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

Abstract

A decision method includes confirming information compromise result based on D-S evidence theory confirming focal element support degree and candidate decision vector, confirming ideal state vector of candidate decision and distance between state vectors; finally confirming total support degree of candidate decision Ai(I=1,2, lambda, m) and then selecting maximum A* as D-S evidence compromise decision result based on state vector distance.

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,, it is characterized in that method step is divided into successively based on the evidence theory information blending decision method of state vector distance:

(1) definite information fusion result based on the D-S evidence theory according to the difference that merges background, selects framework of identification and power set thereof, and based on the D-S evidence theory multi-source information is carried out fusion treatment;

(2) determine burnt meta-attribute support.All as candidate decision-making, burnt meta-attribute is to the attribute level support of candidate's decision-making with each the burnt unit in the power set of framework of identification, just becomes to be the support between the burnt meta-attribute, and this support is $s(i,j)=\frac{\left|A_{i}I{A}_j\right|}{\left|A_{i}Y{A}_j\right|},(i,j=\mathrm{1,2},\mathrm{\Λ},m),$ Wherein || represent the number of the primitive that burnt meta-attribute comprises;

(3) candidate's decision vector determines.Consider burnt first support that basic trust assignment profile that the candidate makes a strategic decision and dependency aspect obtain, 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 $t^{\′}(i,j)=\frac{t(i,j)}{\underset{j=1}{\overset{m}{\mathrm{\Σ}}}t(i,j)},(i,j=\mathrm{1,2},\mathrm{\Λ},m);$

(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 $t^{*}(i,j)=\left\{\begin{array}{cc}1& i=j\\ 0& i\≠j\end{array}\right.,(i,j=\mathrm{1,2},\mathrm{\Λ},m).$ Claim T ^*(A _i) be the perfect condition vector of candidate decision-making;

(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，m)；

(6) decision-making technique is at first determined the candidate A that makes a strategic decision _i(i=1,2, Λ, m) total support TSD (Ai): TSD (A _i)=1-Dis[T _n(A _i), T ^*(A _i)], select wherein maximum A then ^* $(A^{*}=\underset{A_i}{\max }[\mathrm{TSD}\left(A_i\right)\left]\right),$ The D-S evidence that is based on state vector distance merges the result of decision.