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.