生成Fuzzy子群

Generating Fuzzy Subgroups

群X上含Fuzzy子集μ的最小Fuzzy子群称是μ的生成Fuzzy子群,记为[μ],本文一方面从解析要求出发给出了从μ生成[μ]的生成公式,另一方面又蛤出了用对水平集集{μ_λ}的等价分类来直接构成[μ]的过程,还讨论了值城[μ](X)和μ(X)之间的各种内在联系,以及水平集[μ_λ]和[μ]_λ之间的关系。

The X is a group, A fuzzy subgroup ω on X is called a fuzzy subgroup generated by a fuzzy subset μ on X, if the ω is the smallset fuzzy subgroup containing μ on X, We denote ω=[μ]. The main results in this paper are as follows: (1) The generating formular from μ to [μ] is given. (2) We use the λ-level sets of μ to construct the [μ]. (3) Some properties about the left limit point and left isolated point for [μ](X) and μ(X) are discussed. (4) The relation between the λ-level sets [μ_λ] and [μ]_λ is discussed.