An Introduction to Fuzzy Relations

This chapter presents an introduction to the theory of fuzzy relations. First, proximity and similarity relations, their classes and fuzzy partitions are introduced and their main properties are investigated. Then, main classes of fuzzy orderings are defined and classified with respect to the duality relations. Transitivity properties of fuzzy orderings and the Ferrers property of induced fuzzy orderings are established. Finally, we present elementary versions of two representation theorems.

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