On the resummation of series of fuzzy numbers via generalized Dirichlet and generalized factorial series

TL;DR

This paper develops new summation methods for series of fuzzy numbers using generalized Dirichlet and factorial series, establishing conditions for convergence and introducing level Fourier series for fuzzy functions.

Contribution

It introduces semicontinuous summation techniques for fuzzy number series and defines level Fourier series, expanding the analytical tools for fuzzy analysis.

Findings

Tauberian conditions for convergence of fuzzy series

Summation methods via generalized Dirichlet and factorial series

Results on summation of level Fourier series

Abstract

We introduce semicontinuous summation methods for series of fuzzy numbers and give Tauberian conditions under which summation of a series of fuzzy numbers via generalized Dirichlet series and via generalized factorial series implies its convergence. Besides, we define the concept of level Fourier series of fuzzy valued functions and obtain results concerning the summation of level Fourier series.