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Some algebraic properties of rough approximation operators over Boolean algebras are investigated and the concept of rough Stone algebra (by J.Pomykala and J.A.Pomykala) and rough Nelson algebra (it is also called rough sets system by P.Pagliani) are generalized. From two directions, the rough implication operators based on rough set model over Boolean… (More)
Traditional fuzzy reasoning methods have two problems 1) the operators appearing in the fuzzy reasoning methods are fixed; 2) how to select the operations for the reasoning methods. In order to solve the problems, we propose the updating fuzzy reasoning method based on universal logic in this paper. The reasoning rules based on universal logic of five fuzzy… (More)
The aim of this paper is the partial axiomatization for universal logic which was proposed by Prof H.C. He in 2001. Firstly, a propositional calculus formal deductive system UL<sub>hisin(0,1)</sub> <sup>Delta</sup> for 0-level universal AND operator is built up. Secondly, the corresponding algebra LstrokPiG<sub>Delta</sub> is introduced. Finally, we prove… (More)
—The aim of this paper is solving the predicate calculus formal system based on 1-level universal AND operator. Firstly, universal logic and propositional calculus formal deductive system (0 1] h UL − ∈ , are introduced. Secondly, a predicate calculus formal deductive system (0 1] h UL − ∈ , ∀ based on 1-level universal AND operator is built. Thirdly, the… (More)
Logic algebra is important to establish the basis of mathematical logic, so in this paper, complete continuous-valued logic algebra is proposed, the definitions of seven kinds of integrity cluster of logical operation model that may exist in continuous-valued propositional logic are given, which can directly include and deal with the four uncertainties that… (More)
BL algebra is very important in fuzzy logic. In this paper three kinds of extensions of BL algebra which are very important to narrow fuzzy logic are proposed. The properties of these algebras are studied. The definitions and characters of filters on these algebras are given. Moreover, the descriptions of direct product about these algebras are discussed.