Mathematics (Oct 2024)

Dini’s Theorem for Fuzzy Number-Valued Continuous Functions

  • Juan José Font,
  • Sergio Macario,
  • Manuel Sanchis

DOI
https://doi.org/10.3390/math12203209
Journal volume & issue
Vol. 12, no. 20
p. 3209

Abstract

Read online

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