Interval confidence structure conflict evidence reasoning method based on mixed weight

Abstract

The invention relates to an interval confidence structure conflict evidence reasoning method based on mixed weights, and belongs to the technical field of decision-level radiation source type fusion identification conflict evidence reasoning. Comprising the following steps: defining an interval evidence importance degree, designing a solving method, calculating the evidence importance degree by using an interval evidence distance, and reflecting a mutual support degree between evidences; the interval evidence reliability is defined, a solving method is designed, reliability measurement based on confidence entropy is constructed, and subjective setting does not depend on experts or decision makers; an evidence combination and standardization integrated calculation method is adopted, it is guaranteed that the interval evidence combination result is optimal, and the anti-intuition problem of conflict interval evidence combination is solved. The method does not depend on subjective setting of experts or decision makers, not only shows effectiveness in the combination process, but also can solve the problem of conflict interval evidence combination.

Description

Technical Field

[0001] The invention relates to an interval confidence structure conflict evidence reasoning method based on mixed weights, belonging to the technical field of decision-level radiation source type fusion identification conflict evidence reasoning. Background Art

[0002] Evidence theory has been widely used in the field of uncertain information processing. It is an effective tool to solve the uncertainty of intelligent systems and has attracted the attention of experts and scholars from all over the world. After years of development, evidence theory has been successfully applied to various fields, including pattern recognition, fault diagnosis, information fusion, multi-attribute decision-making, risk analysis, etc.

[0003] Evidence theory mainly focuses on the situation where the basic probability assignment (BPA) is a definite real number. However, in many fusion recognition application problems, due to the incompleteness of prior information, the inaccuracy of sensor output information, and the uncertainty of decision makers' subjective judgment, accurate BPA cannot be obtained in many cases. For example, in the problem of radiation source type identification, different identification nodes give different support degrees, and it is difficult to integrate all the results into a unified and definite conclusion. At this time, using interval numbers to represent the basic probability assignment function, namely the interval-valued confidence structure (IBS), is an ideal choice, which can accurately describe uncertain information and reduce information loss. Therefore, using interval numbers to represent the basic probability distribution function, namely the interval-valued confidence structure, is an ideal choice, which can accurately describe uncertain information and reduce information loss. Since its proposal, researchers have conducted research on interval-valued confidence structures, including interval evidence combination, standardization, interval arithmetic operations, etc. Existing methods can be divided into two categories, based on interval arithmetic operations and based on program models. However, the combination and standardization of interval evidence have not been fully solved. In order to overcome the counter-intuitive behavior of conflicting evidence combination, the Evidence Reasoning Rules (ER) are extended to handle the combination of conflicting interval-valued confidence structures, and better evidence weights are proposed to eliminate the evidence conflict problem. Summary of the invention

[0004] In view of the deficiencies in the above-mentioned prior art, the present invention proposes a method for reasoning about conflicting evidence in interval confidence structures based on mixed weights. This method uses the ER rule to construct an interval evidence combination framework in view of the uncertainty of the confidence distribution of the evidence itself, and constructs a reliability measurement method based on confidence entropy. This method does not rely on the subjective settings of experts or decision makers, and not only shows effectiveness in the combination process, but also can solve the problem of conflicting interval evidence combination.

[0005] The invention provides a mixed weight-based interval confidence structure conflict evidence reasoning method, which is special in that it includes the following steps:

[0006] Step 1) Define the importance of interval evidence, design a solution method, and use the interval evidence distance to calculate the importance of evidence, reflecting the degree of mutual support between evidences;

[0007] Step 2) define the reliability of interval evidence, design a solution method, and construct a reliability measure based on confidence entropy that does not rely on subjective settings of experts or decision makers;

[0008] Step 3) adopt an integrated calculation method of evidence combination and normalization to ensure the optimal result of interval evidence combination and overcome the counter-intuitive problem of conflicting interval evidence combination.

