剩余格上的几类n-重模糊滤子  

Several Types of n-fold Fuzzy Filters on Residuated Lattices

作　　者：彭家寅[1] PENG Jia-yin(School of Mathematics and Information Science,Neijiang Normal University,Neiiiang 641199,China)

机构地区：[1]内江师范学院数学与信息科学学院,四川内江641199

出　　处：《模糊系统与数学》2020年第5期17-30,共14页Fuzzy Systems and Mathematics

基　　金：教育部数学与应用数学专业综合改革项目(ZG0464);四川省科技厅重点科技项目(2006J13-035);四川省数学与成用数学专业综合改革项目(01249);四川省解析儿何精品开放课程、精品资源共享课;国家自然科学基金资助项目(11071178);内江师范学院应用数学重点学科项目;四川省教育厅和内江师范学院卓越中学教师协同培养计划项目。

摘　　要：将模糊集应用于剩余格的n-重滤子理论中,初步建立剩余格的n-重模糊理想理论。在剩余格上引入了n-重模糊蕴涵滤子、n-重模糊正蕴含滤子、n-重模糊MV滤子和n-重模糊MTL滤子的概念。通过研究它们的性质,给出了它们的一系列刻画定理,应用这些刻画讨论了这些n-重模糊滤子的扩展定理。研究结果进一步拓展了剩余格的滤子理论,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。Appling the fuzzy set to the n-fold filter theory of residuated lattices,the n-fold fuzzy filter theory on residuated lattices is preliminary established.The notions of n-fold fuzzy implicative filters,n-fold fuzzy positive implicative filters,n-fold fuzzy MV-filters and n-fold fuzzy MTL-filters are introduced on residuated lattices.By studying their properties,a series of their characterization theorems are given,and the extension theorems of these n-fold fuzzy filters are discussed by these characterizations.The results of the study further extend the filter theory of residuated lattices,it lays a theoretical foundations for the application of algebraic logic and computer information processing.

关 键 词：剩余格 滤子 n-重模糊蕴涵滤子 n-重模糊正蕴涵滤子 n-重模糊MV滤子 n-重模糊MTL滤子 

分 类 号：O159[理学—数学]