A new similarity measure for Pythagorean fuzzy sets

Compared to the intuitionistic fuzzy sets, the Pythagorean fuzzy sets (PFSs) can provide the decision makers with more freedom to express their evaluation information. There exist some research results on the correlation coefficient between PFSs, but sometimes they fail to deal with the problems of disease diagnosis and cluster analysis. To tackle the drawbacks of the existing correlation coefficients between PFSs, some novel directional correlation coefficients are put forward to compute the relationship between two PFSs by taking four parameters of the PFSs into consideration, which are the membership degree, non-membership degree, strength of commitment, and direction of commitment. Afterwards, two practical examples are given to show the application of the proposed directional correlation coefficient in the disease diagnosis, and the application of the proposed weighted directional correlation coefficient in the cluster analysis. Finally, they are compared with the previous correlation coefficients that have been developed for PFSs.

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“…From the above result, it can be seen that K 3 P 1 , P always equals to 1 2 when P 1 = v P 1 = u . Hence, it is unreasonable and ineffective.…”

Section: Drawback Of the Correlation Coefficient Proposed Bymentioning

confidence: 67%

Directional correlation coefficient measures for Pythagorean fuzzy sets: their applications to medical diagnosis and cluster analysis

Lin

Huang

Chen

et al. 2021

Complex Intell. Syst.

119

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“…[4], Tang and Fang proposed an efficacy coefficient method to deal with rank reversal. The fuzzy theory was adopted to improve the TOPSIS method for some certain background [5,6], and the TOPSIS method was applied to evaluate the Chinese high-tech industry successfully [7]. The problem in selection of transportation service provider is a typical MCDM problem and it has many factors to be considered in decision making.…”

Section: Introductionmentioning

confidence: 99%

Evaluation and selection of transportation service provider by TOPSIS method with entropy weight

Zhang

Yang

2021

THERM SCI

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In this paper, an improved technique for order of preference by similarity to ideal solution (TOPSIS) is proposed to select the optimal transportation service provider among several alternatives according to a multi-criterion method. An entropy method is embedded to determine the weights of different criteria and it is effective to avoid the subjectivity and arbitrary of choosing the weights. A case study demonstrates the proposed method is reasonable and valid for practical problems.

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“…Therefore, Yager proposed the Pythagorean fuzzy set (PFS) [29], [30], which solved the above-mentioned problem. Based on Yager's research, Pythagorean fuzzy sets (PFSs) have been comprehensively conducted and the valuable results were obtained [31]- [35]. Among them, Wang et al [34] proposed the Pythagorean fuzzy interaction power Bonferroni mean operator and weighted Pythagorean fuzzy interaction power Bonferroni mean operator and Firozja et al [35] studied a new similarity measure for Pythagorean fuzzy sets (PFSs) by using triangular conorms.…”

Section: Introductionmentioning

confidence: 99%

“…Based on Yager's research, Pythagorean fuzzy sets (PFSs) have been comprehensively conducted and the valuable results were obtained [31]- [35]. Among them, Wang et al [34] proposed the Pythagorean fuzzy interaction power Bonferroni mean operator and weighted Pythagorean fuzzy interaction power Bonferroni mean operator and Firozja et al [35] studied a new similarity measure for Pythagorean fuzzy sets (PFSs) by using triangular conorms. But PFSs has a definite requirement that the sum of squares of membership and non-membership does not exceed 1, which limits the development of PFSs to some extent.…”

Section: Introductionmentioning

confidence: 99%

The Extension of TOPSIS Method for Multi-Attribute Decision-Making With q-Rung Orthopair Hesitant Fuzzy Sets

2020

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As a combination of q-rung orthopair fuzzy sets (q-ROFSs) and hesitant fuzzy sets (HFSs), q-rung orthopair hesitant fuzzy sets (q-ROHFSs) are more effective, powerful, and meaningful in solving the complexity, ambiguity, and expert hesitancy of membership and non-membership in multi-attribute decision-making (MADM) problems. And so, based on the advantages of q-ROHFSs, we herein propose an improved TOPSIS model in the q-rung orthopair hesitant fuzzy environment. This model can provide more accuracy in expressing fuzzy and ambiguous information. At first, we propose the distance and similarity measures of q-ROHFSs and the properties related to the distance and similarity measures of q-ROHFSs, and secondly, the axiomatized definition and formula for the entropy of q-ROHFSs. Then, for the case where the attribute weights are totally unknown, a combination of subjective and objective attribute weighting model is proposed. This model not only considers the expert's decision preference, but also the objective situation of the attributes. In addition to the above-mentioned outcomes, this paper also improves the relative closeness formula, increases the preference coefficient, and considers the risk-preference of decision makers. Finally, the proposed model is compared with other methods and used to evaluate the effectiveness of military aircraft overhaul. The method is verified to be scientific, reliable and effective for solving MADM problems.INDEX TERMS q-Rung orthopair hesitant fuzzy sets, distance measure, entropy, multi-attribute decisionmaking, TOPSIS method.

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A new similarity measure for Pythagorean fuzzy sets

Cited by 42 publications

References 39 publications

Directional correlation coefficient measures for Pythagorean fuzzy sets: their applications to medical diagnosis and cluster analysis

Directional correlation coefficient measures for Pythagorean fuzzy sets: their applications to medical diagnosis and cluster analysis

Evaluation and selection of transportation service provider by TOPSIS method with entropy weight

The Extension of TOPSIS Method for Multi-Attribute Decision-Making With q-Rung Orthopair Hesitant Fuzzy Sets

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