B L-代数中（∈,∈∨q）-模糊蕴涵滤子的重数

摘要

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.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.%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n-重蕴涵滤子的概念，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。