Approximate Limit, Approximate Derivative, and Approximate Integral for Fuzzy-Number-Valued Functions

Chao Ma, Zengtai Gong and Yabin Shao

Journal of Mathematics, 2026, vol. 2026, 1-18

Abstract: This paper introduces the concepts of approximate limit, approximate continuity, and approximate derivatives for fuzzy-number-valued functions and examines their fundamental properties. Also, the relationships between approximate limit, approximate derivative of fuzzy-number-valued functions, and their representations of λ-level sets are investigated. In addition, based on the approximate limit and approximate derivative of fuzzy-number-valued functions, we define approximate integrals and strongly approximate integrals of fuzzy-number-valued functions. Furthermore, the strongly generalized approximate absolute continuity ACGap∗ of fuzzy-number-valued functions is proposed. By the characterization of properties of ACGap∗, some characteristics of the primitive of strongly approximately integrable fuzzy-number-valued functions are studied. Finally, the controlled convergence theorem for the strongly approximate integral is established.

Date: 2026
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jjmath:9679908

DOI: 10.1155/jom/9679908

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