Abstract The Fuzzy Decision making plays an important role in our life application especially under fuzzy environment which has rapidly changing in its circumstances. Fuzzy multi criteria decision making problems need a big effort to determine the weight of each criteria as expert’s opinions and also may there is a need to determine the weight of each expert’s opinion to determining the weight each alternatives. Those are depending on linguistic values, which must be converted to numerical values to calculate the mathematical operations, which lead us use fuzzy numbers. Many of researchers used triangle fuzzy number system and some others used trapezoidal fuzzy number system. Each fuzzy number system has its own rules, which may be difficult to convert from system to others to check correctly and accuracy. This paper introduces a generalized polygon fuzzy system method, which can used any fuzzy number system as triangle, trapezoidal, pentagon, hexagon, heptagon, octagon and etc.