[0009] Preferably, the step 1) specifically comprises the following steps:

[0010] 1) Assume P i ,P j are two interval numbers, expressed as ls is P i and P j The interval extension length is, The interval value distance GR-IND divides the interval distance into two parts, one of which is determined by the position of the interval and is expressed as The other part is determined by the span of the interval, expressed as The distance between intervals is defined as

[0011]

[0012] where u k represents the length of the maximum interval of the k-th feature,

[0013] 2) Let Θ be the confidence frame, and the interval evidence BPA is given by P i (i=1,2,L,n) indicates that the method for obtaining the importance of interval evidence is as follows:

[0014] (1) Obtain the interval evidence matrix D, calculate the distance between each pair of evidence, and obtain the interval evidence distance matrix D. D is an n×n square matrix with diagonal elements of 0. Each element in the matrix is ​​d ij , represents the distance between the i-th piece of evidence and the j-th piece of evidence:

[0015]

[0016] (2) Normalize each column of the distance matrix D to obtain the matrix The matrix elements are The vector in the i-th column of the obtained matrix represents the degree of support of the i-th piece of evidence for each piece of evidence;

[0017] (3) The normalized distance matrix Add each row of , and we get a vector s = [s1, s2, L, s n ], where s i Indicates the support of other evidence for the i-th piece of evidence:

[0018]

[0019] (4) The vector s obtained in the above step is normalized to obtain the importance vector of evidence w = [w1,w2,L,w n ];

[0020] w i =s i / max{s1,s2,L,s n}(5)

[0021] (5) Using importance weight w i The interval evidence is discounted, i.e.

[0022] Preferably, the step 2) specifically comprises the following steps:

[0023] 1) Assuming E is any focal element of Θ, Pl(E) and Bel(E) are the plausibility and credibility of θ, respectively. The definition of the Golden Rule method is as follows:

[0024] Rep(E)=m+(0.5-m)r (6)

[0025] Where m=(Pl(E)+Bel(E)) / 2, r=Pl(E)-Bel(E);

[0026] 2) Assume H j is the focal element of the recognition frame Θ, p i is the interval-valued probability of the quality of evidence,

[0027] is the interval-valued probability, and the interval evidence e i The reliability is as follows:

[0028] r i =q i / max{q1,q2,L,q n}(7)

[0029]

[0030] When a piece of evidence i For an interval BPA with L propositions, BE is calculated for each interval BPA separately. IE (p ij), and sum to get the evidence e i The reliability of q i Finally, the interval evidence reliability vector q is processed to obtain the normalized reliability vector r = [r1, r2, L, r n ].

[0031] Preferably, the step 3) specifically comprises the following steps:

[0032] 1) Let p1,L,p n is an n-interval BPA and the interval probability mass function For i=1,L,n, where θ represents the focal element of interval BPA, the optimization model of interval evidence combination is constructed according to the ER rule. The optimization model formula with mixed weights is as follows:

[0033]

[0034] m θ,i =w i p θ,i ,i=1,2,L,n,

[0035]

[0036] where w i is the importance of interval evidence, r i is the reliability of the interval evidence, m θ,i Refers to the focus element θ

[0037] The BPA value of the relevant i-th piece of evidence, m θ,e(1) =m θ,1 ,m P(Θ),e(1) =m P(Θ),1 The above optimization model is a recursive combination process, and the model objective function is the unnormalized probability mass m of the combination of i interval evidences. θ,e(i) Maximum and minimum values, residual confidence m P(Θ),e(i) Assigned to P(Θ), it is assigned to all propositions in the discriminative framework power set, not to any subset, in order to obtain m θ,e(i) and m P(Θ),e(i) Then calculate the confidence p of the proposition θ after combining the i interval evidences θ,e(i) , formula (12) is the constraint condition of the model. The solution of the above nonlinear model is realized through optimization package or optimization toolbox.

