巩增泰.非绝对模糊积分,绝对可积性与积分的绝对值不等式[J].数学研究及应用,2008,28(3):479~488 |
非绝对模糊积分,绝对可积性与积分的绝对值不等式 |
Nonabsolute Fuzzy Integrals, Absolute Integrability and Its Absolute Value Inequality |
投稿时间:2006-06-20 修订日期:2006-12-12 |
DOI:10.3770/j.issn:1000-341X.2008.03.004 |
中文关键词: 模糊数 模糊数值函数 绝对可积性. |
英文关键词:fuzzy numbers fuzzy-number-valued functions absolute integrability. |
基金项目:国家自然科学基金(No.10771171); 甘肃省教育厅科研基金(No.0601-20). |
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中文摘要: |
关于模糊数值函数的绝对可积性及对应的积分不等式,无论在何种绝对值意义下是值得讨论的. 本文借助于模糊数空间到具体的 Banach 空间上的嵌入定理和模糊非绝对积分的刻划定理, 讨论了模糊数值函数的绝对可积性及对应的积分不等式,得到了若干个充分必要条件, 并举出了一些反例. |
英文摘要: |
Absolute integrability and its absolute value inequality for fuzzy-number-valued functions are worth to be considered. In this paper, absolute integrability and its absolute value inequality for fuzzy-number-valued functions are discussed by means of the characteristic theorems of nonabsolute fuzzy integrals and the embedding theorem, i.e., the fuzzy number space can be embedded into a concrete Banach space. Several necessary and sufficient conditions and examples are given. |
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