Solution of Fuzzy Relational Equation by Real-Valued GA

Solving fuzzy relational equation (F.R.E) is a very important research topic because many practical problems end up with F.R.E. Most theoretical results on F.R.E. strongly rely on an assumption that the family of exact solutions is nonempty. However, it´s quite common that F.R.E. have no solutions. Therefore, this paper uses the real-valued genetic algorithm to solve an approximate solution for the F.R.E based on the max-product composition. An example will be illustrated for the proposed method.