2016
DOI: 10.2298/aadm160311004f
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A Hukuhara approach to the study of hybrid fuzzy systems on time scales

Abstract: We introduce a new approach to study the practical stability of hybrid fuzzy systems on time scales in the Lyapunov sense. Our method is based on the delta-Hukuhara derivative for fuzzy valued functions and allow us to obtain new interesting stability criteria. We also show the validity of the results of [M. Sambandham: Hybrid fuzzy systems on time scales, Dynam. Systems Appl. 12 (2003), no. 1-2, 217-227], by embedding the space of all fuzzy subsets into a suitable Banach space.Comment: This is a preprint of a… Show more

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Cited by 11 publications
(4 citation statements)
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“…Salahshour et al [12] apply the technique of fuzzy Laplace transforms and solved some types of FFDEs based on the Riemann-Liouville fuzzy derivative. Based on the delta-Hukuhara derivative for fuzzy valued functions, Fard et al established stability criteria for hybrid fuzzy systems on time scales in the Lyapunov sense [13]. In [14], Fard et al solve a class of fuzzy fractional optimal control problems, where the coefficients of the system can be time-dependent.…”
Section: Introductionmentioning
confidence: 99%
“…Salahshour et al [12] apply the technique of fuzzy Laplace transforms and solved some types of FFDEs based on the Riemann-Liouville fuzzy derivative. Based on the delta-Hukuhara derivative for fuzzy valued functions, Fard et al established stability criteria for hybrid fuzzy systems on time scales in the Lyapunov sense [13]. In [14], Fard et al solve a class of fuzzy fractional optimal control problems, where the coefficients of the system can be time-dependent.…”
Section: Introductionmentioning
confidence: 99%
“…Also, the authors in Leelavathi et al (2019) have studied the existence and uniqueness of solutions to fuzzy nabla initial value problems on time scales. For some related researches, see also Fard et al (2016), Hong et al (2020) and Zhao et al (2017).…”
Section: Introductionmentioning
confidence: 99%
“…The aim is to unify various definitions and results from the theories of discrete and continuous dynamical systems, and to extend them to more general classes of dynamical systems. It has undergone tremendous expansion and development on various aspects by several authors over the past three decades: see, e.g., [3,4,5,6,18,19,35,37,39,40,41].…”
mentioning
confidence: 99%