The generalized fuzzy derivative is interactive

Author(s)

Wasques, Vinicius F. ^[1] ; Esmi, Estevao ^[1] ; Barros, Laecio C. ^[1] ; Sussner, Peter ^[1]

Affiliation

^[1] Univ Estadual Campinas, Dept Appl Math, BR-13083859 Campinas, SP - Brazil

• Document type: Journal article
• Source: INFORMATION SCIENCES; v. 519, p. 93-109, MAY 2020.
• Web of Science Citations: 0

Abstract

In this article, we prove that the generalized difference between A, B is an element of R-Fc, i.e., fuzzy numbers with continuous endpoints, is given by an interactive difference. To be more precise, we construct a certain joint possibility distribution 1 such that the generalized difference coincides with the sup-1 extension of the subtraction. As an immediate consequence, we have that every notion of difference between A, B is an element of R-Fc, that has so far appeared in the literature, can be derived from a sup-J extension for some particular choice of J. Moreover, we show that both the generalized and the generalized Hukuhara derivative of a function f : R -> R-Fc at x is an element of R can be expressed as the limit for h -> 0 of a difference quotient, where the difference is an interactive difference for each h. For short, we say that the generalized (as well as the generalized Hukuhara) difference is interactive. (C) 2020 Elsevier Inc. All rights reserved. (AU)

• FAPESP's process: 18/13657-1 - Some lattice computing approaches towards computational intelligence, image processing and analysis
• Grantee: Peter Sussner
• Support Opportunities: Regular Research Grants
• FAPESP's process: 16/26040-7 - Differential and integral calculus based on arithmetic of interactive fuzzy numbers
• Grantee: Estevão Esmi Laureano
• Support Opportunities: Regular Research Grants