摘要
由M·Sugeno提出的一种带参数λ的Fuzzy测度g_λ,被称为λ—Fuzzy测度,用这种测度产生的Fuzzy积分被称为λ—Fuzzy积分。本文研究λ-Fuzzy积分的收斂定理。主要结果有,如果被积函数f_n(x)依测度g_λ收斂于函数f(x),则f_n(x)关于g_λ测度的积分值也收斂于f(x)关于g_λ测度的积分值。对λ-Fuzzy测度g_λ,所得结果为g_λ(A-B)=g_λ(A)-g_λ(AB)/1+λg_λ(AB)其中A,B是б—代数κ中的任意两个集合,推广了原有的要求B(?)A的相应结果。
Let(X,K,g_λ)be the fuzzy measure space. There are three main resurts in this paper. First, the λ-fuzzy integral convergence theorem, i.e., if{f_n} converges to f in λ-fuzzy measure g_λ,then Secondly, if g_λ g_(λ_n) n=1, 2,…are λ-fuzzy measures and{g_(λ_n)} converges to g_λ with respect to any set in K, then。 Finally, if A and B are two arbitrary sets in K, then the λ-fuzzy measure of A-B is given by the following formula g_λ(A-B)=[g_λ(A)-g_λ(AB)]/1+λg_λ^-(AB)
出处
《暨南大学学报（自然科学与医学版）》
CAS
CSCD
1989年第3期1-7,共7页
Journal of Jinan University(Natural Science & Medicine Edition)
