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

J 2025

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

TRUONG VAN, Tri; Martin BOHNER; Ewa GIREJKO; Agnieszka B MALINOWSKA; Ngo Van HOA et. al.

Basic information

Original name

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

Authors

TRUONG VAN, Tri (704 Viet Nam, belonging to the institution); Martin BOHNER; Ewa GIREJKO; Agnieszka B MALINOWSKA and Ngo Van HOA

Edition

Information Sciences, Elsevier Inc. 2025, 0020-0255

Other information

Language

English

Type of outcome

Article in a journal

Field of Study

10101 Pure mathematics

Country of publisher

United States of America

Confidentiality degree

is not subject to a state or trade secret

References:

URL

Impact factor

Impact factor: 6.800 in 2024

Organization unit

Faculty of Science

DOI

https://doi.org/10.1016/j.ins.2024.121547

UT WoS

001369188400001

EID Scopus

2-s2.0-85207082239

Keywords in English

Fuzzy dynamic equations; Time scales calculus; Horizontal membership functions

Abstract

In the original language

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.

Links

GA23-05242S, research and development project

Name: Oscilační teorie na hybridních časových doménách s aplikacemi ve spektrální teorii a maticové analýze

Investor: Czech Science Foundation, Oscillation theory on hybrid time domains with applications in spectral and matrix analysis

Cite

TRUONG VAN, Tri; Martin BOHNER; Ewa GIREJKO; Agnieszka B MALINOWSKA and Ngo Van HOA. Granular fuzzy calculus on time scales and its applications to fuzzy dynamic equations. Information Sciences. Elsevier Inc., 2025, vol. 690, February, p. 1-32. ISSN 0020-0255. Available from: https://doi.org/10.1016/j.ins.2024.121547.

@article{2471520,
   author = {Truong Van, Tri and Bohner, Martin and Girejko, Ewa and Malinowska, Agnieszka B and Hoa, Ngo Van},
   article_number = {February},
   doi = {https://doi.org/10.1016/j.ins.2024.121547},
   keywords = {Fuzzy dynamic equations; Time scales calculus; Horizontal membership functions},
   language = {eng},
   issn = {0020-0255},
   journal = {Information Sciences},
   title = {Granular fuzzy calculus on time scales and its applications to fuzzy dynamic equations},
   url = {https://www.sciencedirect.com/science/article/pii/S0020025524014610},
   volume = {690},
   year = {2025}
}

TY  - JOUR
ID  - 2471520
AU  - Truong Van, Tri - Bohner, Martin - Girejko, Ewa - Malinowska, Agnieszka B - Hoa, Ngo Van
PY  - 2025
TI  - Granular fuzzy calculus on time scales and its applications to fuzzy dynamic equations
JF  - Information Sciences
VL  - 690
IS  - February
SP  - 1-32
EP  - 1-32
PB  - Elsevier Inc.
SN  - 00200255
KW  - Fuzzy dynamic equations
KW  - Time scales calculus
KW  - Horizontal membership functions
UR  - https://www.sciencedirect.com/science/article/pii/S0020025524014610
N2  - 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.
ER  -

TRUONG VAN, Tri; Martin BOHNER; Ewa GIREJKO; Agnieszka B MALINOWSKA and Ngo Van HOA. Granular fuzzy calculus on time scales and its applications to fuzzy dynamic equations. \textit{Information Sciences}. Elsevier Inc., 2025, vol.~690, February, p.~1-32. ISSN~0020-0255. Available from: https://doi.org/10.1016/j.ins.2024.121547.

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