Dini’s Theorem for Fuzzy Number-Valued Continuous Functions

Juan José Font (), Sergio Macario and Manuel Sanchis
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Juan José Font: Institut Universitari de Matemàtiques i Aplicacions de Castelló (IMAC), Universitat Jaume I, Campus del Riu Sec. s/n, 12071 Castelló, Spain
Sergio Macario: Institut Universitari de Matemàtiques i Aplicacions de Castelló (IMAC), Universitat Jaume I, Campus del Riu Sec. s/n, 12071 Castelló, Spain
Manuel Sanchis: Institut Universitari de Matemàtiques i Aplicacions de Castelló (IMAC), Universitat Jaume I, Campus del Riu Sec. s/n, 12071 Castelló, Spain

Mathematics, 2024, vol. 12, issue 20, 1-13

Abstract: This work aims to provide several versions of Dini’s theorem for fuzzy number-valued continuous functions defined on a compact set K . In this context, there is a wide variety of possibilities since, unlike the real line, we can consider different topologies and orders on the set of fuzzy numbers. For example, we will show that the fuzzy Dini’s theorem holds for the usual partial orders and the most commonly used topologies but does not hold for all orders in general.

Keywords: Dini’s theorem; pointwise and uniform convergence; fuzzy-valued functions (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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