A Distance Measure for Intuitionistic Fuzzy Sets and Its Application to Pattern Classification Problems

Xiao, Fuyuan

doi:10.1109/tsmc.2019.2958635

Cited by 221 publications

(118 citation statements)

References 78 publications

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“…Hence, the Pythagorean fuzzy set was chosen to apply for medical diagnosis in this paper.Distance measure plays a vital role in pattern recognition, information fusion, decision-making, and other fields. The fuzzy set theory and intuitionistic fuzzy sets have been proposed for many years and their distance measurements [50][51][52] have matured compared with Pythagorean fuzzy sets. There are some useful distances for IFS after suffering the practice and the application.…”

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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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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 math models such as network analysis, 48–51 risk and reliability analysis, 52–54 visible graph, 55 and fuzzy sets 56–60 . IFS is an extension of the classical fuzzy sets, which has been used in a wide scope of application 61–65 . It considers three degrees simultaneously, which is more flexible, practical, and efficient than classical FS in dealing with ambiguity and uncertainty.…”

Section: Preliminariesmentioning

confidence: 99%

Entailment for intuitionistic fuzzy sets based on generalized belief structures

Xue

Deng

2020

Int J Intell Syst

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Entailment for measure-based belief structures can extend the possible probability value range of variables on a space and obtain more information from variables. However, if the variable space comes from intuitionistic fuzzy sets, the classical entailment for measure-based belief structures will not work in this issue. To deal with this situation, we propose the entailment for intuitionistic fuzzy sets based on generalized belief structures in this paper to apply the entailment for measure based belief structures on space, which is made up of non-membership degree, membership degree and hesitancy degree of a given intuitionistic fuzzy sets. Numerical examples are mentioned to prove the effectively and flexibility of this proposed entailment model. The experimental results indicate that the proposed algorithm can extend the possible probability value range of variables of space efficiently and obtain more information from intuitionistic fuzzy sets.belief function, Dempster-Shafer evidence theory, entailment, generalized belief structures, intuitionistic fuzzy sets | INTRODUCTIONIn real life, there are a lot of uncertainties in the real world. To address the uncertainties, many mathematical theories are proposed, such as probability theory, 1 fuzzy sets (FS), 2 Dempster-Shafer evidence theory, 3,4 intuitionistic fuzzy sets (IFS), 5,6 information quality, 7-11 Z-number, 12 fuzzy reasoning, 13-15 D-number, 16-18 entropy function, [19][20][21][22] and belief structure. 23,24 Among these theories and models, the IFS 25 considering the degree of hesitancy, membership, and nonmembership of objects, can deal with the uncertainties more flexibly and accurately, which has been used in many fields widely, 26 such as the uncertainty decision making, 27,28 pattern recognition 29 and so on.Recently, Yager proposed the entailment for measure based belief structures with a space, which has the promising aspect. 30 However, what the entailment for measure-based belief structures for a given IFS is still an open issue to be addressed. This paper proposes entailment for intuitionistic fuzzy sets based on generalized belief structures, which treats hesitancy degree, non-membership degree and membership degree of a given intuitionistic fuzzy set as three variables in a space X . Assume V takes its value in the X and is an uncertain variable. If g 1 and g 2 be two generalized belief structures on X and g 2 contains g 1 , then the belief of the statement that V is true based on g 2 will be smaller than that of the statement that V is true based on g 1 and the plausibility of the statement that V is true based on g 2 will be bigger than that of the statement that V is true based on g 1 .The remain of this paper is structured as follows. Section 2 introduces the preliminary. Section 3 presents the entailment for intuitionistic fuzzy sets based on generalized belief structures. Section 4 illustrates the flexibility and accuracy of the entailment for intuitionistic fuzzy sets based on generalized belief structures. Section 5 summarizes the...

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“…In the early stage of an unpredicted emergency event, because of the lack of abundant reliable information, the precise evaluation of the information provided by decision-makers is also difficult, while incomplete information is inevitable [16]. There are many tools to represent uncertain or imprecise information, such as fuzzy numbers [17][18][19], intuitionistic fuzzy sets [20], the Z-number [21,22], hesitant fuzzy information [23], inherent fuzzy entropy [24,25], linguistic information [26], Deng entropy [27,28], the R-number [29], rough sets [30], etc. Among them, linguistic information is related to human language, which has been widely employed to represent the evaluation information during the processes of decision-making [31][32][33].…”

Section: Introductionmentioning

confidence: 99%

An Emergency Decision-Making Method for Probabilistic Linguistic Term Sets Extended by D Number Theory

2020

Symmetry

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Emergency decision-making has become as one of the hot issues in recent years. The aim of emergency decision-making is to reduce the casualties and property losses. All the processes of emergency decision-making are full of incompleteness and hesitation. The problem of emergency decision-making can be regarded as one of the multi-attribute decision-making (MADM) problems. In this manuscript, a new method to solve the problem of emergency decision-making named D-PLTS is proposed, based on D number theory and the probability linguistic term set (PLTS). The evaluation information given by experts is tidied to be the form of PLTS, which can be directly transferred to the form of the D number, no matter whether the information is complete or not. Furthermore, the integration property of D number theory is carried out to fuse the information. Besides, two examples are given to demonstrate the effectiveness of the proposed method. Compared with some existing methods, the D-PLTS is more straightforward and has less computational complexity. Allocation weights that are more reasonable is the future work for the D-PLTS method.

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A Distance Measure for Intuitionistic Fuzzy Sets and Its Application to Pattern Classification Problems

Cited by 221 publications

References 78 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

Entailment for intuitionistic fuzzy sets based on generalized belief structures

An Emergency Decision-Making Method for Probabilistic Linguistic Term Sets Extended by D Number Theory

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