Abstract
Similarity measure, as a tool to measure the similarity degree between two objects, is an important research content in fuzzy set theory. Pythagorean fuzzy set, as a new extension of fuzzy set theory, has been widely used in various fields. It is very necessary to study the similarity measure of the Pythagorean Fuzzy set. Considering that the existing similarity measures cannot distinguish the highly similar but inconsistent Pythagorean fuzzy sets and the calculation results are error-prone in application, this paper introduces the exponential function to propose several new similarity measures of the Pythagorean fuzzy set. Firstly, on the premise of introducing the existing similarity measures, several new similarity measures are defined and their properties are discussed, and then the weighted similarity measures are defined. Then, the new similarity measures and the existing similarity measures are compared by an example, and it is verified that the new similarity measures can effectively distinguish highly similar but inconsistent Pythagorean fuzzy sets. Finally, through three simulation cases, it is verified that the new similarity measures can deal with different practical application problems more accurately and reliable than the existing similarity measures.
Highlights
As an extension of the fuzzy set (FS), the intuitionistic fuzzy set (IFS) has been widely studied after Atanassov [1] proposed it
In order to solve the above two problems, this paper proposes several new similarity measures based on the exponential function, and verifies that the new similarity measures can effectively solve the above two problems by the comparative example and the simulation cases
Considering that the ranking results obtained by the existing weighted similarity measures are not completely consistent with those obtained by the new weighted similarity measures, the five potential enterprise resource planning (ERP) systems Ai are ranked by the verification method
Summary
As an extension of the fuzzy set (FS), the intuitionistic fuzzy set (IFS) has been widely studied after Atanassov [1] proposed it. Tian [26] presented a new fuzzy cotangent similarity measure of the IFS, and applied it to solve the medical diagnosis problem. Based on the centroid points of transformed right-angled triangular fuzzy numbers, Chen et al [43] proposed a new similarity measure between the intuitionistic fuzzy values It can be seen from the above that the similarity measures of the IFS have been successfully applied to different fields, but there are some cases in practical application which cannot be solved by the IFS. Zhang [34] developed a new DM method based on the similarity measures to address MCDM problems within Pythagorean fuzzy environment based on the PFNs. Wei and Wei [27] presented ten similarity measures between the PFSs based on the cosine function by considering the MD, the ND and the HD.
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