Simulating Fuzzy Numbers for Solving Fuzzy Equations with Constraints

This paper investigates the possibility of applying genetic algorithms (GAs) to solve fuzzy equations without defining membership functions for fuzzy numbers, neither using the extension principle, interval arithmetic, and a-cut operations for fuzzy computations, nor using a penalty method for constraint violations. Two famous fuzzy optimization problems are used to illustrate the effectiveness and robustness of the proposed approach. The empirical results show that the GA approach can obtain very good approximate solutions within the given bounds of each uncertain variable of the problems.