Research On Multiple Attribute Decision Making Theory And Its Application In Fuzzy Information Settings

Multiple attribute decision making is an important branch of modern scitentific decision making. Fuzzy multiple attribute decision making is an extension and development of the classical multiple attribute decisiong making. The theory and method have been widely used in managerial decision making, medical diagnosis, pattern recognition, and market prediction, and many other fields. Because of the real decision problems containing uncertain factors and the fuzzyness of the decision makers’ subjective judgment, attribute weights and attribute values are always take the form of fuzzy information. Therefore, explore the multiple attribute decision making theory and application under the condition of fuzzy information has important theoretical significance and practical application value. Aiming at the multiple attribute decision making problems in fuzzy information settings, this dissertation carried on the exploratory research from the following several aspects:1、Research on ranking method of interval numbers. For a finite number of interval numbers, all of them can be converted into the form of interval values by normalization. For the finite number of interval values, a positive ideal interval and a negative ideal interval are defined, respectively. Based on the Euclidean distance of interval numbers and the idea of TOPSIS, the relative closeness degree of compared interval values can be calculated. Interval value with the higher relative closeness degree is closer to the positive interval; the corresponding interval number is also bigger.2、Research on ranking method of intuitionistic fuzzy numbers(IFNs). Because of the score function is in the absolute priority for comparison of IFNs. When we compare the two IFNs, we are forced to conclude that the one is small, although the score of it is a litter bit smaller than the other and the accuracy degree of it is much higher than the other. Based on the Hamming distance of IFNs and the idea of TOPSIS, the closeness degree formula of IFNs is given for ranking IFNs. It is proved that the closeness degree formula can contains the ranking principle of both the score function and the accuracy function. Furthermore, we define the additive(multiplicative) consensus intuitionistic judgement matrix by using the closeness degree formula and the consensus of fuzzy reciprocal judgement matrix. And the ranking and consensus problem of intuitionistic judgement matrix are also studied.3、Research on ranking method of interval-valued intuitionistic fuzzy numbers(IVIFNs). The membership degree and the non-membership degree of IVIFNs take the form of interval numbers. So, many ranking methods can’t distinguish those IFNs having the same midpoint and obviously different interval width. Based on the Euclidean distance of IVIFNs and the idea of TOPSIS, a ranking method of IVIFNs is proposed. Compared with some other ranking methods of IVIFNs in literature, the proposed method shows higher discrimination capability. Besides, the ranking and consensus problem of interval-valued intuitionistic judgement matrix are also studied.4、Hesitant fuzzy pseudo-metric. It is difficult to compute the hesitant fuzzy distance because the numbers of values in different hesitant fuzzy elements(HFEs) may be different. We propose a kind of hesitant fuzzy pseudo-metric to measure the difference between the two HFEs in order to solve this problem. Based on hesitant fuzzy pseudo-metric, a method of hesitant fuzzy multiple attribute decision making is developed by using hesitant fuzzy pseudo-metric clossness degree. Moreover, hesitant fuzzy consistency index is proposed, and then an optimization model is constructed based on the maximization of group consistency index, it provises a new way for solving attribute weight vector of hesitant fuzzy multiple attribute decision making.5、Hesitant fuzzy exponential entropy. Firstly,the axiomatic definition of entropy for hesitant fuzzy sets is proposed. Then, based on exponential entropy of traditional fuzzy sets, we present the concept of hesitant fuzzy exponential entropy and construct hesitant fuzzy exponential entropy measure formula. Meanwhile, it is proved that hesitant fuzzy exponential entropy meets the four axiomatic principles. Finally, the entropy weight method of hesitant fuzzy multiple attribute decision making is developed by applying hesitant fuzzy exponential entropy and minimum entropy principle.6、The possibility degree for interval-valued hesitant fuzzy elements(IVHFEs). Based on extension principle, the possibility degree of interval number is extended to IVHFE settings, so the possibility degree about an IVHFE is greater than the other is introduced, and then its excellent properties are discussed. Finally, the method of interval-valued hesitant fuzzy multi-attribute decision making is developed based on the traditional grey relational analysis(GRA) method.