Toward calculus for functions with fuzzy inputs and outputs

Autor(es)

de Barros, Laecio Carvalho ; Esmi, Estevao ; Simoes, Francielle Santo Pedro ; Shahidi, Mina

• Tipo de documento: Artigo Científico
• Fonte: FUZZY SETS AND SYSTEMS; v. 517, p. 21-pg., 2025-10-01.

Resumo

This article presents a theory of differential and integral calculus for mapping between Banach spaces formed by subsets of fuzzy numbers called A-linearly correlated fuzzy numbers (R-F(A)), where both the domain and codomain are spaces composed of fuzzy numbers. This is one of the main contributions of this study from a theoretical point of view, as well-known approaches to fuzzy calculus in the literature typically deal with fuzzy number-valued functions defined on intervals of real numbers. Notions of differentiability and integrability based on complex functions are proposed. Moreover, we introduce the study of ordinary differential equations for which the solutions are functions R-F(A) -> R-F(A) or D subset of R -> R-F(A). For the latter case, we present an initial study of the solution and its phase portrait for two-dimensional differential equation systems. In particular, for the former case, we examine the Lotka-Volterra model and analyze its phase portrait. (AU)

• Processo FAPESP: 22/00196-1 - Equações diferenciais fuzzy com derivadas interativas em escalas temporais
• Beneficiário: Mina Shahidi
• Modalidade de apoio: Bolsas no Brasil - Pós-Doutorado
• Processo FAPESP: 20/09838-0 - BI0S - Brazilian Institute of Data Science
• Beneficiário: João Marcos Travassos Romano
• Modalidade de apoio: Auxílio à Pesquisa - Programa Centros de Pesquisa em Engenharia