Alternative views on fuzzy numbers and their application to fuzzy differential equations

TL;DR

This paper introduces new concepts for fuzzy valued functions based on two parametric representations of alpha-level sets, explores their relation to fuzzy differential equations, and proves key existence and uniqueness theorems.

Contribution

It presents novel approaches to fuzzy differential equations using two parametric representations, expanding the theoretical framework and connecting with existing principles.

Findings

New concepts for fuzzy valued functions introduced

Existence and uniqueness theorems for fuzzy differential equations proved

Illustrative examples demonstrate the approaches

Abstract

We consider fuzzy valued functions from two parametric representations of $\alpha$-level sets. New concepts are introduced and compared with available notions. Following the two proposed approaches, we study fuzzy differential equations. Their relation with Zadeh's extension principle and the generalized Hukuhara derivative is discussed. Moreover, we prove existence and uniqueness theorems for fuzzy differential equations. Illustrative examples are given.