A new derivative concept for set-valued and fuzzy-valued functions. Differential and integral calculus in quasilinear metric spaces

Donal O'Regan

doi:10.1016/j.fss.2020.04.002

A new derivative concept for set-valued and fuzzy-valued functions. Differential and integral calculus in quasilinear metric spaces

Donal O'Regan

Mathematics

Constantin Brancusi University

Research output: Contribution to a Journal (Peer & Non Peer) › Article › peer-review

17 Citations (Scopus)

Abstract

The aim of this paper is to develop a differential calculus for functions with values in a quasilinear metric space. Using only the metric on a quasilinear metric space and without using the Hukuhara difference, a new concept of derivative is introduced for functions with values in a quasilinear metric space. This new derivative concept generalizes known concepts of derivatives for set-valued and fuzzy value functions. (C) 2020 Elsevier B.V. All rights reserved.

Original language	English (Ireland)
Pages (from-to)	75-110
Number of pages	36
Journal	Fuzzy Sets And Systems
Volume	404
DOIs	https://doi.org/10.1016/j.fss.2020.04.002
Publication status	Published - 1 Feb 2021

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Authors
Lupulescu, V,O'Regan, D

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10.1016/j.fss.2020.04.002

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abstract = "The aim of this paper is to develop a differential calculus for functions with values in a quasilinear metric space. Using only the metric on a quasilinear metric space and without using the Hukuhara difference, a new concept of derivative is introduced for functions with values in a quasilinear metric space. This new derivative concept generalizes known concepts of derivatives for set-valued and fuzzy value functions. (C) 2020 Elsevier B.V. All rights reserved.",

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AB - The aim of this paper is to develop a differential calculus for functions with values in a quasilinear metric space. Using only the metric on a quasilinear metric space and without using the Hukuhara difference, a new concept of derivative is introduced for functions with values in a quasilinear metric space. This new derivative concept generalizes known concepts of derivatives for set-valued and fuzzy value functions. (C) 2020 Elsevier B.V. All rights reserved.

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A new derivative concept for set-valued and fuzzy-valued functions. Differential and integral calculus in quasilinear metric spaces

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