Modeling And Analyzing Of Decision Problems With Fuzzy Asymmetric Information

This dissertation studies decision-making problems with fuzzy asymmetricinformation, and it can be divided into five parts: a single-person decision-makingproblem with imprecise information; the nature of the fuzzy asymmetric informa-tion; fuzzy parametric statistical inference method; multi-person decision makingproblem; and fuzzy principal-agent problem.From the perspective of a single-person decision-making problem, the con-cept of fuzzy mapping is proposed to describe the decision problem, where thetarget is a?ected by several fuzzy parameters. It proves that the continuity andconvexity can be inherited after calculating the expected value on the hypothesesof monotonicity of the corresponding function and the upper semi-continuous ofthe membership functions of independent fuzzy variables. This method providesa theoretical approach to analyze such problem qualitatively as well as quantita-tively, and helps to make decisions rationally.The nature of the fuzzy asymmetric information is studied next. As onekind of non-common knowledge, this dissertation considers how a fuzzy eventcan be analyzed as an approximate common knowledge with some credibility,which is defined iteratively and mutually, iteratively and mutually knows withsome credibility.Fuzzy parametric statistical inference method is developed to renew thejudgment about the fuzzy parameters. This method can be applied by the deci-sion maker to update his subjective beliefs of the fuzzy environment, especiallywhen there is only a small sample available.For the multi-person decision making problem, this dissertation studies aspecial game with incomplete information, in which the payo?s of the players areboth random and fuzzy. A static fuzzy Bayesian game is then introduced andthe decision rules for players are given based on credibility theory. We furtherprove the existence of the equilibrium of the game. For the principal-agent problem, where the agent has some private informa-tion which is characterized as a fuzzy variable by the principal, a fuzzy principal-agent model is proposed in this dissertation. In the model, a contract variable isdevised with two dimensions: an action variable and a transfer variable. The suf-ficient conditions and necessary conditions for the optimal contract are explored.Furthermore, we provide an optimal contract for a special case, where the actionvariable and the transfer variable have finite first-order derivatives.Three practical problems, i.e., retailer's optimization problem under fuzzyenvironments, Cournot competition with fuzzy e?ciency and the optimal con-tract design in supply chain management under fuzzy environments are discussedseparately to verify the e?ectiveness of the models and methods developed in thisdissertation.