The Infromation Content of Fuzzy Relations and Fuzzy Rules

The appraisement of fuzzy relations is a significant problem in fuzzy theory. The related literatures done before almost focused on the similarity or equivalence fuzzy relations with a probability distribution preassigned. In this paper, a new measure named the information content of fuzzy relations is proposed, which estimates the information conveyed by a general fuzzy relations defined on multiple-domain without probability distribution preassigned. When fuzzy relation is taken as fuzzy set, the information content of fuzzy relation is compared with fuzzy entropy and specificity of fuzzy sets. Based on this new measure, a new concept, the information content of fuzzy rules, is defined, which focuses on the corresponding relation between input domain and output domain and can be used to appraise and choose fuzzy rules in rule mining.