An Approach to Generation of Decision Rules Based on a Fuzzy Semi-equivalence Relation 1
Mingyi Zhang, Danning Li, Ying Zhang · 2010
Abstract: 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