[0038] The present invention provides a method for reasoning conflict evidence based on interval confidence structure based on mixed weights, which has the following beneficial effects: interval values ​​can effectively represent uncertainty, and using interval values ​​to describe the basic probability assignment of propositions will expand the application field of evidence theory. The present invention provides a theoretical basis and technical support for interval evidence conflict reasoning, and also expands the ER rule. The model established by this method not only considers the composite evidence weight, but also considers the evidence combination and normalization process, which can ensure that the interval evidence combination result has the optimal value, and can effectively overcome the counterintuitive problem caused by combining conflicting evidence; the importance solution method based on interval evidence distance is given, which can effectively measure the mutual support degree of interval evidence; the reliability of interval evidence is solved from the perspective of information entropy, which can reflect the ability of evidence itself to provide correct information. The new interval evidence combination method is verified by using examples, and compared with the existing combination method, which shows that it has good superiority, stability and convergence in solving conflicting evidence combination. BRIEF DESCRIPTION OF THE DRAWINGS

[0039] In order to more clearly illustrate the technical solutions in the embodiments of the present application or the conventional technology, the drawings required for use in the embodiments or the conventional technology descriptions are briefly introduced below. Obviously, the drawings described below are only some embodiments of the present application. For ordinary technicians in this field, other drawings can be obtained based on these drawings without creative work.

[0040] Figure 1 This is a comparison chart of the importance of different interval evidence combination methods;

[0041] Figure 2 It is a reliability comparison chart of different interval evidence combination methods;

[0042] Figure 3 This is the BPA result diagram for the proposition interval evidence combination. DETAILED DESCRIPTION

[0043] In order to make the purpose, technical solution and advantages of the present application more clearly understood, the present application is further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present application and are not used to limit the present application.

[0044] The present embodiment provides a mixed weight-based interval confidence structure conflict evidence reasoning method, comprising the following steps:

[0045] Step 1) Define the importance of interval evidence, design a solution method, and use the interval evidence distance to calculate the importance of evidence, reflecting the degree of mutual support between evidences;

[0046] Step 1) specifically includes the following steps:

[0047] 1) Assume P i ,P j are two interval numbers, expressed as ls is P i and P j The interval extension length is, The interval value distance GR-IND divides the interval distance into two parts, one of which is determined by the position of the interval and is expressed as The other part is determined by the span of the interval, expressed as The distance between intervals is defined as

[0048]

[0049] where u k represents the length of the maximum interval of the k-th feature,

[0050] 2) Let Θ be the confidence frame, and the interval evidence BPA is given by P i (i=1,2,L,n) indicates that the method for obtaining the importance of interval evidence is as follows:

[0051] (1) Obtain the interval evidence matrix D, calculate the distance between each pair of evidence, and obtain the interval evidence distance matrix D. D is an n×n square matrix with diagonal elements of 0. Each element in the matrix is ​​d ij , represents the distance between the i-th piece of evidence and the j-th piece of evidence:

[0052]

[0053] (2) Normalize each column of the distance matrix D to obtain the matrix The matrix elements are The vector in the i-th column of the obtained matrix represents the degree of support of the i-th piece of evidence for each piece of evidence;

[0054] (3) The normalized distance matrix Add each row of , and we get a vector s = [s1, s2, L, s n ], where s i Indicates the support of other evidence for the i-th piece of evidence:

[0055]

[0056] (4) The vector s obtained in the above step is normalized to obtain the importance vector of evidence w = [w1,w2,L,w n ];

[0057] w i=s i / max{s1,s2,L,s n} (5)

[0058] (5) Using importance weight w i The interval evidence is discounted, i.e.

[0059] Step 2) define the reliability of interval evidence, design a solution method, and construct a reliability measure based on confidence entropy that does not rely on subjective settings of experts or decision makers;

[0060] Step 2) specifically includes the following steps:

[0061] 1) Assuming E is any focal element of Θ, Pl(E) and Bel(E) are the plausibility and credibility of θ, respectively. The definition of the Golden Rule method is as follows:

[0062] Rep(E)=m+(0.5-m)r (6)

[0063] Where m=(Pl(E)+Bel(E)) / 2, r=Pl(E)-Bel(E);

[0064] 2) Assume H j is the focal element of the recognition frame Θ, p i is the interval-valued probability of the quality of evidence, is the interval-valued probability, and the interval evidence e i The reliability is as follows:

[0065] r i =q i / max{q1,q2,L,q n} (7)

[0066]

[0067]

[0068] When a piece of evidence i For an interval BPA with L propositions, BE is calculated for each interval BPA separately. IE (p ij ), and sum to get the evidence e i The reliability of q i Finally, the interval evidence reliability vector q is processed to obtain the normalized reliability vector r = [r1, r2, L, r n ].

