摘要
通过对模糊逻辑代数中传统MP-滤子的定义进行改造,在蕴涵格中引入MP*-滤子的概念,并由此构作了完整的同余关系和商代数结构;同时,引入优蕴涵格的概念,证明了优蕴涵格的素滤子定理,从而完蔓地建立了蕴涵格的一般滤子理论。研究结果表明,当蕴涵格特化为IMTL-代数、R0-代她、MV-代数时,MP*-滤子正好特化为传统的MP-滤子,且IMTL-代数、R0-代数、MV-代数必是优蕴涵格,因此本文的结果大幅度扩展了相应逻辑代数滤子理论的系列已有结果。
By revising the definition of MP-filter in fuzzy logical algebraic systems, the new notion of MP-filter in implication lattice is introduced. Using MP-filter, the congruence and quotient algebra are constructed. Moreover, the notion of well implication lattice is introduced, and the prime MP-filter theorem of well implication lattice is proved, so general filter theory of implication lattice is completely established. The facts are showed that (1) MP-filter and MP-filter coincide when an implication lattice is an IMTL-algebra (or R0-algebra or MV-algebra) ; (2) any IMTL-algebra (or R0-atgebra or MV-algebra) is a well implication lattice, and there exists well implication lattice which is not IMTL-algebra.
出处
《模糊系统与数学》
CSCD
北大核心
2011年第1期1-12,共12页
Fuzzy Systems and Mathematics
基金
国家自然科学基金资助项目(60775038)
浙江省自然科学基金资助项目(Y605389)