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Generalized Differentiability of Fuzzy-Valued Convex Functions and Applications
(Springer Science and Business Media Deutschland GmbH, 2023) Allahviranloo, T.; Baloochshahryari, M.R.; Sedaghatfar, O.
In this paper, the concept of generalized differentiability and level-wise generalized Hukuhara differentiability are extended for one-dimensional fuzzy-valued convex functions from R into E. In addition, the properties of generalized differentiability and characterization for fuzzy-valued convex functions in terms of generalized differentiability and the fundamental theorem of calculus generalized differential and fuzzy integral are presented in detail. Moreover, the concepts of generalized subgradient and generalized subdifferential in terms of level-wise generalized Hukuhara differentiability are extended for fuzzy-valued convex functions. Finally, by using their properties, the convex fuzzy optimization for the one-dimensional fuzzy-valued convex functions is discussed. © 2023, The Author(s), under exclusive license to Springer Nature Switzerland AG.