BL-代数中(∈,∈∨q)-模糊蕴涵滤子的重数
Foldnessof(∈,∈∨q)-fuzzyimplicativefiltersinBL-algebars
-
摘要:利用模糊点与模糊集之重于关系,在BL-代数中引入了(∈,∈∨q)-模糊滤子的概念,推广了经典的模糊n-重蕴涵滤子,给出了(∈,∈∨q)-模糊n-重蕴涵滤子的一些刻画. 研究了(∈,∈∨q)-模糊蕴涵滤子与(∈,∈∨q)-模糊n-重蕴涵滤子的关系、(∈,∈∨q)-模糊n-重蕴涵滤子与(∈,∈∨q)-模糊(n+1)-重蕴涵滤子的关系. 提出门限模糊n-重蕴涵滤子的概念,以此获得了非平凡的经典模糊n-重蕴涵滤子、非平凡的(∈,∈∨q)-模糊n-重蕴涵滤子,研究了门限模糊n-重蕴涵滤子和(∈,∈∨q)-模糊n-重蕴涵滤子的性质.Abstract:By using the concept of quasi-coincidence of a fuzzy point with a fuzzy set, the notion of(∈,∈∨q)-fuzzy n-fold implicative filters in BL-algebras which is a generalization of ordinary fuzzy n-fold implicative filters, is defined, and several characterizations of(∈,∈∨q)-fuzzy n-fold implicative filters are given. The relation between(∈,∈∨q)-fuzzy filters and(∈,∈∨q)-fuzzy n-fold implicative filters and the relation between(∈,∈∨q)-fuzzy n-fold implicative filters and(∈,∈∨q)-fuzzy(n+1)-fold implicative filters are investigated. The concept of a fuzzy n-fold implicative filters with thresholds in BL-algebras is proposed. The acceptable nontrivial concepts obtained in this manner were the ordinary fuzzy n-fold implicative filters and(∈,∈∨q)-fuzzy n-fold implicative filters. The extension properties for fuzzy n-fold implicative filters with thresholds and(∈,∈∨q)-fuzzy n-fold implicative filters are established.
下载: