Painlevé–Kuratowski convergence of the solution sets for controlled systems of fuzzy vector quasi-optimization problems with application to controlling traffic networks under uncertainty

Abstract

The purpose of this article is to establish some new results on the Painlevé-Kuratowski convergence of the solution sets for controlled systems of fuzzy vector quasi-optimization problems with a sequence of mappings Γ C -converging. First, we introduce a new class of controlled systems for fuzzy vector quasi-optimization problems and establish some conditions for the existence of approximate solutions to these problems using the Kakutani-Fan-Glicksberg fixed-point theorem. Then, we study the Painlevé-Kuratowski lower convergence, Painlevé-Kuratowski upper convergence and Painlevé-Kuratowski convergence of the solution sets for such problems. Finally, as a real-world application, we consider the special case of controlled systems of fuzzy traffic network problems. Existence conditions and the Painlevé-Kuratowski convergence of the solution sets for these problems are also investigated and studied. The results presented in the paper are new and extend the main results given by some authors in the literature.

Error bound analysis for vector equilibrium problems with partial order provided by a polyhedral cone

“…Equilibrium problems have remarkable applications in the fields of mechanics, network analysis, transportation, finance, economics, operations research and optimization. For details, we refer the readers to works [9,13,18,20,25,26] and the references therein.…”

Existence and generic stability conditions of equilibrium points to controlled systems for n-player multiobjective generalized games using the Kakutani–Fan–Glicksberg fixed-point theorem

“…Recently, Hung [9] established the Levitin-Polyak wellposedness for a class of the controlled systems of fuzzy mixed quasi-hemivariational inequalities of the Minty type. Very recently, Hung and Keller [8] obtained some new results on the Painlevé-Kuratowski convergence of the solution sets for the controlled systems of fuzzy vector quasi-optimization problems. Then, this study [8] developed a class of controlled systems for fuzzy real life traffic networks problems.…”

“…Very recently, Hung and Keller [8] obtained some new results on the Painlevé-Kuratowski convergence of the solution sets for the controlled systems of fuzzy vector quasi-optimization problems. Then, this study [8] developed a class of controlled systems for fuzzy real life traffic networks problems. The Painlevé-Kuratowski convergence of the solution sets to this problem are also obtained by using a sequence of mappings C -converging.…”

Algorithms for the Pareto solution of the multicriteria traffic equilibrium problem with capacity constraints of arcs

“…Finally, using two examples, we illustrate the application of the algorithms. For other results regarding the algorithms of traffic equilibrium flows with capacity constraints of arcs, we refer to [13], and for those for the MTEPCCA, we refer to [3,14,16,17], and for other results with respect to traffic equilibrium, we refer to [1,[5][6][7][8][9][10] and the references therein. is call an arc flow, where R η + = {z = (z 1 , z 2 , .…”

“…l 3 , l 4 } and E 1 = {e 2 , e 3 , e 4 , e 5 , e 7 , e 8 , e 9 }, P 1 ω1 = {l 1 , l 3 }, P 1 ω2 = {l 2 , l 4 }, and t = 1 (6)…”