Multi-Objective Programming Models In Uncertain Systems And Its Application

Multi-objective programming problems are prevalent and play important roles in politics,economy,military and daily life.Multi-objective programming has been widely used in significant decision making areas such as financial investment,asset liability management,engineering design,transportation,environmental protection,military science and national security.Owing to the uncertainty or inaccuracy impacting on complex systems in reality,the research on multi-objective programming model and its algorithm under uncertain environment becomes a hot topic.By utilizing interval number,intervaltyped triangular fuzzy number,interval-typed random variable and intuitionistic fuzzy random variable to respectively describe uncertainty information in uncertain systems,this thesis studies multi-objective programming models and their algorithms in uncertain systems and explores the application for multi-objective programming in portfolio selection and insurance company risk assessment.The main contents and results of this thesis are as follows:(1)Multi-objective linear programming model based on interval-typed triangular fuzzy numbers.A multi-objective linear programming problem(ITF-MOLP)is presented,in which coefficients of both the objective functions and constraints are interval-typed triangular fuzzy numbers.An algorithm of the ITF-MOLP is provided by introducing the cut set of interval-typed triangular fuzzy numbers and the dominance possibility criterion when compared with two interval-typed triangular fuzzy numbers.For a given level,the ITFMOLP is firstly converted to the maximization of the sum of membership degrees of each objective in ITF-MOLP,whose membership degrees are established based on the deviation from optimal solutions of individual objectives,and the constraints are transformed to normal inequalities by utilizing the dominance possibility criterion.Then the equivalent linear programming model is obtained which could be solved by Matlab toolbox.Finally several examples are provided to illuminate the proposed method by comparing with the existing methods and sensitive analysis demonstrates the stability of the optimal solution.(2)A portfolio selection model with interval-typed random variables and the empirical analysis.A portfolio selection model with interval-typed random variables is presented.Firstly,the historical average return of every asset is considered as an interval number,the return of every asset is described by an interval-typed random variable and the risk of every asset is treated by probabilistic measure.A fuzzy random portfolio selection model is established,where the goal is to maximize the expected portfolio return and meanwhile minimize the risks of all the assets.Then an algorithm for solving the portfolio selection problem is given through introducing a probabilistic level of risk measure.Meanwhile,the sufficient condition for the existence of Pareto-maximal solution is investigated.In particular,if the set of the historical average returns of assets consists of a total ordered set under some order relation,then the Pareto-maximal solution of the model could be obtained.Finally,the empirical analysis is presented to show the feasibility and robustness of the model.(3)Two objective portfolio selection models based on interval numbers.Based on the given return and risk levels of portfolio selection,this thesis firstly establishes a new model for portfolio selection with expected return maximized and the risk minimized,in which average returns and risk of every asset are treated as interval numbers respectively.Then an algorithm for solving portfolio selection problems is explored,which could be transformed to a classical linear programming by virtue of interval order method.Therefore,the optimal solution for portfolio selection in fuzzy uncertain environment could be obtained by Matlab.Finally,the model and its algorithm obtained are illustrated by a case study.(4)The application of intuitionistic fuzzy random programming to risk evaluation in insurance companies.This thesis firstly presents a scalar expected value operator of intuitionistic fuzzy random variables,and discusses some properties concerning the measurability of intuitionistic fuzzy random variables.Secondly,a risk model based on intuitionistic fuzzy random individual claim amount in insurance companies is established,in which the claim number process is regarded as a Poisson process and the claim amount is characterized as an intuitionistic fuzzy random variable respectively.Thirdly,based on zero initial surplus and arbitrary initial surplus respectively,the mean chance of the ultimate ruin is investigated in detail.In particular,the expressions of the mean chance of the ultimate ruin are presented in the cases of zero initial surplus and arbitrary initial surplus respectively,if individual claim amount is an exponentially distributed intuitionistic fuzzy random variable.Finally,two illustrated examples are provided to approve the effectiveness of the model.