2020•Frontiers in artificial intelligence and applicationsOpen access

Study on Generalized Directional Differentiability Problems of Fuzzy Mappings

Yue Bao, Tingting Li, Linfen Zhang

Abstract

This paper discusses the gH-directional differentiability of fuzzy mappings, and proposes the concept of gH-directional differentiability of fuzzy mappings. Based on the concept of gH-directional differentiability of interval-valued mappings and its related properties, two properties of gH-directional differentiability fuzzy mappings are proposed. At the same time, the relation between gH-differentiability and gH-directional differentiability for a fuzzy mapping is discussed, and it is proved that both gH-derivative and gH-partial derivative are directional derivatives of fuzzy mappings in the direction of the coordinate axis.

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Key concepts: Differentiable function, Directional derivative, Fuzzy logic, Mathematics, Pure mathematics, Applied mathematics, Mathematical analysis, Computer science