# Basic trigonometric Korovkin approximation for fuzzy valued functions of two variables

## TL;DR

This paper establishes a fundamental approximation theorem for fuzzy-valued functions of two variables using trigonometric methods, introduces double level Fourier series, and explores their convergence via Cesàro and Abel summation techniques.

## Contribution

It extends Korovkin approximation theory to fuzzy functions of two variables and develops new Fourier series methods for their approximation.

## Key findings

- Proved the basic trigonometric Korovkin approximation theorem for fuzzy functions.
- Introduced double level Fourier series for fuzzy functions.
- Analyzed convergence using Cesàro and Abel summation methods.

## Abstract

We prove the basic trigonometric Korovkin approximation theorem for fuzzy valued functions of two variables and verify the approximation by the help of fuzzy modulus of continuity. Also, we introduce double level Fourier series of fuzzy valued functions and investigate corresponding approximation through the use of Ces\`{a}ro and Abel methods of summation of infinite series.