Research On Uncertain Multiple Attribute Decision Making Based On Prospect Theory

The multiple attribute decision making problem is aiming to determine the best solution by decision makers when considering many attributes.Multiple attribute decision making is widely used in the area of project investment,product development and government management and so on.Most of the existing multiple attribute decision making problems are based on the expected utility theory,but this type of decision making can not reflect human preference information clearly.As the process of decision making is complicated and uncertain,the probabilities of different events are diverse,the states of different attributes under the different conditions are various,and the expression ways of attribute value are disparate.Therefore,decision makers need to consider the probabilities of various states.In addition,the weight of each attributes is ambiguous which are found in nature,and the attribute weight is also directly concluded or determined by a single method.To determine attribute weights scientifically and reasonably,decision makers need to combine subjective methods and objective methods.Therefore,this thesis proposes a method based on prospect theory for uncertain hybrid multiple attribute decision making problems with unknown attribute weights,and an optimization model is established to determine the subjective and objective weight.Firstly,this thesis introduces the basic knowledge of the prospect theory and uncertain hybrid multiple attribute decision problem,analyzes the characteristic and decision making patterns about expected utility theory and prospect theory and cumulative prospect theory,and introduce the usual methods refer to multiple attribute decision making problem and determining the attribute weights.Meanwhile,this thesis clarifies the advantages and problems about the prospect theory that should be paid attention in the process of decision-making.By analyzing the difference between prospect theory and the other theories,the feasibility of applying prospect theory to multiple attribute decision making problems is clarified.Secondly,this thesis studies the method which transfers the interval numbers,linguistic numbers,and triangular fuzzy numbers to clear numbers.After convertingthe attribute value to a clear number,it is compared with the expected value,the risky gain matrix and risky loss matrix are constructed.Then,by the combination of subjective and objective methods,the optimization model of Lagrange function solution is established according to the fuzzy preference relationship and deviation maximization algorithm.The subjective and objective weights are obtained.Thus,the weight model is optimized to obtain the comprehensive weighted values of each attribute.Finally,the prospect matrix is calculated by the risky gain matrix and risky loss matrix which are obtained.The prospect values are concluded by integrating weighted values,and then the comprehensive prospect values of each scheme,the best scheme and scheme ranking are concluded.An illustration example is given to verify the feasibility of the method which is proposed.