Fuzzy relations: Past, present, and future

Abstract

Relations are used in many branches of mathematics to model concepts like is lower than, is equal to, etc. Initially, only crisp relations were considered, but in the last years, fuzzy relations have been revealed as a very useful tool in psychology, engineering, medicine, economics or any mathematically based field. A first approach to the concept of fuzzy relations is given in this chapter. Thus, operations among fuzzy relations are defined in general. When considering the particular case of fuzzy binary relations, their main properties are studied. Also, some particular cases of fuzzy binary relations are considered and related among them. Of course, this chapter is just a starting point to study in detail more specialized literature.