Fuzzy Multi-criteria Decision Making Method Based On Prospect Theory

Decision-making is a basic human activity, which is widely used in economic, management and other areas. In real life, because of vagueness and uncertainty of the external world, the complexity of decision problems, and the limitation of the decision-makers'level of personal knowledge, we often can't get the value of some alternatives accurately and can only acquire the approximate range of values or the degree of satisfiability and the non-satisfiability of each alternative with respect to a set of the criteria. Therefore, this study is of great theoretical and practical significance whose criteria values are interval numbers or intuitionistic fuzzy numbers based on prospect theory. On the basis of the existing methods and prospect theory, we investigate interval and intuitionistic fuzzy multiple criteria decision making problems based on prospect theory. The effectiveness of the developed approaches are verified by empirical method. The mail work and achievements are as follows:(1)With respect to decision making problems whose criteria values are interval numbers, we propose a fuzzy multi-criteria decision making method. This method firstly regardes the criteria value as N arithmetic random numbers in the given interval, and the regularities of criteria value distribution for the interval is expressed by the normal distribution function. On the basis of the given reference points of every criteria, use value function and decision weight function to calculate the prospect value of criteria, and then calculate the whole prospect value of every alternative. At last, sort all the alternatives and choose the best one. Use a simple illustrative example to demonstrate the feasibility of the fuzzy multi-criteria decision making method.(2)With respect to decision making problems whose criteria values are intuitionistic fuzzy numbers and the criteria weight is completely unknown, we propose a fuzzy multi-criteria decision making method. Firstly, by the intuitionistic fuzzy entropy, it can get the information entropy of each criterion and calculate the criteria weight. Secondly, determine the positive and negative ideal solution, gains and losses results set according to score function and accuracy function. Thirdly, define the prospect value function with intuitionistic fuzzy numbers by using score function. By combining weighting function of prospect theory, we establish a fuzzy multi-criteria decision making model based on prospect theory and intuitionistic fuzzy number, and then calculate the prospect value of every alternative. At last, sort all the alternatives and choose the best one. Use a simple illustrative example to demonstrate the feasibility of the fuzzy multi-criteria decision making method.(3)Multi-criteria decision making methods proposed in chapters III and IV are applied to stock investment research, in which individual investors determine the investment value in the stock market. Through the research literature, three indicators are selected to evaluate the investment value of the stock. Then we develop questionaire ourselves and collect forcast data that investors predict stock movements of eight representative stocks in the coming six months. We obtain investment value and order of the eight stocks according to the multi-criteria decision making mathod based on prospect theory. At the same time, we compare the order of the individual stock investors willingness to invest eight stocks with the order of the prospect value. Through analysis, the effectiveness of multi-criteria decision making method is validated.