Optimization of banks' foreign exchange portfolios aiming to determine an optimized combination of foreign exchange assets is in such a manner that it leads to a minimum risk and maximum yield. The approach used in this article, which is actually a priority over other methods is to use a combination of inexact mathematical models (fuzzy) and optimization. Thus, in this research, linear programming with fuzzy target coefficients has been used. The target coefficients are the same as the exchange rate. In other words, the daily rates of all currencies due to fluctuations are considered as fuzzy numbers. Therefore, in this investigation, by developing a multi-purpose mathematical model and by applying the fuzzy data relating to transaction rate of six foreign exchanges in year ended on March 20, 2020, including US dollar, Emirates Dirham, Japanese Yen, Turkish Lira, Korean Won and Euro, case by case risks related to the fluctuations of noted foreign exchanges and also their yield in the foreign exchange portfolio of Bank Mellat were measured and estimated for the future time horizon. All banks may benefit from the developed model. By determination of the optimal weight of each foreign exchange, upon describing and analyzing the existing status it specifies the optimal status, enabling banks to fulfill their foreign exchange obligations on due dates by properly and optimally making investment in foreign exchange assets meanwhile gaining a competitive advantage. "Gams Software" was used for solving the model.