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 Painleve–Kuratowski convergence of the solution sets for controlled systems of fuzzy vector quasi-optimization problems with a sequence of mappings $$\varGamma _C$$ -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 Painleve–Kuratowski lower convergence, Painleve–Kuratowski upper convergence and Painleve–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 Painleve–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.