Some results on generalized Hukuhara diamond-{\alpha} derivative and integral of fuzzy valued functions and on time scales

TL;DR

This paper introduces a generalized Hukuhara diamond-alpha integral for fuzzy functions on time scales, explores its fundamental properties, and links it with differentiation, advancing fuzzy calculus on dynamic domains.

Contribution

It defines a new generalized integral for fuzzy functions on time scales and establishes its relationship with differentiation, expanding the theoretical framework of fuzzy calculus.

Findings

Defined the generalized Hukuhara diamond-alpha integral for fuzzy functions.

Established fundamental properties of the new integral.

Linked diamond-alpha differentiation with the integral on time scales.

Abstract

In this paper, we define generalized Hukuhara diamond-alpha integral for fuzzy functions on time scales and obtain some of its fundamental properties and also we establish the relationship between diamond-alpha differentiation and integration.