Jackson-type approximation for fuzzy-valued functions by means of trapezoidal functions

TL;DR

This paper introduces new Jackson-type approximation results for continuous fuzzy-number-valued functions, utilizing innovative techniques from Interval Analysis to improve existing approximation methods.

Contribution

It presents novel approximation results for fuzzy functions using alternative Interval Analysis techniques, addressing limitations of previous methods.

Findings

Improved approximation bounds for fuzzy functions.

Application of gH-difference and generalized difference in approximation.

Enhanced accuracy over previous Jackson-type results.

Abstract

In this paper we provide new several Jackson-type approximations results for continuous fuzzy-number-valued functions which improve several previous ones. We use alternative techniques adapted from Interval Analysis which rely on the gH-difference (which might not exist) and the generalized difference (which might lack the cancellation law ) of fuzzy numbers.