Assessment of the Degree of Consistency of the System of Fuzzy Rules

Pospelova Lyudmila Yakovlevna ()
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Pospelova Lyudmila Yakovlevna: Institution of Russian Academy of Sciences Dorodnicyn Computing Centre of RAS

Business Inform, 2013, issue 12, 124_129

Abstract: The article analyses recent achievements and publications and shows that difficulties of explaining the nature of fuzziness and equivocation arise in socio-economic models that use the traditional paradigm of classical rationalism (computational, agent and econometric models). The accumulated collective experience of development of optimal models confirms prospectiveness of application of the fuzzy set approach in modelling the society. The article justifies the necessity of study of the nature of inconsistency in fuzzy knowledge bases both on the generalised ontology level and on pragmatic functional level of the logical inference. The article offers the method of search for logical and conceptual contradictions in the form of a combination of the abduction and modus ponens. It discusses the key issue of the proposed method: what properties should have the membership function of the secondary fuzzy set, which describes in fuzzy inference models such a resulting state of the object of management, which combines empirically incompatible properties with high probability. The degree of membership of the object of management in several incompatible classes with respect to the fuzzy output variable is the degree of fuzziness of the "Intersection of all results of the fuzzy inference of the set, applied at some input of rules, is an empty set" statement. The article describes an algorithm of assessment of the degree of consistency. It provides an example of the step-by-step detection of contradictions in statistical fuzzy knowledge bases at the pragmatic functional level of the logical output. The obtained results of testing in the form of sets of incompatible facts, output chains, sets of non-crossing intervals and computed degrees of inconsistency allow experts timely elimination of inadmissible contradictions and, at the same time, increase of quality of recommendations and assessment of fuzzy expert systems.

Keywords: contradictions; fuzzy production knowledge base; abduction; status word; carrier of the secondary fuzzy set; membership function; degree of consistency (search for similar items in EconPapers)
Date: 2013
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