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Firstly in this paper we introduce a new concept of the 2nd power of a fuzzy number. It is exponent to production (EP) method that provides an analytical and approximate solution for fully fuzzy quadratic equation (FFQE) :    F  (    X   ˜   )  =    D   ˜    , where    F  (    X   ˜   )  =    A   ˜X   ˜2    +    B   ˜X   ˜   +    C   ˜    . To use the mentioned EP method, at first the 1-cut solution of FFQE as a real root is obtained and then unknown manipulated unsymmetrical spreads are allocated to the core point. To this purpose we find  λ  and  μ  as optimum values which construct the best spreads. Finally to illustrate easy application and rich behavior of EP method, several examples are given.

The Solution of Fully Fuzzy Quadratic Equation Based on Optimization Theory