Hierarchical structure and applications of fuzzy logical systems

Authors:
Daowu Pei;Rui Yang
Affiliations:
Department of Mathematics, Zhejiang Sci-Tech University, Hangzhou 310018, China and Key Laboratory of Advanced Textile Materials and Manufacturing Technology, Zhejiang Sci-Tech University, Ministr ...;Department of Mathematics, Zhejiang Sci-Tech University, Hangzhou 310018, China and Key Laboratory of Advanced Textile Materials and Manufacturing Technology, Zhejiang Sci-Tech University, Ministr ...
Venue:
International Journal of Approximate Reasoning
Year:
2013

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Abstract

This paper focuses on hierarchical structures of formulas in fuzzy logical systems. Basic concepts and hierarchical structures of generalized tautologies based on a class of fuzzy logical systems are discussed. The class of fuzzy logical systems contains the monoidal t-norm based system and its several important schematic extensions: the Lukasiewicz logical system, the Godel logical system, the product logical system and the nilpotent minimum logical system. Furthermore, hierarchical structures of generalized tautologies are applied to discuss the transformation situation of tautological degrees during the procedure of fuzzy reasoning.