An Approach to Generation of Decision Rules

Classical classification and clustering based on equivalence relations are very important tools in decision-making. an equivalence relation is usually determined by properties of objects in a given domain. when making decision, anything that can be spoken about in the subject position of a natural sentence is an object, properties of which are fundamental elements of the knowledge of the given domain. this gives the possibility of representing the concept related to a given domain. in general, the information about a set of the objects is uncertain or incomplete. various approaches representing uncertainty of a concept were proposed. in particular, zadeh?s fuzzy set theory and pawlak?s rough set theory have been most influential on this research field. zadeh characterizes uncertainty of a concept by introducing a membership function and a similarity (fuzzy equivalence) relation of a set of objects. pawlak then characterizes uncertainty of a concept by union of some equivalence classes of an equivalence relation. as one of particular important and widely used binary relations, equivalence relation plays a fundamental role in classification, clustering, pattern recognition, polling, automata, learning, control inference and natural language understanding, etc. an equivalence relation is a binary relation with reflexivity, symmetry and transitivity. however, in many real situations, it is not sufficient to consider equivalence relations only. in fact, a lot of relations determined by the attributes of objects do not satisfy transitivity. in particular, information obtained from a domain of objects is not transitive, when we make decision based on properties of objects. moreover, the information about symmetry of a relation is mostly uncertain. so, it is needed to approximately make decision and reasoning by indistinct concepts. this provokes us to explore a new class of relations, so-called class of fuzzy semi-equivalence relations. in this paper we introduce the notion of fuzzy semi-equivalence relations and study its properties. in particular, a constructive method of fuzzy semi-equivalence classes is presented. applying it we present approaches to the fuzzyfication of indistinct concepts approximated by fuzzy relative and semi-equivalence classes, respectively. and an application of the fuzzy semi-equivalence relation theory to generate decision rules is outlined.