Research On Hesitant Fuzzy Information Aggregation Techniques And Their Application

As an extention of fuzzy set, hesitant fuzzy set permits the membership degree of an element to a set be several possible values between the interval [0, 1]. When the decision-makers are not sure about the membership degree of an element and they can not persuade each other, hesitant fuzzy set is a useful tool to deal with such situation that the multiple decision information can be expressed. Now, the research on hesitant fuzzy set has catched the attention from researchers at home and abroad, and the hesitant fuzzy set has been widely used in decision-making, medical diagnosis, clustering analysis and other fields. However, as a new direction for research, there are still deficiencies that need to be improved.According to the research ideas from the shallower to the deeper, this thesis on the information aggregation under hesitant fuzzy environment is mainly divided into six parts as following.(1) Approaches to hesitant fuzzy multiple attribute decision making based on ideal solution are developed. An integrated method that combines the LINMAP(the linear programming technique for multidimensional analysis of preference) and TOPSIS(the technique for order preference by similarity to ideal solution) is proposed to overcome the drawbacks of the LINMAP or TOPSIS. The TOPSIS is extended to accommodate hesitant fuzzy environment. To make up the disadvantages, the consistency and inconsistency between the order of alternatives and the decision-makers’ preference based on the positive and negative ideal solution are defiend. A mathematical model, which aims to minimize the total inconsistency or maximize the total consistency, is constructed to determine the attribute weights. In the last, we obtain the appropriate alternative by using the TOPSIS.(2) A bidirectional projection method is proposed to deal with hesitant fuzzy multiple attribute decision making problem. The projection and vertical projection method is extended to accommodate hesitant fuzzy environment. The hesitant fuzzy information is expressed in the form of vector. Several decision methods based on ideal solution, such as TOPSIS, projection and vertical projection method, may not be effective to differentiate between alternatives. Then a bidirectional projection method based on positive and negative ideal solution is proposed to cope with this situation. Based on the Jaynes maximum entropy principle, an optimization model, which combines the subjective and objective information, is constructed to determine the attribute weights. Then the bidirectional projection method is utilized to solve the hesitant fuzzy multiple attribute decision making problem.(3) The hesitant fuzzy multiple attribute decision making with preference information over alternatives is investigated. From two different aspects, approaches to fuse subjective and objective preference information are developed to cope with hesitant fuzzy multiple attribute decision making problem with preference information over alternatives. The hesitancy degree based on the number and deviation degree of elements in the hesitant fuzzy element is proposed to express the uncertainty of the decision group. The deviation degree between hesitant fuzzy elements based on the hesitancy degree is defined. A mathematical model that aims to minimize the deviation between the subjective and objective preference information is constructed. According to the confidence level of attribute value, another mathematical model that aims to maximize the correlation between the subjective and objective preference information is constructed. Then the hesitant fuzzy information is aggregated to rank the alternatives.(4) The dynamic decision making problem with hesitant fuzzy information is investigated. In order to deal with multi-stage multiple attribute decision making problem, two optimization models for determining the stage weights and the attribute weights are designed to aggregate the decision information over different stages. The maiximizing deviation model based on hesitancy degree of hesitant fuzzy element is constructed to determine the attribute weights at different stages. Another mathematical model based on the data features, such as the average value, dispersion and correlation degree of the decision information, is then constructed to determine the attribute weights. According to the principle that the new information is preferred and the deviation of the decision information in the adjacent stage should not be much different, a mathematical model is constructed to determine the stage weights. Then the alternatives are ranked in accordance with the similarity between the alternatives and the positive ideal solution.(5) The clustering analysis with hesitant fuzzy information is conducted. Two novel similarity degree formulas between hesitant fuzzy elements are proposed to overcome the disadvantages of the existing similarity degree, and the netting clustering method is adopted to cluster the hesitant fuzzy information. From the viewpoint of geometry, a novel similarity degree for measuring hesitant fuzzy elements based on the idea of TOPSIS is presented. From the viewpoint of information theory, the relative entropy and the symmetric cross entropy between hesitant fuzzy elements are proposed. Then, another similarity degree between hesitant fuzzy elements is presented. In the last, we conducted the clustering analysis by the netting clustering method.(6) The green manufacturing system for iron and steel enterprises with hesitant fuzzy information is evaluated at multiple stages. Approaches to evaluate the green manufacturing system for iron and steel enterprises are investigated. The evaluation index system for the green manufacturing system is built. Several experts are invited to evaluate the green manufacturing system, and the hesitant fuzzy element is utilized to express their judgements on the manufacturing system. The green degree of the manufacturing system for four iron and steel enterprises is then evaluated. Additionally, the method proposed in this thesis is utilized to assess the green degree of the manufacturing system, which would verify its rationality and feasibility.