On the Analysis of Regularized Fuzzy Systems of Uncertain Differential Equations

This article analyzes a regularized set of fuzzy differential equations with respect to an uncertain parameter. We provide sufficient conditions for the correctness of a new regularization scheme. For the resulting family of regularized fuzzy differential equations, the following properties are anal...

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Bibliographic Details
Published in:Entropy (Basel, Switzerland) Switzerland), 2023-06, Vol.25 (7), p.1010
Main Authors: Martynyuk, Anatoliy, Stamov, Gani, Stamova, Ivanka, Martynyuk-Chernienko, Yulya
Format: Article
Language:English
Subjects:
Analysis
approximate solutions
Approximation
continuity
Differential equations
fuzzy differential equations
Fuzzy sets
Fuzzy systems
global solutions
Mathematical analysis
Parameter uncertainty
Regularization
regularization correctness
Stability criteria
successive approximation
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Summary:This article analyzes a regularized set of fuzzy differential equations with respect to an uncertain parameter. We provide sufficient conditions for the correctness of a new regularization scheme. For the resulting family of regularized fuzzy differential equations, the following properties are analyzed, and efficient criteria are proposed: successive approximations, continuity, global existence of solutions, existence of approximate solutions, existence of solutions in the autonomous case. In addition, we develop stability criteria for the regularized family of fuzzy differential equations on the basis of the comparison technique and the method of nonlinear integral inequalities. We expect that the derived results will inspire future research work in this direction.
ISSN:1099-4300
1099-4300
DOI:10.3390/e25071010