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

摘要

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.