BL代数的区间值(∈,∈∨q)-模糊滤子理论

Theory of interval valued (∈,∈∨ q)-fuzzy filters in BL-algebras

研究了BL代数的区间值(∈,∈∨q)-模糊滤子理论。在BL代数中引入区间值(∈,∈∨q)-模糊对合滤子和区间值(∈,∈∨q)-模糊结合滤子两类新概念,获得了它们的几个等价刻画。详细讨论了BL代数中各类区间值(∈,∈∨q)-模糊滤子间的关系,证明了一个区间值模糊集为区间值(∈,∈∨q)-模糊布尔(关联)滤子当且仅当它既是区间值(∈,∈∨q)-模糊正关联滤子又是区间值(∈,∈∨q)-模糊对合滤子的结论。

The theory of interval valued（ ∈,∈∨ q）-fuzzy filters in BL-algebras is studied systematically. Firstly,two notions of interval valued（ ∈,∈∨ q）-fuzzy involution filters and interval valued（ ∈,∈∨ q）-fuzzy associative filters are introduced and some characterizations of them are obtained. Secondly,the relations among all kinds of interval valued（ ∈,∈∨ q）-fuzzy filters are discussed. It is proved that an interval valued fuzzy set is an interval valued（ ∈,∈∨ q）-fuzzy Boolean（ implicative） filter if and only if it is both an interval valued（ ∈,∈∨ q）-fuzzy positive implicative and an interval valued（ ∈,∈∨ q）-fuzzy involution filter.