| 一类模糊测度的扩张 |
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| 引用本文： | 宋仁明.一类模糊测度的扩张[J].河北大学学报(自然科学版),1984(2). |
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| 作者姓名： | 宋仁明 |
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| 作者单位： | 河北大学数学系 |
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| 摘 要： | 本文引进了关于某经典测度m连续的模糊测度的概念,证明如下的扩张定理: 定理:设X是一个集合,F是X上的一个域,m是定义在σ(F)上的一个全有限的测度。那么任意一个定义在F上且关于m连续的模糊测度可以唯一地扩张到σ(F)上。
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The Extensions of a Class of Fuzzy Measures |
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| Abstract: | In this paper, we introduce a class F fuzzy measures which are continuous with respect to a classical measure, and prove the following extension theorem.
Theorem. Suppose that X is a set, F is a field on X, and that m is a totally finite measure defined on o(F). Then any fuzzy measure which is defined on F and continuous with respect to m can be extended uniquely to 0(F). |
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