A game theoretic approach to solve multiple group decision making problems with interval-valued intuitionistic fuzzy decision matrices

ABSTRACT

The objective of this paper is to develop a two person zero-sum game theoretic solution approach for multiple attribute group decision making (MAGDM) problems under interval-valued intuitionistic fuzzy environment. In this way, a new order function is introduced to defuzzify the interval-valued intuitionistic fuzzy numbers (IVIFNs) and discuss its properties. In complicated and uncertain group decision-making problems, decision makers face a problem for assessing the group weights for alternatives and attributes. In this paper, the weights of present MAGDM problem with interval-valued intuitionistic fuzzy decision matrices (matrices in which entries are represented by IVIFNs) are calculated by converting it into a traditional two person zero-sum game problem. Then, the expected score for each alternative is calculated using the optimal solution of this game problem. On the basis of the calculated expected score values, the prespecified alternatives are ranked in order to find the best alternative. The validity and applicability of the developed approach are given by a numerical example.

KEYWORDS:

• Multiple attribute group decision making
• interval-valued intuitionistic fuzzy number
• interval-valued intuitionistic fuzzy decision matrix
• order function
• two person zero-sum game

Acknowledgments

The authors would like to thank Editor-in-Chief and the anonymous referees for their suggestions which helped to improve the quality of the presentation.

Disclosure statement

No potential conflict of interest was reported by the authors.