Solving a system of fuzzy relation equations by using a hierarchical process

The authors propose a method to compute the solution of a system of fuzzy relations with a continuously differentiable composed rule. The modelization of any system behavior by a fuzzy relation leads to an implication between causes and effects. The input and output vectors become, after fuzzification, fuzzy sets linked with a fuzzy relation, R. The identification of R, in the case of t-conorm/t-norm composition where the conorm is different from max, is obtained by an error criterion optimization. The method proposed is based on a hierarchical process