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Extension of TOPSIS to Multiple Criteria Decision Making with Pythagorean Fuzzy Sets
Author(s) -
Zhang Xiaolu,
Xu Zeshui
Publication year - 2014
Publication title -
international journal of intelligent systems
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.291
H-Index - 87
eISSN - 1098-111X
pISSN - 0884-8173
DOI - 10.1002/int.21676
Subject(s) - pythagorean theorem , ideal solution , topsis , ideal (ethics) , closeness , mathematics , mathematical optimization , fuzzy set , computer science , fuzzy logic , measure (data warehouse) , extension (predicate logic) , artificial intelligence , data mining , mathematical economics , law , geometry , programming language , mathematical analysis , physics , political science , thermodynamics
Recently, a new model based on Pythagorean fuzzy set (PFS) has been presented to manage the uncertainty in real‐world decision‐making problems. PFS has much stronger ability than intuitionistic fuzzy set to model such uncertainty. In this paper, we define some novel operational laws of PFSs and discuss their desirable properties. For the multicriteria decision‐making problems with PFSs, we propose an extended technique for order preference by similarity to ideal solution method to deal effectively with them. In this approach, we first propose a score function based comparison method to identify the Pythagorean fuzzy positive ideal solution and the Pythagorean fuzzy negative ideal solution. Then, we define a distance measure to calculate the distances between each alternative and the Pythagorean fuzzy positive ideal solution as well as the Pythagorean fuzzy negative ideal solution, respectively. Afterward, a revised closeness is introduced to identify the optimal alternative. At length, a practical example is given to illustrate the developed method and to make a comparative analysis.