Category-theoretic formalization in designing fuzzy intelligent systems

Abstract

A complex of problems related to the category-theoretic formalization of fuzzy UML diagrams, fuzzy graphs, and fuzzy-graph transformation systems is examined. The basic constraints that must be satisfied by UML diagrams, which are the basis of fuzzy models of intelligent systems, are investigated. The category-theoretic approach is used to analyze the properties of inference specification based on a distributed system of fuzzy-graph transformations. Means for the compositional construction of fuzzy systems are developed using morphisms and categories of fuzzy graphs.