模糊σ-代数上的模糊数值测度及应用(Ⅱ):广义矢值测度的约当分解  

A Fuzzy NumberValued Measure on Fuzzy σ-algebra and Its Applications(Ⅱ): Jordan Decomposition of Signed Vector-valued Measure

作　　者：张忠旺[1] 

机构地区：[1]南开大学数学学院数学系

出　　处：《内蒙古师范大学学报（自然科学汉文版）》2005年第1期10-14,18,共6页Journal of Inner Mongolia Normal University(Natural Science Edition)

基　　金：中国民航总局民航教育教学研究基金(03-3-13)

摘　　要：设(X,A,μ)是一个全有限测度空间,H为由 A生成的模糊σ代数.通过计算 H中模糊子集的截集的测度,运用一维模糊数的嵌入定理,构造了一种定义在 H上取值于一维模糊数空间的测度,这种测度限制在 A上就是测度μ,并且这个测度继承了μ的可列可加性、下连续性、上连续性、自连续性等性质.作为应用之一,在合理定义了广义矢值测度后,得到了约当分解定理,并且这种广义矢值测度就是一个模糊数值测度.In the total finite measure space(X,A,μ) set of fuzzy subsets of X whose membership functions are measurable functions is a fuzzy σalgebra H.To measure fuzzy subsets in detail,a new measure is constructed.In this paper a fuzzy number-valued measure is defined on H.The fuzzy number-valued measure restricted on A is just the measure μ,and it has almost the same properties of μ.As one of applications,the Jordan decomposition theorem of a properly defined signed vector-valued measure is obtained,and the signed vector-valued measure is just a fuzzy number-valued measure.

关 键 词：模糊数 Σ-代数 测度空间 连续性 一维 嵌入定理 截集 数值 定义 合理 

分 类 号：N37[自然科学总论] O159[理学—数学]