A new approach to construct similarity measure for intuitionistic fuzzy sets

Song, Yafei; Wang, Xiaodan; Wen, Quan; Huang, Wenlong

doi:10.1007/s00500-017-2912-0

Cited by 140 publications

(101 citation statements)

References 36 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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“…Note that here we first consider the alternative supplier A 1 to better illustrate the calculation process. First, the IVEDFs can be obtained based on Equation (17). The specific results are shown in Table 3 On the basis of Equation (6), the normalization results can be calculated.…”

Section: Application Analysismentioning

confidence: 99%

“…Multicriteria decision‐making (MCDM) is an important part of modern decision‐making science, which is also widely used in many fields, such as supplier selection, medical diagnosis, sensor fusion, uncertainty modeling, risk analysis, reliability, and so forth . Many effective techniques have been used in solving MCDM problems, such as intuitionistic fuzzy sets, soft sets, evidence theory, evidential reasoning, D number, and Z number . With the development of information science, these problems have attracted many researchers …”

Section: Introductionmentioning

confidence: 99%

An interval‐valued exceedance method in MCDM with uncertain satisfactions

Liu

Xiao

2019

Int J Intell Syst

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Multicriteria decision‐making problems have been applied to many applications for its practicality. Nevertheless, when the evaluated satisfactions are more complex, such as interval‐valued distributions, how to reasonably obtain the aggregation results of alternatives is still an open issue. In this paper, an interval‐valued exceedance method is proposed to solve such a question based on the Golden Rule representative value and probabilistic exceedance method. Due to good performance of expressing uncertain information, the Golden Rule representative value method is used to order interval‐valued satisfactions after an effective normalization process. In addition, a quantifier‐based ordered weighted averaging operator is also introduced to consider the preferences of decision makers. A realistic application of supplier selection is shown to illustrate the practicality of the proposed method.

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“…Ye put forward two similarity measures based on cosine functions and illustrated their effectiveness by comparing them with existing trigonometric similarity measures. Song et al proposed a measure of similarity based on the direct operation of the membership, nonmembership, and hesitation degrees of IFSs and applied it to medical diagnosis problem. Garg and Kumar defined the similarity measures based on the connection numbers of the set pair analysis theory to solve the DM problems under the IFS environment.…”

Section: Introductionmentioning

confidence: 99%

Some results on information measures for complex intuitionistic fuzzy sets

Garg

Rani

2019

Int J Intell Syst

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Complex intuitionistic fuzzy sets (CIFSs), modeled by complex‐valued membership and nonmembership functions with codomain the unit disc in a complex plane, handle two‐dimensional information in a single set. Under this environment, the primary objective of the present study is to introduce some novel formulae of information measures (similarity measures, distance measures, entropies, and inclusion measures) and discuss the transformation relationships among them. To demonstrate the efficiency of the proposed similarity measures, we apply it to pattern recognition problem and a detailed comparative analysis is conducted with some of the existing measures. Further, algorithms based on proposed measures are developed for handing multicriteria decision‐making problems and their working is illustrated with the help of an example. Besides this, the practicality of the proposed similarity measure is demonstrated by developing a clustering algorithm under CIFS environment.

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A new approach to construct similarity measure for intuitionistic fuzzy sets

Cited by 140 publications

References 36 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

An interval‐valued exceedance method in MCDM with uncertain satisfactions

Some results on information measures for complex intuitionistic fuzzy sets

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