,0,0,0,0,0,0);

The perfect condition vector T of candidate's decision-making ^*(II)=(0,0,1,0,0,0,0,0);

The perfect condition vector T of candidate's decision-making ^*(II III)=(0,0,0,1,0,0,0,0)

The perfect condition vector T of candidate's decision-making ^*(III)=(0,0,0,0,1,0,0,0);

The perfect condition vector T of candidate's decision-making ^*(III IV)=(0,0,0,0,0,1,0,0);

The perfect condition vector T of candidate's decision-making ^*(IV)=(0,0,0,0,0,0,1,0);

The perfect condition vector T of candidate's decision-making ^*(Θ)=(0,0,0,0,0,0,0,1)

(5) determine distance between the state vector.The candidate A that makes a strategic decision _iNormalized vector T _n(A _i) with the perfect condition vector T of this candidate decision-making ^*(A _i) between distance D is: $\mathrm{Dis}[T_n\left(A_i\right),T^{*}\left(A_i\right)]=\frac{1}{m}\underset{j=1}{\overset{m}{\mathrm{\Σ}}}|t^{\′}(i,j)-t^{*}(i,j)|$ (i＝1，2，Λ，8)。

Distance D is[T _n(I), T ^*(I)]=0.0113; Distance D is[T _n(I II), T ^*(I II)]=0.0959

Distance D is[T _n(II), T ^*(II)]=0.0379; Distance D is[T _n(II III), T ^*(II III)]=0.1114;

Distance D is[T _n(III), T ^*(III)]=0.0518; Distance D is[T _n(III IV), T ^*(III IV)]=0.103

Distance D is[T _n(IV), T ^*(IV)]=0.0731; Distance D is[T _n(Θ), T ^*(Θ)]=0.1230

(6) decision-making technique.At first determine the candidate A that makes a strategic decision _iSupport TSD:TSD (the A that (i=1,2, Λ, 8) are total _i)=1-Dis[T _n(A _i), T ^*(A _i)], see Table 4.Select wherein maximum then $A^{*}(A^{*}=\underset{A_i}{\max }[\mathrm{TSD}\left(A_i\right)\left]\right),$ Promptly based on the D-S evidence fusion results of state vector distance, adjudicating this basin water quality classification is I class water.

Table 4 is based on BOD ₅Candidate's decision support degree with permanganate index achievement data fusion results

I I、II II II、III III III、IV IV Θ

This paper method 0.9887 0.9041 0.9621 0.8886 0.9482 0.897 0.9269 0.877

Claims (1)

1. The evidence-theoretic information fusion decision-making method based on state vector distance, which is characterized in that the method steps are divided into: (1) Determine the information fusion result based on the D-S evidence theory, select the identification frame and its power set according to the different fusion backgrounds, and perform fusion processing on the multi-source information based on the D-S evidence theory; (2) Determine the support degree of focal element attributes. Each focal element in the power set of the identification framework is regarded as a candidate decision, and the support degree of the focal element attribute to the attribute level of the candidate decision becomes the support degree between the focal element attributes, and the support degree is $\mathrm{the\; s}(i,j)=\frac{\left|A_{i}I{A}_j\right|}{\left|A_{i}Y{A}_j\right|},(i,j=\mathrm{1,2},\mathrm{\Λ},m),$ Where |·| indicates the number of primitives contained in the focal element attribute; (3) Determination of candidate decision vectors. Considering the basic trust distribution distribution of the candidate decision and the focal element support obtained from the attribute level, the candidate decision vector is expressed as T(A _i )=[t(i,1),t(i,2),Λ,t( i, m)], where t(i, j)=s(i, j)*m(A _j ), (i, j=1, 2, Λ, m). Normalize the candidate decision vectors to get T _n (A _i )=[t′(i, 1), t′(i, 2), Λ, t′(i, m)], where $t^{\′}(i,j)=\frac{t(i,j)}{\underset{j=1}{\overset{m}{\mathrm{\Σ}}}t(i,j)},(i,j=\mathrm{1,2},\mathrm{\Λ},m);$ (4) Determine the ideal state vector of the candidate decision. The decision-making focal element that 100% meets the decision maker's requirements is regarded as an ideal focal element, and its degree of satisfaction can be expressed by the following state vector: T ^* (A _i ) = [t ^* (i, 1), t ^* (i, 2 ), Λ, t ^* (i, m)], where $t^{*}(i,j)=\left\{\begin{array}{cc}1& i=j\\ 0& i\≠j\end{array}\right.,(i,j=\mathrm{1,2},\mathrm{\Λ},m).$ Call T ^* (A _i ) the ideal state vector of the candidate decision; (5) Determine the distance between state vectors. The distance Dis between the normalized vector T _n (A _i ) of the candidate decision A _i and the ideal state vector T ^* (A _i ) of the candidate decision: $\mathrm{dis}[T_{\mathrm{no}}\left(A_i\right),T^{*}\left(A_i\right)]=\frac{1}{m}\underset{j=1}{\overset{m}{\mathrm{\Σ}}}|t^{\′}(i,j)-t^{*}(i,j)|$ (i=1, 2, Λ, m); (6) Decision-making method, first determine the total support degree TSD(Ai) of the candidate decision A _i (i=1, 2, Λ, m): TSD(A _i )=1-Dis[T _n (A _i ), T ^* (A _i )], and then choose the largest A ^* $(A^{*}=\underset{A_i}{\max }[\mathrm{TSD}\left(A_i\right)\left]\right),$ It is the decision result of DS evidence fusion based on the state vector distance.