[0069] Step 3) adopt an integrated calculation method of evidence combination and normalization to ensure the optimal result of interval evidence combination and overcome the counter-intuitive problem of conflicting interval evidence combination.

[0070] Step 3) specifically includes the following steps:

[0071] 1) Let p1,L,p n is an n-interval BPA and the interval probability mass function For i=1,L,n, where θ represents the focal element of interval BPA, the optimization model of interval evidence combination is constructed according to the ER rule. The optimization model formula with mixed weights is as follows:

[0072]

[0073] where w i is the importance of interval evidence, r i is the reliability of the interval evidence, m θ,i refers to the BPA value of the i-th piece of evidence related to the focal element θ, m θ,e(1) =m θ,1 ,m P(Θ),e(1) =m P(Θ),1 The above optimization model is a recursive combination process, and the model objective function is the unnormalized probability mass m of the combination of i interval evidences. θ,e(i) Maximum and minimum values, residual confidence m P(Θ),e(i) Assigned to P(Θ), it is assigned to all propositions in the discriminative framework power set, not to any subset, in order to obtain m θ,e(i) and m P(Θ),e(i) Then calculate the confidence p of the proposition θ after combining the i interval evidences θ,e(i) , formula (12) is the constraint condition of the model. The solution of the above nonlinear model is realized through optimization package or optimization toolbox.

[0074] ER rule is an extension of the traditional Dempster combination rule. It can handle conflicting evidence combination problems and avoid counter-intuitive behavior. This is mainly because it clearly distinguishes between evidence importance and reliability. However, ER rule does not provide a calculation method for evidence importance and reliability, and there are few corresponding studies. Therefore, the present invention first studies the importance and reliability of interval evidence, and on this basis, combines interval evidence through ER rule with composite weights, and provides an interval evidence combination optimization model.

[0075] 1. Determination of the importance of interval evidence

[0076] Counterintuitive behavior is mainly caused by contradictory evidence. When combining interval evidence using the ER rule, the importance of evidence should be able to truly reflect the weight of different evidence. In order to obtain the importance of interval evidence, we first need to determine the conflict measurement function, and then calculate the distance between two pieces of evidence to obtain the distance matrix. The distance matrix is ​​added row by row and normalized to obtain the importance vector of each piece of evidence, which represents the relative importance of one piece of evidence relative to other pieces of evidence.

[0077] There is a certain distance between different evidences. GR-IND distance is a widely used interval value distance. Since it is necessary to measure the distance of interval evidence, the distance between intervals is defined as

[0078] The method to obtain the importance of interval evidence is as follows:

[0079] (1) Obtain the interval evidence matrix D, calculate the distance between each pair of evidence, and obtain the interval evidence distance matrix D. D is an n×n square matrix with diagonal elements of 0. Each element in the matrix is ​​d ij , represents the distance between the i-th piece of evidence and the j-th piece of evidence;

[0080] (2) Normalize each column of the distance matrix D to obtain the matrix The matrix elements are The vector in the i-th column of the obtained matrix represents the degree of support of the i-th piece of evidence for each piece of evidence;

[0081] (3) The normalized distance matrix Add each row of , and we get a vector s = [s1, s2, L, s n ], where s i Indicates the support of other evidence for the i-th piece of evidence;

[0082] (4) The vector s obtained in the above step is normalized to obtain the importance vector of evidence w = [w1,w2,L,w n ];

[0083] (5) Using importance weight w i The interval evidence is discounted, i.e.

[0084] 2. Determination of the reliability of interval evidence

[0085] In the ER rule, evidence e i The reliability of i Reflects the evidence i The ability to provide precise confidence estimates for a given proposition is an inherent property of evidence. iThe existing research is mainly based on precise measurement data, calculating the mean of the data, and then finding the average distance between the observed value and the mean, and normalizing the distance to obtain the reliability. The above method is not feasible under the condition of only evidence BPA, especially for interval evidence. Therefore, this section focuses on how to obtain the reliability of interval evidence r i , a calculation method based on information entropy is proposed. Compared with the traditional method, the reliability calculation method based on information entropy only depends on the confidence distribution of evidence, has less calculation amount, and can reflect the ability of the evidence itself to provide correct information.

