APPROXIMATELY SOLVING FUZZY RELATION EQUATIONS - SOME MATHEMATICAL RESULTS AND SOME HEURISTIC PROPOSALS

Fuzzy relation equations are intimately connected with the approach toward fuzzy control. Unfortunately, systems of such equations are solvable only under quite restrictive conditions. Therefore a notion of approximate solution is discussed which applies also in cases where such systems do not have solutions. For some types of fuzzy equations best possible approximate solutions are known, for other types some strategies are considered to suitably guess approximate solutions. Furthermore, that approach is applied to some types of ''cascaded'' fuzzy relation equations which are connected with ideas to join neural network structures with fuzzy control.