AIMS Mathematics, 2020, 5(6): 7107-7121. doi: 10.3934/math.2020455.

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On the stability of projected dynamical system for generalized variational inequality with hesitant fuzzy relation

1 College of Social Development and Public Administration, Northwest Normal University, Lanzhou 730070, China
2 Institute of Modern Physics, Chinese Academy of Sciences, Lanzhou 730000, China

In this paper, we investigate the projected dynamical system associated with the generalized variational inequality with hesitant fuzzy relation. We establish the equivalence between the generalized variational inequality with hesitant fuzzy relation and the fuzzy fixed point problem. And we analyze the existence theorem and iterative algorithm of solutions to such problem. Furthermore, using the projection method, we propose a projection neural network for solving the generalized variational inequality with hesitant fuzzy relation and discuss the stability of the proposed projected dynamical system.
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Keywords generalized variational inequalities; hesitant fuzzy relations; level sets; projection methods; Lyapunov stability

Citation: Ting Xie, Dapeng Li. On the stability of projected dynamical system for generalized variational inequality with hesitant fuzzy relation. AIMS Mathematics, 2020, 5(6): 7107-7121. doi: 10.3934/math.2020455

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