Soft Matrix Game: A Hesitant Fuzzy MCDM Approach

Abstract

Soft set theory has emerged recently as a new mathematical tool to handle uncertainty. Sometimes decision makers are not sure about the decision-making criteria, where soft set theory provides an idea to deal with such uncertainties. Multi-criteria decision making (MCDM) involves choosing the best from several alternatives. MCDM methods such as TOPSIS and VIKOR depend on an aggregating function for presenting “closeness to the ideal” which arises due to the compromise solution. The VIKOR method of compromise ranking describes a compromise solution, providing a maximum for the “maximizing player” and minimum for the “opponent”, which is an effective approach in an MCDM game. TOPSIS method presents a solution with the shortest distance to the positive ideal solution (PIS) and largest distance from the negative ideal solution (NIS). Also, hesitant fuzzy soft set is an appropriate tool to tackle the imprecise parameters introduced in MCDM problems by the decision maker (DM). In this paper, we extend the VIKOR and TOPSIS methods for solving MCDM game problems with hesitant fuzzy soft payoffs to determine the optimal strategies. Finally, a numerical example is incorporated to verify the extended VIKOR approach and the results are compared with those for the TOPSIS method. The paper ends with conclusions and outlooks.