Classifying fuzzy rules construction based on inverse logical inference

Abstract

An approach to the classifying fuzzy knowledge bases construction based on fuzzy relations and inverse logical inference, which allows avoiding the laborious procedures of the generation and selection of expert rules, is suggested in the paper. The matrix of «causes — effects» fuzzy relations is the support of the expert information. It is shown, that the classifying fuzzy IF-THEN rules represents the solution set of fuzzy relational equations in the form of the composite fuzzy terms, where causes and effects significance measures are described by fuzzy quantifiers. The problem of the classifying fuzzy rules construction, which consists of renewal the values of the input variables for the given output classes, is amounted to solving the system of fuzzy relational equations using the genetic algorithm. The number of rules in the class is defined by the number of solutions, and the form of the composite fuzzy terms membership functions in the rule is defined by the cause’s significance measures.