The aim of this paper is to develop a new methodology for solving bimatrix games with payoffs of triangular intuitionistic fuzzy numbers (TIFNs), which are called TIFN bimatrix games for short. In this methodology, we define the concepts of the value-index and ambiguity-index and hereby develop a difference-index based ranking method, which is proven to be a total order. The parameterized bilinear programming models are derived from a pair of auxiliary TIFN mathematical programming models, which are used to determine solutions of TIFN bimatrix games. Validity and applicability of the models and method proposed in this paper are illustrated with a practical example.
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