A walk through fuzzy relations and their application to information retrieval, medical diagnosis and expert systems

One of the most fundamental notions in pure and applied sciences is the concept of a relation. Science has been described as the discovery of relations between objects, states and events. The concept of a fuzzy relation-where instead of dealing with related or nonrelated objects, one is considering objects that are related in some degree-has thoroughly enriched the applicability of this fundamental concept. Due to recently introduced notions of after- and fore-set, some important compositions of fuzzy relations have been introduced. The paper presents an overview of the most important theoretical notions and set-theoretic operations on fuzzy relations in terms of after- and fore-sets. It then considers three possible areas of application of fuzzy relations: information retrieval, medical diagnosis and expert system inference mechanisms