Extension of TOPSIS to Multiple Criteria Decision Making with Pythagorean Fuzzy Sets

• Published in: International journal of intelligent systems Vol. 29; no. 12; pp. 1061 - 1078
• Main Authors: Zhang, Xiaolu, Xu, Zeshui
• Format: Journal Article
• Language: English
• Published: Hoboken, NJ Blackwell Publishing Ltd 01-12-2014; Wiley; Hindawi Limited
• Subjects: Applied sciences; Computer science; control theory; systems; Data processing. List processing. Character string processing; Decision making; Decision theory. Utility theory; Exact sciences and technology; Fuzzy; Fuzzy logic; Fuzzy set theory; Fuzzy sets; Intelligent systems; Mathematical models; Memory organisation. Data processing; Operational research and scientific management; Operational research. Management science; Optimization; Similarity; Software; Uncertainty; Fuzzy logic; Uncertain system; Proximity; Decision support system; Multicriteria analysis; Decision making; Positive solution; Case based reasoning; Decision analysis; Modeling; Comparative study; Pythagor theorem
• ISSN: 0884-8173; 1098-111X
• DOI: 10.1002/int.21676

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.