A Complete Characterization Theorem for Fuzzy Differentiability on Time Scales

TL;DR

This paper provides a comprehensive characterization theorem for fuzzy differentiability on arbitrary time scales, unifying and extending previous results in fuzzy calculus and delta calculus.

Contribution

It introduces a complete and unified theorem for fuzzy differentiability on time scales, improving upon and covering cases missed by earlier research.

Findings

Unified characterization of fuzzy differentiability

Addresses limitations in previous results

Covers a wide range of differentiability behaviors

Abstract

This paper investigates the generalized Hukuhara differentiability of fuzzy number-valued functions on arbitrary time scales using delta calculus. By carefully examining and improving existing results, we develop a unified and complete characterization theorem that covers a wide range of differentiability behaviors, including some cases that were previously missed. Our approach addresses important limitations and redundancies in earlier work, providing a clearer and more flexible understanding of fuzzy differentiability.