Partitioned fuzzy measure-based linear assignment method for Pythagorean fuzzy multi-criteria decision-making with a new likelihood

Abstract

The aim of this paper is to develop an extended linear assignment method to solve multi-criteria decision-making (MCDM) problems under the Pythagorean fuzzy environment, where the criteria values take the form of the Pythagorean fuzzy numbers (PFNs) and the information about criteria weights are correlative. In order to obtain the criteria-wise rankings of the linear assignment method, we firstly define a new likelihood for the comparison between PFNs. Then, we introduce the fuzzy measure to determine the weighted-rank frequency matrix of the linear assignment method. Unlike the existing literature of the fuzzy measure, this paper incorporates the partitioned structure of the criteria set into it and proposes a new partitioned fuzzy measure. Further, we design the extended linear assignment method by using the new likelihood of PFNs and partitioned fuzzy measure for Pythagorean fuzzy multi-criteria decision-making (PFMCDM). Finally, a practical example is used to illustrate and verify our proposed method.

Keywords:

• Pythagorean fuzzy sets
• linear assignment method
• fuzzy measure
• likelihood

Acknowledgement

The authors would like to extend the sincere gratitude to journal editors and the anonymous reviewers for their significant comments and suggestions.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work is partially supported by the National Natural Science Foundation of China (Nos. 71401026, 71432003, 61773352), the Fundamental Research Funds for the Central Universities of China (No. ZYGX2014J100), and the Social Science Planning Project of the Sichuan Province (No. SC15C009).