Linguistic Pythagorean hesitant fuzzy matrix game and its application in multi-criteria decision making

In this study, a new Linguistic Pythagorean Hesitant Fuzzy Set (LPHFS) is introduced by considering the notions of linguistic fuzzy set and Pythagorean hesitant fuzzy set. LPHFS is a suitable path to deal with the hesitant situation in decision making, which is characterized by linguistic membership and non-membership degrees. Multi-Criteria Decision Making (MCDM) process determines multiple competing criteria in decision making. The traditional decision making approaches assume that each player is independent. But in real world competitive situation, the real fact is that each player tries to maximize individual benefit which causes a negative impact on other player. Here we propose a Linguistic Pythagorean Hesitant Fuzzy (LPHF) distance measure based on game theoretical framework to terminate the cross-influence problem. So our intention is to explore the generalized hybrid Euclidean distance measures of LPHFS. Then we analyze the application of LPHFS to MCDM game by using Technique for Order Preference by Similarity to Ideal Solution (TOPSIS). The LPHFS is assumed to explore the uncertainty of Decision Makers (DMs), and the game theory is used to optimize the combination of criteria in interactive conditions. A modified version of TOPSIS and Ambika method are designed in the context of MCDM game with LPHFS. Finally, two real-life problems are considered to illustrate the applicability and feasibility of our proposed method, and then a comparison analysis is drawn among the obtained results with the existing methods to depict the usefulness of it.