Geodesic
Fuzzy-valued integrals based on a constructive methodology
Applications of Mathematics, Tome 52 (2007) no. 1, pp. 1-23.

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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.
DOI : 10.1007/s10492-007-0001-x
Classification : 03E72, 28E10
Keywords: dominated convergence theorem; fuzzy number; fuzzy-valued function; fuzzy-valued integral; resolution identity 
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Wu, Hsien-Chung. Fuzzy-valued integrals based on a constructive methodology. Applications of Mathematics, Tome 52 (2007) no. 1, pp. 1-23. doi : 10.1007/s10492-007-0001-x. http://geodesic.mathdoc.fr/articles/10.1007/s10492-007-0001-x/

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