Fuzzy relational calculus (Q2447324)

This paper provides a survey on the basic concepts and results on fuzzy binary relations. A nice historical overview on the development of the presented concepts is given and applications of fuzzy relations are mentioned. Basic definitions and results related to fuzzy sets, fuzzy connectives (conjunction, disjunction, negation, implication, equivalence) and fuzzy relations are listed. Furthermore, some crucial properties of crisp relations are recalled. With respect to the main topic of fuzzy relations, the following ideas are considered: probabilistic relations, proximity and similarity relations, equivalence relations (diverse types), order relations (\(T\)-transitive fuzzy order relations), and continuous fuzzy relations. The concept of a fuzzy inclusion is also discussed. Moreover, the preference structures of crisp and fuzzy relations are presented.