Learning Fuzzy Rules from Data

Abstract

We present an algorithm, FUZZEX, for learning fuzzy rules from a corpus of data mapping input antecedents to output consequents. The input and output spaces are first divided into a grid of cells and primitive if % then rules formulated from each occupied input cell in the role of an antecedent The distribution of output cells into which data in the input cell maps, plays the role of the consequent interpreted as a fuzzy set. Those input cells associated with sufficiently similar fuzzy output sets are then combined to form a composite rule. A concise set of rules in Disjunctive Normal Form (DNF) is formed by combining adjacent input cells belonging to the same rule, thereby simplifying the logical expression of the antecedents. Optionally, more succinctness of expression may be obtained by recruiting into a rule, adjacent input cells with (little or) no data, but which happen to simplify rule expression. Preliminary testing on testbed datasets is presented. FUZZEX can be applied effectively to problems of large dimensionality.