Ranking Of Fuzzy Numbers And Its Application In Multiple Attribute Decision-Making

Multiple attribute decision-making, which is in fact a selection and ranking problem between some alternatives about two or more attributes, is very important in the study of decision-making. Because of the complexity of the objective world and random of the decision maker, in practice, decision data are often fuzzy numbers. Ranking of fuzzy numbers is therefore essential in multiple attribute decision-making.Firstly, the thesis emphasizes on the interval multiple attribute decision-making, Under the assumption that the attribute value in each interval has a normal distribution, two approaches for the quantitative analysis of intervals are proposed. By assigning an assessable value to each interval, a optimization model is constructed to obtain the the ranking of each alternative.In order to study the difference of the fuzzy numbers, an improved distance measure between fuzzy numbers is introduced to overcome the shortcoming of the Hamming distance, the method is based on the left distance and right distance between fuzzy numbers. In the meanwhile, an improved similarity method between the fuzzy numbers is also presented with regard to the difficiency of Zwick's method. Finally, we study the relation of distance and similarity between fuzzy numbers, and some translation methods are presented between distance and similarity.Furthermore, a ranking method of fuzzy numbres is proposed based on fuzzy preference relation. The ranking method is proved to be a fuzzy order relation. Finally, a numerical example is presented to illustrate the efficiency of the method.At last, for multiple group attribute decidion-making problem, a new method for aggregating individual opinions into a group consensus opinion is proposed based on the distance and similarity of fuzzy numbers. The importance of each expert is also taken into consideration in the process of the aggragation.