Study On Multi-Attribute Group Decision Making Approaches With Uncertain Preference Information Based On Fuzzy Set And Stochastic Statistical Theory

Decision making is a basic human activity, which is widely used in engineering design, economics, management, military, etc. However, in many decision making context, decision makers often feel it difficult to describe their preference information precisely because of the problem complexity, time press and unfamiliar problem area. Therefore, it makes sense to conduct the research on the theory and approach of multi-attribute group decision making (MAGDM) problem. This paper is dedicated to the MAGDM problem with fuzzy and stochastic uncertain preference information. Several MAGDM approaches are proposed with corresponding models and solutions. The effectiveness and practicability of the proposed approaches are approved by instances. The main work and innovations are listed as follows:(1) An expert weights determination and schemes sorting method based on fuzzy numbers is brought up for MAGDM problem. Firstly, the individual expert decision matrix is normalized, after which the group expert decision matrix is calculated by weighting. The expert objective weights are obtained by comparing the differences between each individual expert decision matrix with the group expert decision matrix. Then the stable results of integrated expert weights are achieved using the expert subjective and objective weights after several iterations. The normalized attribute weights are achieved by utilizing fuzzy numbers gravity ordering method. In the end, the MAGDM integrated utility index is synthesized with integrated expert weights and attribute weights and the schemes sorting is finished by using the gravity ordering method again.(2) With respect to the uncertain multi-attribute group decision making problem, whose candidate schemes have random attribute values and weights, a method combing the estimation theory of statistical signal processing and fuzzy numbers operation is proposed to solve the multi-attribute group decision making schemes ordering. A linear estimation model is firstly build up based on Bayesian framework. Then the scheme attributes and weights estimations are aggregated using every expert's fuzzy number estimation by means of Bayesian Gauss-Markov theorem or Gauss-Markov theorem with or without a priori knowledge. Lastly, the ordering of all the schemes is obtained by the weighted sum comparison.(3) Referring to the enterprise construction requirements of the sub-subject "Two-oriented Normative Enterprise Guidance system of Hunan Province" of the subject "Two-oriented of Social Constructive Standard Series system in Hunan Province", the employees'group decision results for the enterprise two-oriented construction are calculated by using the above mentioned weights algorithm and stochastic statistical model method. Firstly, the expert integrated weights are obtained by iterations, and then the integrated utility index values of four sub-index series of each enterprise are synthesized by weighting. Secondly, the integrated values of four sub-index series of each enterprise are calculated by using the stochastic statistical model method. Thirdly, the value sorting of four sub-index series and integrated scores of each enterprise are compared respectively. At last, the ordering results of two algorithms are compared and analyzed, and the conclusions are drawn.