This work is motivated by the fact that very little is known about the fuzzy variational inequalities controlled differential equation problems in finite dimension real numeral spaces, which are studied more difficult than differential variational inequalities. It is interesting and challenging that how to solve the fuzzy variational inequalities in a fuzzy environment. The purpose of this paper is to introduce and study a class of new fuzzy parametric variational inequality controlled initial-value differential equation problems in finite dimensional Euclidean spaces. We establish existence of Carathéodory weak solutions for the fuzzy parametric variational inequality controlled initial-value differential equation problem under suitable conditions. Further, using method of centres with entropic regularization techniques and time-stepping methods, we emerge convergence analysis on iterative process for solving the initial-value differential fuzzy parametric inequalities. Finally, we give some open questions for our future research.

中文翻译：

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有限维空间中一类模糊参数变分不等式控制的微分方程问题

这项工作的动机是，对有限维实数空间中的模糊变分不等式控制的微分方程问题了解甚少，而对它们的研究比微分变分不等式要难得多。如何解决模糊环境中的模糊变分不等式是有趣且具有挑战性的。本文的目的是介绍和研究有限维欧氏空间中的一类新的模糊参数变分不等式控制的初值微分方程问题。我们建立了在适当条件下针对模糊参数变分不等式控制的初值微分方程问题的Carathéodory弱解的存在。此外，使用带有熵正则化技术的中心方法和时间步长方法，我们提出了迭代过程的收敛性分析，以解决初值差分模糊参数不等式。最后，我们对我们的未来研究提出了一些未解决的问题。