[0086] Compared with traditional methods, the reliability calculation method based on information entropy only relies on the BPA of evidence, has a small amount of calculation, and can reflect the ability of the evidence itself to provide correct information. Information entropy can represent the uncertainty of evidence through the disorder of information. Confidence entropy is an extension of information entropy, which is more flexible in evaluating uncertainty than information entropy. The above method can characterize the reliability of evidence based on the uncertainty of deterministic evidence itself, and then modify and combine the evidence.

[0087] According to the uncertainty of interval evidence, a measurement method of interval evidence uncertainty is given to further express the reliability of interval evidence. i Reliability i =q i / max{q1,q2,…,q n}, when a piece of evidence i For an interval BPA with L propositions, BE is calculated for each interval BPA separately. IE (p ij ), and sum to get the evidence e i The reliability of q i Finally, the interval evidence reliability vector q is processed to obtain the normalized reliability vector r = [r1, r2, L, r n ].

[0088] 3. Composite Weight Interval Evidence Combination Optimization Model

[0089] After obtaining the importance w and reliability r of the interval evidence, the composite weight can be used to combine and normalize the interval evidence based on the ER rule.

[0090] Let p1,…,p n is an n-interval BPA and the interval probability mass function For i=1,…,n, where θ represents the focal element of interval BPA, in order to overcome the shortcomings of previous methods, an optimization model for interval evidence combination can be constructed according to the ER rule. The combination result of the optimization model with mixed weights is Max / Min mθ,e(i) and m P(Θ),e(i) The optimization model is a recursive combination process that considers both combination and normalization issues. The model objective function is the unnormalized probability mass m of the combination of i interval evidences. θ,e(i) Maximum and minimum values, residual confidence m P(Θ),e(i) Assign to P(Θ). After getting m θ,e(i) and m P(Θ),e(i) Then calculate the confidence p of the proposition θ after combining the i interval evidences θ,e(i) .

[0091] Assume that Θ = {A, B, C} is the identification framework, and the basic probability assignment of evidence is a standardized random interval number between 0 and 1.

[0092] According to the calculated interval evidence, there is no obvious conflict between the interval evidence. According to the given interval evidence importance algorithm, the importance vector of the interval evidence can be obtained as w = (0.2499, 0.2496, 0.2504, 0.2501). According to the given interval evidence reliability algorithm, the reliability vector of the interval evidence can be obtained as r = (0.2592, 0.2711, 0.2305, 0.2392). From the values ​​of w and r, it can be seen that the distribution of each interval evidence is relatively balanced, and the conflict between the evidence is small, which shows that the evidence weight calculation method proposed in this method is reasonable. The importance of different interval evidence combination methods is as follows Figure 1 As shown, the reliability is Figure 2 shown.

[0093] It can be seen from the evidence combination results that the combination results obtained by the method proposed in the present invention are basically consistent with the results of other methods and are in line with intuitive judgment. Compared with other methods, the interval value probability mass width in the evidence combination results obtained by the method proposed in the present invention is narrower, that is, the result is more accurate. Figure 3 It can be seen that the results of the method proposed in the present invention are consistent with those of other methods, but the upper and lower boundaries of BPA are closer, and the interval evidence combination results are more accurate.

[0094] The above embodiments only express several implementation methods of the present application, and the descriptions thereof are relatively specific and detailed, but they cannot be understood as limiting the scope of the invention patent. It should be pointed out that, for a person of ordinary skill in the art, several variations and improvements can be made without departing from the concept of the present application, and all of them belong to the protection scope of the present application. Therefore, the protection scope of the patent of the present application shall be subject to the attached claims.

