Existence And Stability Of Solutions To Fuzzy Fixed Points And Related Problems In Generalized Fuzzy Multi-objective Game

This dissertation focuses on the application of fuzzy set theory in fixed point problem,generalized multiobjective game problem and the equilibrium problem.Firstly,we study the existence of fixed points of fuzzy mappings and the stability of the set of fuzzy fixed points under the condition of bounded rationality.Secondly,we study the stability of equilibria for a group of generalized fuzzy multiobjective games from the perspective of essential stability.Finally,we establish the existence of solutions and well-posedness for symmetric vector quasi-equilibrium problems with fuzzy mappings.The full text is divided into 5 chapters as follows:Chapter 1 introduces the background and current situation of fuzzy fixed points,fuzzy games and equilibrium problems,and clarify the main research work and the innovation of this paper.Chapter 2 introduces the necessary preliminaries in this paper,including the continuity of set-valued mappings,convexity and continuity of vector-valued functions,convexity and continuity of fuzzy mappings,etc.In chapter 3,the existence result for fixed points of fuzzy mappings is investigated by applying maximal element and Fan-Glicksberg fixed point theorems.And the stability result for a special class of fuzzy fixed point problems is studied by utilizing a technique of bounded rationality.That is,we prove that most of the fuzzy fixed point problems are stable on the meaning of Baire category with the perturbation of fuzzy mappings and feasible sets.Moreover,an approximation theorem for fuzzy fixed point problems is proved under appropriate conditions.In chapter 4,under the assumption that the constraint mappings of players are fuzzy,we study the stability of equilibria for a group of generalized multiobjective games.First,we prove that most of generalized multiobjective games with fuzzy constraint mappings are essential on the meaning of Baire category by Fort theorem.Furthermore,an example is constructed to reveal that not all generalized multiobjective games with fuzzy constraint mappings come into possession of essential points.Finally,we obtain the existence of essential components for the games.In chapter 5,we consider the symmetric fuzzy vector quasi-equilibrium problems and establish the existence of solutions by applying Fan-Glicksberg fixed point theorem.Furthermore,we study Levitin-Polyak well-posedness for symmetric fuzzy vector quasiequilibrium problems after giving the concepts of Levitin-Polyak approximating solution sequence of the problem.