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The generalized fuzzy derivative is interactive

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Autor(es):
Wasques, Vinicius F. [1] ; Esmi, Estevao [1] ; Barros, Laecio C. [1] ; Sussner, Peter [1]
Número total de Autores: 4
Afiliação do(s) autor(es):
[1] Univ Estadual Campinas, Dept Appl Math, BR-13083859 Campinas, SP - Brazil
Número total de Afiliações: 1
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
Linha de fomento: Auxílio à Pesquisa - Regular
Processo FAPESP: 16/26040-7 - Cálculo diferencial e integral baseado aritmética de números fuzzy interativos
Beneficiário:Estevão Esmi Laureano
Linha de fomento: Auxílio à Pesquisa - Regular