Study On Some Prolems In Multiple Attribute Decision Making Based On Interval Complementary Judgement Matrices

Multi-attribute decision making and group decision making problems are common during production and living, but also are important in decision making science domain, which bring people wider attention. But sometimes preference information expressed by interval number form accords with thought habit even more. This paper researches some problems of multiple attribute decision making based on interval number complementary judgment matrices. The main research contents are as follows.1. The mutual transformation relations of the four preference information, including interval number preference ordings, interval number utility value, interval number complementary judgement matrices and interval number reciprocal judgement matrices, are researched. Firstly, this paper reviews transformation methods lieing in concern references of preference ordings, utility value, complementary judgement matrices and reciprocal judgement matrices. Furthermore, the four new, more reasonable transformation equations are acquired. Secondly, this paper constructs the relation functions based on four interval number preference information, namely interval number preference ordings, interval number utility value, interval number complementary judgement matrices and interval number reciprocal judgement matrices, which uniforms different uncertain prefence information, and an example is given to prove the simplicity and practicality of the proposed methods.2. The problem about determination of associated weights in OWA operator theory is researched. From practical problem need, a two objective (maximal entropy and minimal variability) programming model is constructed to obtain the weights associated with OWA operator for a given level of orness and known sampleobserved value and its unknown aggregated data. Then it is transformed a one objective programming model by linear weight method or ideal point method, and is solved by Lagrange multiplier. Finally a numerical example is given to illustrate the use of proposed approach.3. The aggregation problem about the group preference information of interval number complementary judgement matrices is researched. Based on error propagation theory, uncertain interval number preference information is transformed into certain preference information, namely median and limit error information. Then ordering of given schemes is obtained by using OWA operator. Finally a numerical example is given to show the feasibility and effectiveness of the proposed approach.