Uncertainty measure based on Tsallis entropy in evidence theory

Gao, Xiaozhuan; Liu, Fan; Pan, Lipeng; Deng, Yong; Tsai, Sang‐Bing

doi:10.1002/int.22185

Cited by 71 publications

(39 citation statements)

References 81 publications

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“…The Dempster-Shafer evidence theory [58,59] is proposed to deal with conditions that are weaker than Bayes probability [63,64], which can directly express uncertainty and unknown information [65,66], so that it has been widely used in various applications, FMEA [67][68][69], evidential reasoning [70][71][72], evaluation [73], target recognition [74], industrial alarm system [75,76], and others [77,78]. Definition 3.…”

Section: Dempster-shafer Evidence Theorymentioning

confidence: 99%

A New Divergence Measure of Pythagorean Fuzzy Sets Based on Belief Function and Its Application in Medical Diagnosis

2020

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As the extension of the fuzzy sets (FSs) theory, the intuitionistic fuzzy sets (IFSs) play an important role in handling the uncertainty under the uncertain environments. The Pythagoreanfuzzy sets (PFSs) proposed by Yager in 2013 can deal with more uncertain situations than intuitionistic fuzzy sets because of its larger range of describing the membership grades. How to measure the distance of Pythagorean fuzzy sets is still an open issue. Jensen–Shannon divergence is a useful distance measure in the probability distribution space. In order to efficiently deal with uncertainty in practical applications, this paper proposes a new divergence measure of Pythagorean fuzzy sets, which is based on the belief function in Dempster–Shafer evidence theory, and is called PFSDM distance. It describes the Pythagorean fuzzy sets in the form of basic probability assignments (BPAs) and calculates the divergence of BPAs to get the divergence of PFSs, which is the step in establishing a link between the PFSs and BPAs. Since the proposed method combines the characters of belief function and divergence, it has a more powerful resolution than other existing methods. Additionally, an improved algorithm using PFSDM distance is proposed in medical diagnosis, which can avoid producing counter-intuitive results especially when a data conflict exists. The proposed method and the magnified algorithm are both demonstrated to be rational and practical in applications.

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Section: Dempster-shafer Evidence Theorymentioning

confidence: 99%

A New Divergence Measure of Pythagorean Fuzzy Sets Based on Belief Function and Its Application in Medical Diagnosis

2020

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“…Many researchers have proposed definitions of entropy of BPA 68,69,70,71 . The concept of entropy in D‐S theory can play a role in many applications 72,73,74 . Based on the proposed method, two types of definition of entropy are given.…”

Section: Entropy Of Bpasmentioning

confidence: 99%

A vector and geometry interpretation of basic probability assignment in Dempster‐Shafer theory

Luo

Deng

2020

Int J Intell Syst

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Because of the superiority in dealing with uncertainty expression, Dempster-Shafer theory (D-S theory) is widely used in decision theory. In D-S theory, the basic probability assignment (BPA) is the basis and core. Recently, some researchers represent BPA on a N -dimension frame of discernment (FOD) as 2 N -dimension vector in Descartes coordinate system. This representation treats a BPA as a point in the 2 N -dimensional space. A new vector and geometry interpretation of BPA is proposed in this paper.The BPA on a N -dimension FOD is represented as N -dimension vector with parameters in this method.Then BPA is expressed as subset of N -dimension Cartesian space rather than a point. The proposed method is a new way to represent BPA with vector and geometry. The essence of this method is to convert BPA to probability distribution with parameters.The applications of this representation method in D-S theory have been studied. Based on this method, problems in D-S theory can be solved, which include the fusion of BPAs, the distance between BPAs, the correspondence between BPA and probability, and the entropy of BPAs.basic probability assignment, data fusion, dempster-shafer theory, distance, entropy Dempster-Shafer theory (D-S theory), 1,2 as an important and widely used uncertain reasoning method, has been receiving increasingly attention. 3,4 D-S theory assigns probabilities to the power set of events, so it can effectively deal with uncertainty and unknown problems. Because of the effectiveness in pattern recognition, 5,6 decision making, 7,8,9,10,11,12 reasoning, 13,14,15 and uncertainty analysis, 16,17,18,19 D-S theory has been applied in various fields. 20,21,22,23 In D-S theory, A complete set of incompatible basic hypotheses is called a frame of discernment (FOD), which represents all possible answers to a problem. The degree of trust assigned to each subset of FOD is called the basic probability assignment (BPA). Since the N -dimension FOD has 2 N subsets, some researchers represent the BPA as 2 N -dimension vector in Descartes coordinate system. 24,25 A BPA is a point in the 2 N -dimensional space in this representation method.Based on the idea of converting BPA to probability distribution (PD), a new interpretation of D-S theory is proposed in this paper. The BPA on a N -dimension FOD is represented as N -dimension vector with parameters in this method. Each dimension indicates a hypothesis in FOD. In fact, BPA is represented as a subset of N -dimension space rather than a point because of the variable parameters. In this way, BPAs have an intuitive vector and geometry representation. Based on this representation method, several problems in D-S theory have been studied, which include the fusion of BPAs, the distance between BPAs, the correspondence between BPA and probability, and the entropy of BPAs. The example shows that our method provides a new way to solve these basic problems of D-S theory, and can get reasonable results.Combination of BPAs from different information sources is a major problem in D...

