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

• Autoři: TRUONG VAN Tri; BOHNER Martin; GIREJKO Ewa; MALINOWSKA Agnieszka B; HOA Ngo Van
• Rok publikování: 2025
• Druh: Článek v odborném periodiku
• Časopis / Zdroj: Information Sciences
• Fakulta / Pracoviště MU: Přírodovědecká fakulta
• Citace: TRUONG VAN, Tri, Martin BOHNER, Ewa GIREJKO, Agnieszka B MALINOWSKA a Ngo Van HOA. Granular fuzzy calculus on time scales and its applications to fuzzy dynamic equations. Information Sciences. Elsevier Inc., 2025, roč. 690, February, s. 1-32. ISSN 0020-0255. Dostupné z: https://dx.doi.org/10.1016/j.ins.2024.121547.
• www: https://www.sciencedirect.com/science/article/pii/S0020025524014610
• Doi: http://dx.doi.org/10.1016/j.ins.2024.121547
• Klíčová slova: Fuzzy dynamic equations; Time scales calculus; Horizontal membership functions
• Popis: 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.

Související projekty

• Oscilační teorie na hybridních časových doménách s aplikacemi ve spektrální a maticové analýze