Generalized morphisms, a new tool for comparative evaluation of performance of fuzzy implications, t-norms and co-norms in relational knowledge elicitation

摘要

This paper describes a technique for identification of the knowledge structures implicit in scientific data and further develops the supporting methodology for analysis of fuzzy relational structures using the mathematical theory of Fuzzy Relations and Generalized Morphism. Initial knowledge elicited using repertory grid with semiotic descriptors is transformed to fuzzy relational knowledge structures which capture semantic relationships in a problem domain by means of BK-product. In analysis, the fuzzy relational structures computed in the different sized domains or those computed by means of various fuzzy logics can be analyzed using generalized morpohism; namely (global) structure embedding, or structure preserving as well as meta analysis of fuzzy relational structures. The result of meta analysis is represented as the Hasse Diagram structure of meta relations by classifying equivalent classes of fuzzy relational structures. The paper is concluded with a case study using real-life engineering data from the aviation industry.