Fuzzy Reasoning In Lukasiewicz Logic Systems And Attribute Reducation In Fuzzy Concept Lattices

Implication operators play a very important role in the development of fuzzy set theory. For example, in the aspect of building up the semantics of many-valued logic, different logic systems involve different implication operators, and in the theory of knowledge discovery (such as the theory of fuzzy concept lattices), implication operators also play an important role. The solution of fuzzy modus ponens in Lukasiewicz logic system and attribute reduction based on the Godel implication operator are investigated in this article, and we obtain some meaningful results.In order to build up a solid logical foundation for the logical semantics of the fuzzy reasoning, professor Guo-jun Wang proposed the reasoning model of FMP in classical logic, with the method of using the symbol A(v) to denote v(A), where v ∈ Ω is an evaluation and A ∈ F(S) is a logic formula. Furthermore, the triple-I solution was obtained. When this method is used in Lukasiewicz 3-valued normal systems, the problem-Valuationally Decided Formula question ( abbreviated as the VDF problem), plays a crucial role in the matter. In Chapter 2, the reasonable condition of VDF is studied first, and based on the analysis on the principles of VDF and the structure of McNaughton function induced by the single atom logic formula, the logic foundation of FMP, whose evaluation filed is finite sets, countable infinite sets or the unit interval respectively, is surveyed. Moreover, we prove that fuzzy reasoning can be achieved in any Lukasiewicz many-valued logic system.In 1982, according to the crisp relation between object set and attribute set, Will.R established a theory of concept lattices which is a kind of concept hiberarchy based on the foundation of Galois connection. Since this theory plays a crucial role in software engineering, data analysis and information engineering, many researchers show great interest in it recently. In realistic life, generally, the relation between objects and attributes is fuzzy, and so many kinds of fuzzy concepts have been proposed based on different backgrounds. In Chapter 3, the fuzzy concept at the level δ ∈ [0,1], which was proposed by S.Elloumi, is furtherly analyzed, and a new fuzzy concept lattices with respect to Godel implication operator is built up.