效应代数的不分明化滤子  

Fuzzifying Filters of Effect Algebras

作　　者：彭家寅[1] PENG Jia-yin(Key Laboratory of Numerical Simulation of Sichuan Provice // School of Mathematics and Information Science Neijiang Normal University, Neijiang 641112, Chin)

机构地区：[1]四川省高等学校数值仿真重点实验室//内江师范学院数学与信息科学学院

出　　处：《数学的实践与认识》2018年第6期196-203,共8页Mathematics in Practice and Theory

基　　金：四川省科技厅重点科技项目(2006J13-035);四川省教育厅重点实验室专项(2006ZD050)

摘　　要：在连续格值逻辑的语义框架下，以Lukasiewicz蕴涵算子为工具定义了连续格值逻辑上的效应代数之不分明化滤子的概念，将用G．Cantor集合理论所刻画的效应代数的滤子概念在连续格值谓词演算下给予重新刻画，给出了不分明滤子的几个等价描述和性质．在两个经典效应代数的效应态射与效应同构意义下，讨论了这种不分明滤子的像和前像问题．Under the semantic frame of continuous lattice valued logic, the concept of fuzzi- fying filters of effect algebras on continuous lattice valued logic are defined using Lukasiewicz implication operator as tool. In effect algebra, the concept of filter have ever been depicted by G.Cantor＇s set theory, but now, it will be redefined by a unary predicate calculus on continuous lattice valued logic, the equivalence descriptions and propertied of fuzzifying filters are given. In the sense of effect morphism and effect isomorphism between two classical effect algebras, the image and preimage of this kind of fuzzifying filters are discussed.

关 键 词：效应代数 连续值逻辑 LUKASIEWICZ蕴涵算子 不分明滤子 效应态射(同构) 

分 类 号：O413.1[理学—理论物理]