The aim of this paper is to develop a new methodology for solving bi-matrix games with payoffs of Atanassov’s intuitionistic fuzzy (IF) numbers (IFNs), which are called IF bi-matrix games for short. In this methodology, we propose a weighted mean-area ranking method of IFNs, which is proven to satisfy the linearity. Hereby, the concept of Pareto optimal solution of IF bi-matrix games is introduced and the Pareto optimal solution can be obtained through solving the parameterized non-linear programming model, which is derived from an IF mathematical programming model based on the proposed weighted mean-area ranking method of IFNs. Validity and applicability of the model and method proposed in this paper are illustrated with a practical example of two commerce retailers’ strategy choice problem.
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