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In a competitive electricity market, Gencos should schedule their generators' maintenance plan to maximize their profit. Many of previous works are concentrated on short term bidding strategies. Besides, in the mid-term plan, several items such as reliability, fuel, pollution, and risk constraints are considered. Unit Maintenance Scheduling (UMS) has a significant effect on the Genco's profit in a competitive electricity market. In a regulated power system, UMS is usually determined by a central system, such as System Operator (SO). On the other hand, in a de-regulated power system, UMS is determined through multiple interactions between the market players, mainly Gencos and SO. Considering these, it would be a desire to solve both short term and mid-term problems, in a single framework. In this case, Gencos can offer a price curve with an outlook to mid-term goals in a game-theoretic approach. The approach would be based on some predictions of parameters such as production cost factors. This article, addresses the uncertainty in the cost factors in a fuzzy game theoretic scheme and experimental results show the effectiveness of the proposed approach.