Category-theoretic formalization in designing fuzzy intelligent systems

Authors:
N. Parasyuk;S. V. Yershov
Affiliations:
V. M. Glushkov Institute of Cybernetics, National Academy of Sciences of Ukraine, Kyiv, Ukraine;V. M. Glushkov Institute of Cybernetics, National Academy of Sciences of Ukraine, Kyiv, Ukraine
Venue:
Cybernetics and Systems Analysis
Year:
2009

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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.