基于可交换剩余格上的几类n-重模糊滤子及其性质  

The Structure of Several Kinds of n-fold Fuzzy Filter in the Residuated Lattice

作　　者：刘莉君[1,2] 

机构地区：[1]陕西理工大学数学与计算机科学学院,陕西汉中723001 [2]陕西师范大学数学与信息科学学院,陕西西安710062

出　　处：《模糊系统与数学》2018年第1期60-65,共6页Fuzzy Systems and Mathematics

基　　金：国家自然科学基金资助项目(11401357);陕西省教育厅专项科研项目(17JK0145);陕西理工大学科研基金重点资助项目(SLGKY16-02)

摘　　要：运用模糊集的方法和原理,在剩余格中引入了n-重模糊蕴涵滤子,n-重模糊极滤子和n-重模糊布尔滤子的概念,通过研究它们的特征及性质,证明了剩余格上这几类n-重模糊滤子之间的关系,获得了这几类模糊滤子之间相互等价的充要条件。研究结果进一步拓展了剩余格上的模糊滤子理论,并为其在代数逻辑及计算机信息处理等方面的应用奠定了理论基础。By using the principle and method of fuzzy sets, in this paper, the concept of n-fold fuzzy implicative filter, n-fold fuzzy fantastic filter and n-fold fuzzy boolean filter are introduced in residuated lattice. By studying their properties and characterizations, the relation among these n-fold fuzzy filter are discussed systematically. The results of the study further extend the fuzzy filter theory of the residuated lattice, It lays a theoretical foundation for the application of algebraic logic and computer information processing.

关 键 词：剩余格 模糊滤子 n-重模糊蕴涵滤子 n-重模糊极滤子 n-重模糊布尔滤子 

分 类 号：O159[理学—数学]