BL-代数的(∈,∈∨q)-模糊素滤子

(∈,∈∨q)-fuzzy prime filters in BL-algebras

利用模糊拓扑中模糊点重于和属于模糊集的概念研究模糊逻辑代数结构,在BL-代数中引入(∈,∈∨q)-模糊素滤子的概念并研究其性质.获得了BL-代数中(∈,∈∨q)-模糊素滤子的若干等价刻画,讨论了BL-代数中素滤子与(∈,∈∨q)-模糊素滤子间的关系,考察了BL-代数中(∈,∈∨q)-模糊素滤子的同态性质,证明了BL-代数中(∈,∈∨q)-模糊素滤子的同构(同态)像(原像)仍为(∈,∈∨q)-模糊素滤子这一结论.

Based on the fuzzy points quasi coincide with and belong to fuzzy sets in fuzzy topology, structures of fuzzy logical algebras are studied. The concept of （∈,∈Vq）-fuzzy prime filters in BL-algebras is introduced and its properties are studied. Some equivalent characterizations of （∈, ∈Vq）-fuzzy prime filters in BL-algebras are obtained. Relations between prime filters and （∈,∈Vq）-fuzzy prime filters in BL-algebras are discussed. The homomorphic properties of （∈,∈Vq）-fuzzy prime filters in BL-algebras are investigated. It is proved that the isomorphic （resp. homomorphic） image （resp. inverse image） of a （∈,∈Vq）-fuzzy prime filter in BL-algebras is also a （∈,∈Vq）-fuzzy prime filter.