Fuzzy Relations and Applications

Abstract

This chapter explores fuzzy relations and their applications, which have been the result of the rapid development of computer technology during the past two decades, from an industrial to an information society. There is a real need for solid mathematical models that are capable of grasping the imprecision and uncertainty intrinsically present in the information systems. Fuzzy relations are based on formal models capable of grasping the human way of tackling complex phenomena, thus, aiming towards completeness of information. Fuzzy relations are based on Zedah's model that states—instead of a sharp boundary or a set of definite borderline cases, an abrupt, transition from non-membership to full membership allows partial degrees of membership. The structural considerations of this model are illustrated in the chapter with the help of algebraic equations.