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Fuzzy-valued integrals based on a constructive methodology

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Abstract

The procedures for constructing a fuzzy number and a fuzzy-valued function from a family of closed intervals and two families of real-valued functions, respectively, are proposed in this paper. The constructive methodology follows from the form of the well-known “Resolution Identity” (decomposition theorem) in fuzzy sets theory. The fuzzy-valued measure is also proposed by introducing the notion of convergence for a sequence of fuzzy numbers. Under this setting, we develop the fuzzy-valued integral of fuzzy-valued function with respect to fuzzy-valued measure. Finally, we provide a Dominated Convergence Theorem for fuzzy-valued integrals.

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  1. Department of Mathematics, National Kaohsiung Normal University, Kaohsiung, 802, Taiwan

    Hsien-Chung Wu

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  1. Hsien-Chung Wu
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Wu, HC. Fuzzy-valued integrals based on a constructive methodology. Appl Math 52, 1–23 (2007). https://doi.org/10.1007/s10492-007-0001-x

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  • DOI: https://doi.org/10.1007/s10492-007-0001-x

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