A general framework for level continuous fuzzy-valued functions

TL;DR

This paper introduces a comprehensive framework for level continuous fuzzy-valued functions by embedding them into a product space of real-valued functions with specific continuity and monotonicity properties.

Contribution

It provides a novel general setting for analyzing level continuous fuzzy-valued functions through an embedding into structured function spaces.

Findings

Establishes a new embedding approach for fuzzy-valued functions.

Characterizes level continuity via properties of real-valued functions.

Lays groundwork for further analysis of fuzzy functions in structured spaces.

Abstract

In this paper we provide a general setting to deal with level continuous fuzzy-valued functions. Namely, we embed such functions into a product of spaces of real-valued functions of two variables satisfying certain types of left-continuity, right-continuity and monotonicity.