Research On Multi-Attribute Decision Making Method Based On Normal Fuzzy Number

Multi-Attribute Decision-Making is the important branch of modern decision-making science, whose theory and method have wide applications in business management, economics development, engineering system, military defense and many other fields. Some specific problems in life, which are transformed appropriately, often can be solved as multiple attribute decision making problems. So, it has important significance to study practical and effective methods on multiple attribute decision making.As decision makers often confront complicated things, uncertain environment and the ambiguity of human thinking, decision makers are often unable or difficult to determine affirmatory value of decision-making information. However, uncertain decision-making information usually can be given easily in the form of fuzzy number. So, Fuzzy Multi-Attribute Decision-Making has caused a great deal of academics concern.In recent years, there is extensive research on the multiple attribute decision making type of the triangular fuzzy numbers, interval-valued intuitionistic fuzzy numbers. But it can more objectively reflect the distribution of data with normal fuzzy numbers for some decision-making problems in real life. Although the concept of normal fuzzy number has been proposed, but multiple attribute decision making problems on the normal fuzzy number type, are seldom reported. Therefore, it has a very important and practical significance to study multiple attribute decision making problems of normal fuzzy number and the related theory. Based on the normal fuzzy number, this paper completed the following research work:1. It introduces the research background and the research status of fuzzy multiple attribute decision making problems, especially for fuzzy multiple attribute decision making, elaborates related algorithm separately on the basis of the representation of fuzzy information; it recounts the basic operation thoughts of fuzzy multiple attribute decision making, which includes the structure of decision problem, construction of decision model and solution of decision process. Then the related algorithms in the process of decision making (standardization of the decision matrixes, determination of attribute weights, comprehensive ranking of schemes) are summarized. 2. Based on normal fuzzy number and some concepts (expectation, variance, similarity), it improves the acquisition method and usage of the ideal points of TOPSIS method, by putting forward one score function (comprehensive index of expectation and variance) to obtain ideal points and get the ideal solution, which considers the integrity of each attribute fully. Then, according to the similarity between each scheme and the ideal solution, all schemes are ranked, which takes into account various attributes, and acquire more objective and reasonable result.3. According to the different situations where attribute weights are known or partly known and attribute values are shown in the form of normal fuzzy number, it proposes new methods based on the similarity and the improved standardized ideal solution. At last, some examples analysis show that the methods are feasible and effective.