Pythagorean fuzzy multiple criteria decision analysis based on Shapley fuzzy measures and partitioned normalized weighted Bonferroni mean operator

Abstract

Pythagorean fuzzy sets are powerful techniques for modeling vagueness in practice. The aim of this article is to investigate an effective means to aggregate uncertain information and then employ it into settling multiple criteria decision making (MCDM) problems within the Pythagorean fuzzy circumstances. To capture the nature of the reality, some special cases should be comprehensively considered. First, though correlation commonly exist among criteria, a deep insight should also be provided into some realistic situations, in which not all the criteria are interrelated to others. Besides, it is more reasonable to take the importance of the input arguments into consideration. Effected by aforementioned point, this article explores a Pythagorean fuzzy partitioned normalized weighted Bonferroni mean (PFPNWBM) operator with the combination of partitioned Bonferroni mean (BM) and normalized weighted BM operators considering Shapley fuzzy measure. Subsequently, in the context of partially known weight information, models are established to identify the optimal Shapley fuzzy measure. Moreover, integrated the PFPNWBM operator with the optimal Shapley fuzzy measure identification model, a Pythagorean fuzzy MCDM approach is designed. Finally, an illustrative example and detailed analyses are performed to demonstrate its feasibility and reliability.

Generalized orthopair fuzzy weighted distance‐based approximation (WDBA) algorithm in emergency decision‐making

“…In the future, we will employ the outstanding WDBA method to dispose of the EDM issues under diverse fuzzy environment and take the idea of combined weight into gene selection …”

Some q ‐rung orthopair fuzzy Hamy mean operators in multiple attribute decision‐making and their application to enterprise resource planning systems selection

“…The degree of indeterminacy is given as π x μ x ν x μ x ν x ( ) = ( ( )) + ( ( )) − ( ( )) ( ( )) (4) to evaluate the degree of accuracy of the q-ROFN p μ ν = ( , ). The larger the value of H p ( ), the more the degree of accuracy of the q-ROFN p is.…”

“…More recently, Pythagorean fuzzy set (PFS) has appeared as an effective and useful tool for depicting uncertainty of the multiple attribute decision‐making (MADM) problems . The PFS is also characterized by the membership degree and the nonmembership degree, whose sum of squares is less than or equal to 1, and the PFS is more general than intuitionistic fuzzy set (IFS) .…”

“…Finally, a practical example for enterprise resource planning system selection is given to verify the developed approach and to demonstrate its practicality and effectiveness.K E Y W O R D S enterprise resource planning system, multiple attribute decisionmaking, Pythagorean fuzzy set, q-rung orthopair fuzzy sets, q-rung orthopair fuzzy weighted dual Hamy mean operator, q-rung orthopair fuzzy weighted Hamy mean operator 1 | INTRODUCTION More recently, Pythagorean fuzzy set (PFS) 1 has appeared as an effective and useful tool for depicting uncertainty of the multiple attribute decision-making (MADM) problems. [2][3][4][5][6][7][8] The PFS is also characterized by the membership degree and the nonmembership degree, whose sum of squares is less than or equal to 1, and the PFS is more general than intuitionistic fuzzy set (IFS). [9][10][11][12][13][14][15][16][17] In some cases, the PFS can solve some problems that the IFS cannot, for example, if a DM gives the membership degree and the nonmembership degree as 0.8 and 0.6, respectively; then it is only valid for the PFS.…”

Similarity Measures of q-Rung Orthopair Fuzzy Sets Based on Cosine Function and Their Applications

“…In other words, all the intuitionistic fuzzy decision-making problems are the special case of Pythagorean fuzzy decision-making problems, which means that PFS can more efficiently deal with MADM problems. In previous literatures, some researching works have been studied by a large amount of investigators [24][25][26][27][28]. Zhang and Xu [29] defined the Pythagorean fuzzy TOPSIS model to deal with the MADM problems.…”