On the Generalized Hukuhara Nabla Differentiability of Fuzzy Functions on Time Scales via Characterization Theorem

TL;DR

This paper investigates the generalized Hukuhara nabla derivative for fuzzy functions on time scales, providing characterizations and extending previous results from real domains to time scales, including a generalized product rule.

Contribution

It introduces new characterizations of fuzzy functions' differentiability on time scales and extends the product rule to fuzzy number valued functions in this context.

Findings

Characterizations of generalized Hukuhara nabla differentiability via endpoint functions

Extension of differentiability results from real domain to time scales

Generalization of the product rule for fuzzy number valued functions

Abstract

In this paper, we provide a comprehensive investigation of the generalized Hukuhara nabla derivative for fuzzy functions on time scales. We establish some characterizations of generalized Hukuhara nabla differentiable fuzzy functions on time scales via the nabla differentiability of their endpoint functions. These characterizations complete and extend previous findings of fuzzy number valued functions from the real domain to those on time scales. Additionally, we generalize the product rule, previously proven for interval valued functions in the real case, to fuzzy number valued functions on time scales.