Granular fuzzy calculus on time scales and its applications to fuzzy dynamic equations

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Authors	TRUONG VAN Tri BOHNER Martin GIREJKO Ewa MALINOWSKA Agnieszka B HOA Ngo Van
Year of publication	2025
Type	Article in Periodical
Magazine / Source	Information Sciences
MU Faculty or unit	Faculty of Science
Citation
web	https://www.sciencedirect.com/science/article/pii/S0020025524014610
Doi	http://dx.doi.org/10.1016/j.ins.2024.121547
Keywords	Fuzzy dynamic equations; Time scales calculus; Horizontal membership functions
Description	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.
Related projects:	Oscillation theory on hybrid time domains with applications in spectral and matrix analysis