The objective of this research is employ the special cases of function trapezoid in the composition of fuzzy sets to make decision within the framework of the theory of games traditional to determine the best strategy for the mobile phone networks in the province of Baghdad and Basra, has been the adoption of different periods of the functions belonging to see the change happening in the matrix matches and the impact that the strategies and decision-making available to each player and the impact on society as a community goal of the strategies the players. the most important thing was reached this research is the region fuzzy to influence the setting of optimal strategies and point of balance in the matrix matches companies contact, especially when approaching the total membership of groups and underemployment in the research problem, the strategy dominant company Asiacell and Zain Iraq in Baghdad and Basra province - the peak time is billing line, the best return for the company Asiacell and Zain Iraq strategies bill line and prepayment when the connection to the same network, you get less return Asiacell and Zain Iraq strategies prepayment line when the connection to other networks.