Claims

1. A mixed weight-based interval confidence structure conflict evidence reasoning method, characterized by The following steps are involved: Step 1) Define the importance of interval evidence, design a solution method, and use the interval evidence distance to calculate the importance of evidence, reflecting the degree of mutual support between evidences; Step 2) define the reliability of interval evidence, design a solution method, and construct a reliability measure based on confidence entropy that does not rely on subjective settings of experts or decision makers; Step 3) adopt an integrated calculation method of evidence combination and normalization to ensure the optimal result of interval evidence combination and overcome the counter-intuitive problem of conflicting interval evidence combination.

2. A mixed weight interval confidence structure conflict evidence reasoning method according to claim 1, characterized in that The step 1) specifically comprises the following steps: 1) Assume P i ,P j are two interval numbers, expressed as ls is P i and P j The interval extension length is, The interval value distance GR-IND divides the interval distance into two parts, one of which is determined by the position of the interval and is expressed as The other part is determined by the span of the interval, expressed as The distance between intervals is defined as where u k represents the length of the maximum interval of the k-th feature, 2) Let Θ be the confidence frame, and the interval evidence BPA is given by P i (i=1,2,L,n) indicates that the method for obtaining the importance of interval evidence is as follows: (1) Obtain the interval evidence matrix D, calculate the distance between each pair of evidence, and obtain the interval evidence distance matrix D. D is an n×n square matrix with diagonal elements of 0. Each element in the matrix is ​​d ij , represents the distance between the i-th piece of evidence and the j-th piece of evidence: (2) Normalize each column of the distance matrix D to obtain the matrix The matrix elements are The vector in the i-th column of the obtained matrix represents the degree of support of the i-th piece of evidence for each piece of evidence; (3) The normalized distance matrix Add each row of , and we get a vector s = [s1, s2, L, s n ], where s i Indicates the support of other evidence for the i-th piece of evidence: (4) The vector s obtained in the above step is normalized to obtain the importance vector of evidence w = [w1,w2,L,w n ]; w i =s i / max{s1,s2,L,s n }(5) (5) Using importance weight w i The interval evidence is discounted, i.e.

3. A mixed weight interval confidence structure conflict evidence reasoning method according to claim 1, characterized in that The step 2) specifically comprises the following steps: 1) Assuming E is any focal element of Θ, Pl(E) and Bel(E) are the plausibility and credibility of θ, respectively. The definition of the Golden Rule method is as follows: Rep(E)=m+(0.5-m)r(6)where m=(Pl(E)+Bel(E)) / 2, r=Pl(E)-Bel(E); 2) Assume H j is the focal element of the recognition frame Θ, p i is the interval-valued probability of the quality of evidence, is the interval-valued probability, and the interval evidence e i The reliability is as follows: r i =q i / max{q1,q2,L,q n }(7) When a piece of evidence i For an interval BPA with L propositions, BE is calculated for each interval BPA separately. IE (p ij ), and sum to get the evidence e i The reliability of q i Finally, the interval evidence reliability vector q is processed to obtain the normalized reliability vector r = [r1, r2, L, r n ].

4. A mixed weight interval confidence structure conflict evidence reasoning method according to claim 1, characterized in that The step 3) specifically comprises the following steps: 1) Let p1,L,p n is an n-interval BPA and the interval probability mass function For i=1,L,n, where θ represents the focal element of interval BPA, the optimization model of interval evidence combination is constructed according to the ER rule. The optimization model formula with mixed weights is as follows: where w i is the importance of interval evidence, r i is the reliability of the interval evidence, m θ,i refers to the BPA value of the i-th piece of evidence related to the focal element θ, m θ,e(1) =m θ,1 ,m P(Θ),e(1) =m P(Θ),1 The above optimization model is a recursive combination process, and the model objective function is the unnormalized probability mass m of the combination of i interval evidences. θ,e(i) Maximum and minimum values, residual confidence m P(Θ),e(i) Assigned to P(Θ), it is assigned to all propositions in the discriminative framework power set, not to any subset, in order to obtain m θ,e(i) and m P(Θ),e(i) Then calculate the confidence p of the proposition θ after combining the i interval evidences θ,e(i) , formula (12) is the constraint condition of the model. The solution of the above nonlinear model is realized through optimization package or optimization toolbox.

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