"Granular Fuzzy Calculus on Time Scales and its Applications to Fuzzy D" by Tri Truong, Martin Bohner et al.
 

Granular Fuzzy Calculus on Time Scales and its Applications to Fuzzy Dynamic Equations

Abstract

This paper introduces the foundational theory of fuzzy calculus on time scales, utilizing granular arithmetic operations between fuzzy intervals. These operations are developed based on the concept of the horizontal membership function (HMF), which is applied in multidimensional fuzzy arithmetic (MFA). Furthermore, the paper explores the existence of a unique solution and the continuous dependence of the solution to fuzzy dynamic equations on initial data, employing the Banach fixed-point theorem under a new metric for fuzzy functions in time scales involving the generalized exponential function. Finally, to highlight the practical significance of these results and their potential applications, the paper presents mathematical models relevant to nuclear physics and biology.

Department(s)

Mathematics and Statistics

Comments

Grantová Agentura České Republiky, Grant GA23–05242S

Keywords and Phrases

Fuzzy dynamic equations; Horizontal membership functions; Time scales calculus

International Standard Serial Number (ISSN)

0020-0255

Document Type

Article - Journal

Document Version

Citation

File Type

text

Language(s)

English

Rights

© 2025 Elsevier, All rights reserved.

Publication Date

01 Feb 2025

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