An uncertainty measure and fusion rule for conflict evidences of big data via Dempster–Shafer theory

Dutta, Palash

doi:10.1080/19479832.2017.1391336

Cited by 38 publications

(26 citation statements)

References 45 publications

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“…Decision theory [17][18][19] has been widely applied in this field, containing a variety of theories and methods. For instance, evidence theory and its extension [20][21][22], evidential reasoning [23,24], D numbers theory [25], R numbers theory [26,27], Z numbers theory [28,29], and other hybrid methods have been used to research it from lots of aspects. The rationality and practicality of these methods have also been proven by their employment in…”

Section: Introductionmentioning

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: Introductionmentioning

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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“…Information fusion based on D‐S theory has achieved good results in some engineering applications 58,59 . The core of using D‐S theory in information fusion is the combination rule of BPAs and how to deal with the conflict between BPAs 60,32 . Equation (8) is the classic Dempster's rule of combination.…”

Section: Combination Of Bpasmentioning

confidence: 99%

“…Combination of BPAs from different information sources is a major problem in D‐S theory 26,27,28,29,30,31,32 . Dempster's rule plays an important role in solving the problem.…”

Section: Introductionmentioning

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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“…To handle uncertainty, a lot of theories have been developed, for example, probability theory, Dempster‐Shafer (D‐S) evidence theory, fuzzy sets, gray model, and Z number . Among these methods, D‐S evidence theory has attracted many research’ attention due to its extension of Bayesian theory, with the efficiency to deal with imprecise information . Measuring the uncertainty of basic probability assignment function (BPA) in D‐S theory is essential and can be applied in many applications …”

Section: Introductionmentioning

confidence: 99%

Uncertainty measure based on Tsallis entropy in evidence theory

et al. 2019

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Dempster-Shafer evidence theory has been widely used in many applications due to its advantages with weaker conditions than Bayes probability. How to measure the uncertainty of basic probability assignment (BPA) in Dempster-Shafer evidence theory is an open and essential issue. Tsallis entropy as nonextensive entropy proposed according to multifractals has been used in many fields. In this paper, a new uncertainty measure of BPA is presented based on Tsallis entropy. The key issue is to determine the value of q in Tsallis entropy. In addition, this paper also analyzes the properties of proposed uncertainty measure. Some numerical examples are used to illustrate the efficiency of the proposed method. Finally, the paper also discusses the application of the proposed method in decision-making. K E Y W O R D S basic probability assignment, belief function, Dempster-Shafer evidence theory, Tsallis entropy, uncertainty | INTRODUCTIONUncertainty plays an important role in real-world and is inevitable in decision-making. 1-5 To handle uncertainty, a lot of theories have been developed, for example, probability theory, 6,7 Dempster-Shafer (D-S) evidence theory, 8,9 fuzzy sets, 10-13 gray model, 14 and Z number. [15][16][17][18] Among these methods, D-S evidence theory has attracted many research' attention due to its extension of Bayesian theory, [19][20][21][22] with the efficiency to deal with imprecise information. 8,23 Measuring the uncertainty of basic probability assignment function (BPA) in D-S theory is essential [24][25][26][27] and can be applied in many applications. [28][29][30]

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An uncertainty measure and fusion rule for conflict evidences of big data via Dempster–Shafer theory

Cited by 38 publications

References 45 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

Uncertainty measure based on Tsallis entropy in evidence theory

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