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    高師機構典藏 NKNUIR > 理學院 > 數學系 > 期刊論文 >  Item 987654321/10374
    Please use this identifier to cite or link to this item: http://ir.nknu.edu.tw/ir/handle/987654321/10374


    題名: Fuzzy-Valued Integrals of Fuzzy-Valued Measurable Functions with Respect to Fuzzy-Valued Measures Based on Closed Intervals
    Authors: 吳憲忠
    Hsien-Chung Wu
    貢獻者: 數學系
    Keywords: Hausdorff metric;Closed fuzzy numbers;Fuzzy-valued measures;Fuzzy-valued measurable functions;Fuzzy-valued integrals
    Date: 1997-04-01
    Issue Date: 2010-11-09 14:23:39 (UTC+8)
    Abstract: In this paper we consider the fuzzy-valued integrals of fuzzy-valued measurable functions with respect to fuzzy-valued measures. We invoke the Hausdorff metric to define the metric between two fuzzy numbers, and then to consider the limit of a sequence of fuzzy numbers. In the meantime, we define the supremum and infimum of a sequence of fuzzy numbers. In this setting, the meaning of convergence of a sequence of fuzzy-valued integrals becomes clear; thus we can prove the Monotone Convergence Theorem, Fatou's Lemma and the Dominated Convergence Theorem. Furthermore, the α-level set of this fuzzy-valued integral is a closed interval whose end points are the classical Lebesgue integrals, which are more tractable.
    關聯: Fuzzy Sets and Systems / Volume 87, Issue 1, P.65–78
    Appears in Collections:[數學系] 期刊論文
    [數學系] 吳憲忠

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