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“…Uncertainty exist in the real world and uncertainty modeling has many math tools, such as fuzzy sets, probabilistic model, Z numbers, IFS, D numbers, entropy function, decision tree, pattern recognition, network analysis, and so on. D‐S evidence theory is a hot topic in decision theory, and the theory has a wide range of applications in many fields.…”

Section: Preliminariesmentioning

confidence: 99%

An association coefficient of a belief function and its application in a target recognition system

Pan

Deng

2019

Int J Intell Syst

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The conflict problem in D-S evidence theory has attracted the attention of many scholars. Conflict coefficients are proposed to describe conflicts between bodies of evidence. The association coefficient as the opposite of the conflict coefficient is also used to measure the conflict. The larger the association coefficient, the smaller the conflict degree, and the higher the similarity between the evidence bodies, and vice versa.In this paper, the degree of association is defined by Deng Entropy, and a new association coefficient is proposed based on the basic inequality. The nature of the new association coefficient and conflict coefficients is explored using examples. Finally, the association coefficient combined with the D-S combination rule is applied to the target recognition system, and accurate results are obtained.association coefficient, conflict coefficients, conflict problem, Deng entropy, D-S evidence theory, target recognition system | INTRODUCTIONThe D-S evidence theory was first proposed by Dempster 1 in 1967 and later developed by his student Shafer 2 in 1976 as an imprecise reasoning theory, which is widely promoted. [3][4][5][6] The theory was first applied to expert systems, 7-9 and it was gradually applied in the fields of information fusion, 10-12 intelligence analysis, 9,13-16 evidential reasoning, [17][18][19] and multiattribute decision analysis. [20][21][22][23][24] As an indeterminate reasoning method which satisfies the conditions weaker than Bayesian probability theory; it has the ability to directly express "uncertainty" 25 and "don't know." 26 Therefore, the D-S evidence theory is flexible and convenient for describing uncertainties. However, D-S evidence theory has produced counterintuitive results in the fusion of a highly conflicting example proposed by Zadeh. 27 Therefore, the issue of conflict between bodies of evidence has attracted more and more researchers so far. [28][29][30][31][32] Domestic and foreign scholars have proposed a large number of improved methods, which can be divided into two major categories: (a) modification of the combination rules of the classical D-S evidence theory to achieve the redistribution of conflicts in the case of evidence conflicts. [33][34][35][36] Such measures alleviate the conflict between the bodies of evidence to a certain extent, but at the same time, it is difficult for the new rules to maintain the original properties of the D-S combination rules. (b) Keep the classic combination rules unchanged, and preprocess conflict data before combination. [37][38][39][40][41][42] Haenni 43 believes that the modification of the data model is in engineering, mathematics and philosophically more reasonable. However, regardless of the type of method used to deal with conflicts between evidence, the conflict coefficient is an extremely important parameter. Therefore, the most critical step before choosing the right combination of evidence is the measure of evidence conflict.To measure the conflict between evidence bodies, many researchers have proposed...

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Uncertainty measure based on Tsallis entropy in evidence theory

Cited by 71 publications

References 81 publications

A New Divergence Measure of Pythagorean Fuzzy Sets Based on Belief Function and Its Application in Medical Diagnosis

A New Divergence Measure of Pythagorean Fuzzy Sets Based on Belief Function and Its Application in Medical Diagnosis

A vector and geometry interpretation of basic probability assignment in Dempster‐Shafer theory

An association coefficient of a belief function and its application in a target recognition system

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