|||Ekkart Bolten, Martin Spott, Fuzzy Rule Extraction from Fuzzy Relations, Proc. of EUFIT 97, p. 1019-1023, Sep 1997.
In several applications, we observe fuzzy data that is represented by fuzzy relations. We are interested in an interpretation of fuzzy relations in the sense that we extract the main information from them. The idea is to describe parts of the relation by fuzzy rules of the form "If x is A then y is B". Each rule forms a fuzzy relation and the aggregation of all rules approximates the fuzzy relation we want to examine. As a result, we obtain a fuzzy rule-base that can easily be understood by human beings and can be verified formally. Besides, it represents the given information in a more compact form than the fuzzy relation does. In this paper, we present an algorithm that is based on the semantics of possibility and support distributions, i.e. we mainly use GĂ¶del and Mamdani rule-bases. In contrast to other approaches, we do not search for exact solutions of relational equations but try to hold the balance between quality of approximation and comprehensibility.