The generalized fuzzy derivative is interactive

Autor(es)

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

Afiliação do(s) autor(es)

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

• Tipo de documento: Artigo Científico
• Fonte: INFORMATION SCIENCES; v. 519, p. 93-109, MAY 2020.
• Citações Web of Science: 0

Resumo

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)

• Processo FAPESP: 18/13657-1 - Algumas abordagens de computação em reticulados a inteligência computacional, processamento e análise de imagens
• Beneficiário: Peter Sussner
• Modalidade de apoio: Auxílio à Pesquisa - Regular
• Processo FAPESP: 16/26040-7 - Cálculo diferencial e integral baseado aritmética de números fuzzy interativos
• Beneficiário: Estevão Esmi Laureano
• Modalidade de apoio: Auxílio à Pesquisa - Regular