SOLVING FUZZY EQUATIONS - A NEW SOLUTION CONCEPT

We have previously shown [2] that many fuzzy equations do not have solutions when the solution concept is based on the extension principle. We therefore introduce two new solution procedures, one based on the unified extension [6] and the other based on possibility theory, after we solve the non-fuzzy equation for the unknown variable. We show, for many types of equations, that: (1) the two new solutions are identical; (2) the solution is either a real, or generalized complex, fuzzy number (all uncertain parameters are modeled as a real fuzzy numbers); and (3) the previous solution based on the extension principle (when it exists) is a subset of of new solution. In particular, we show that the fuzzy quadratic equation, with real fuzzy number coefficients, always has a (new) solution.