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In the last three to four decades, Fuzzy decision and Game theory are received great attention from the scientists, engineers, economists and businessmen, and achieved tremendous success as well. To realize the day-to-day problems, researchers use fuzzy and vague sets in their discussions of the game problems. In this article, we consider a matrix game whose payoffs are triangular intuitionistic fuzzy numbers and also apply robust ranking technique as ranking of fuzzy numbers to solve the matrix game. Different types of score function approaches, and accuracy function approaches are used in matrix games, but robust ranking technique to solve matrix games is rare in use. We utilize the robust ranking technique to solve matrix game and analyze numerical examples to validate the proposed technique. We describe a conclusion about the proposed study with an outlook of future study.