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.
Recommended Citation
T. Truong et al., "Granular Fuzzy Calculus on Time Scales and its Applications to Fuzzy Dynamic Equations," Information Sciences, vol. 690, article no. 121547, Elsevier, Feb 2025.
The definitive version is available at https://doi.org/10.1016/j.ins.2024.121547
Department(s)
Mathematics and Statistics
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
Comments
Grantová Agentura České Republiky, Grant GA23–05242S