关于生成L-Fuzzy子群

On Generating L-Fuzzy Subgroup

主要研究生成L -Fuzzy子群。首先引入生成L -Fuzzy子群的概念 ,给出了生成L -Fuzzy子群的代数刻画式 :[A] (x) =A(x) =∨ {[A(x1 )∨A(x1 ) - 1 ]∧…∧ [A(xn)∨A(xn- 1 ) ] ,x =x1 …xn}, x∈G。基于L -Fuzzy集上的Zadeh型映射和双诱导映射理论 ,深入地研究了生成L -Fuzzy子群的若干性质 ,得到L -Fuzzy正规子群A ,B的并A∪B的生成子群仍是L-Fuzzy正规子群 ,L -Fuzzy子集A的同态映象的生成子群 [( f ,φ) (A) ]等于L -Fuzzy子集A的生成子群的同态映象 (f ,φ) [A]等一系列颇有意义的结论。

The generating L-Fuzzy subgroups are mainly studied in this paper. The notion of generated L-Fuzzy subgroup is given. We introduce the algebra characterization formula of generating L-Fuzzy subgroup and study some basic properties of generating L-Fuzzy subgroups based on Zadeh’s mapping and bi-induced mapping theories. It is induced that the generating L-Fuzzy subgroup of the unit of two L-fuzzy normal subgroup is also L-fuzzy normal subgroup, and the generating L-fuzzy subgroup of the homomorphic image of L-fuzzy subset is equal to the homomorphic image of the generating L-fuzzy subgroup of L-fuzzy subset.