BL代数的(∈,∈∨q)-模糊滤子格

The Lattice of (∈,∈∨q)-fuzzy Filters in a Given BL-algebra

对BL代数的(∈,∈∨q)-模糊滤子理论作进一步深入研究。给出了(∈,∈∨q)-模糊滤子的若干新性质。建立了由BL代数上的一个模糊集生成的(∈,∈∨q)-模糊滤子的表示定理。证明了BL代数的全体(∈,∈∨q)-模糊滤子之集在偏序匚下构成一个完备的分配格。

In this paper, the （∈,∈∨q）-fuzzy filter theory in BL-algebras is further studied. Some new properties of （∈,∈∨q）-fuzzy filters are given. Representation theorem of （∈,∈∨q）-fuzzy filter which is generated by a fuzzy set is established. It is proved that the set consisting of all （∈,∈∨q）-fuzzy filters in a given BL-algebra, under the partial order , forms a complete distributive lattice.