Some Novel Interactive Hybrid Weighted Aggregation Operators with Pythagorean Fuzzy Numbers and Their Applications to Decision Making

Na Li,Lei Wang,Harish Garg

doi:10.3390/math7121150

Na Li, Lei Wang + Show 1 more

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https://doi.org/10.3390/math7121150

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Abstract

A Pythagorean fuzzy set (PFS) is one of the extensions of the intuitionistic fuzzy set which accommodate more uncertainties to depict the fuzzy information and hence its applications are more extensive. In the modern decision-making process, aggregation operators are regarded as a useful tool for assessing the given alternatives and whose target is to integrate all the given individual evaluation values into a collective one. Motivated by these primary characteristics, the aim of the present work is to explore a group of interactive hybrid weighted aggregation operators for assembling Pythagorean fuzzy sets to deal with the decision information. The proposed aggregation operators include interactive the hybrid weighted average, interactive hybrid weighted geometric and its generalized versions. The major advantages of the proposed operators to address the decision-making problems are (i) to consider the interaction among membership and non-membership grades of the Pythagorean fuzzy numbers, (ii) it has the property of idempotency and simple computation process, and (iii) it possess an adjust parameter value and can reflect the preference of decision-makers during the decision process. Furthermore, we introduce an innovative multiple attribute decision making (MADM) process under the PFS environment based on suggested operators and illustrate with numerous numerical cases to verify it. The comparative analysis as well as advantages of the proposed framework confirms the supremacies of the method.

Highlights

Multiple attribute decision making (MADM) is one of the processes to find the most desirable alternative among all given alternatives in the light of finite attributes or criteria
To demonstrate the feasibility of the presented approach, we compare our methods with the PFIHA and PFIHG operators developed by Wei [33], the SPFWA and SPFWG(symmetric Pythagorean fuzzy weighted geometric) operators developed by Ma and Xu [19], and the PFEWA(Pythagorean fuzzy Einstein weighted averaging) and PFEWG(Pythagorean fuzzy Einstein weighted geometric) operators developed by Garg [22] and
We can obtain that the decision outcomes by the PFIHA operator [33] and PFIHG operator [33] are the same as our generalized PFIHWG (GPFIHWG) operator, and are slightly different with our generalized PFIHWA (GPFIHWA) operator, but the most desirable alternative by the PFIHA

Summary

Introduction

Multiple attribute decision making (MADM) is one of the processes to find the most desirable alternative among all given alternatives in the light of finite attributes or criteria. In the decision-making process, it is commonly supposed that the evaluation information of alternatives for attributes described by decision-makers (DMs) is precise numbers. An appropriate way to deal with such problems is to adopt uncertain evaluations rather than crisp ones, for instance, an intuitionistic fuzzy set (IFS) [1] and fuzzy set (FS) [2]. Similar to the IFS, the PFS is still depicted by the membership and non-membership degrees, but their square sum within interval (0, 1). If the membership grade is given as 0.4 by DM, while the non-membership grade is 0.8, it can be seen

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Discussion

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