The aim of this paper is to establish some new results on the Levitin–Polyak well-posedness (in short, LP well-posedness) to a new class of the controlled systems of fuzzy mixed quasi-hemivariational inequalities of the Minty type (in short, FMQHI). First, we introduce a new class of the controlled systems for FMQHI. Then, we show, under suitable conditions, the equivalence between the LP well-posedness and existence of solution to this problem. Further, results on metric characterization of the LP well-posedness and the LP well-posedness in the generalized sense for such problem in terms of the behavior of the approximate solution set are provided. Finally, we introduce a new class of the gap function for controlled systems of FMQHI and use it to study criterion of the LP well-posedness for controlled systems of FMQHI. The results presented in the paper are new.

本文的目的是建立关于Levitin-Polyak适定性（简称LP适定性）的新结果，以建立一类新的Minty型混合混合半拟不等式不等式（简而言之）的控制系统。 ，FMQHI）。首先，我们为FMQHI引入了一类新的受控系统。然后，我们证明了在适当条件下LP适定性与该问题的解的存在之间的等价性。此外，提供了关于在近似解集的行为方面针对该问题的广义意义上的LP良好姿势和LP良好姿势的度量表征的结果。最后，我们介绍了一类新的FMQHI受控系统的间隙函数，并将其用于研究FMQHI受控系统的LP适定性准则。