M. R. Seikh - Department of Mathematics, Kazi Nazrul University, Asansol-۷۱۳ ۳۴۰, India
S. Karmakar - Department of Mathematics, Kazi Nazrul University, Asansol-۷۱۳ ۳۴۰, India
M. Xia - School of Economics and Management, Beijing University, Beijing, China

The objective of this paper is to develop matrix games with pay-offs of triangular hesitant fuzzy elements (THFEs). To solve such games, a new methodology has been derived based on the notion of weighted average operator and score function of THFEs. Firstly, we formulate two non-linear programming problems with THFEs. Then applying the score function of THFEs, we transform these two problems into two non-linear multi-objective programming problems with triangular fuzzy numbers (TFNs). Finally, the Lexicographic method is used to solve these two multi-objective programming problems. A market share problem is considered to show the validity and applicability of the proposed methodology.

Matrix game, Triangular hesitant fuzzy set, Score function, Multi-objective optimization, Lexicographic method