Fuzzy relation equations and fuzzy inference systems: An inside approach

This paper investigates and extends the use of fuzzy relation equations for the representation and study of fuzzy inference systems. Using the general ized sup-t (t is a triangular norm) composition of fuzzy relations and the study of sup-t fuzzy relation equations, interesting results are provided c oncerning the completeness and the theoretical soundness of the representat ion, as well as the ability to mathematically formulate and satisfy applica tion-oriented design demands. Furthermore, giving a formal study of fuzzy p artitions and some useful aspects of fuzzy associations and fuzzy systems, the paper can be used as a theoretical background for designing consistent fuzzy inference systems.