Several Decision-making Methods Based On Gray Correlation Analysis And Their Applications

The multiple attribute decision-making (MADM) methodologies have been successfully applied in many real-life problems in engineering, finances, market analysis, management and others. Decision is usually made under uncertain condition from some available alternatives, that is, these alternatives should be compared, ranked or chosen. .Therefore, it is worth studying on the MADM methods. Through studying on PCA and TOPSIS, introducing the gray system theory, this paper establishes several decision-making models, and presents new idea for the limited data samples decision-making problems. Based on gray correlation analysis, presents a new kind of TOPSIS. First take the gray correlation coefficient matrix between primitive data sample and ideal scheme as new decision-making matrix, and then use TOPSIS to evaluate and arrange all schemes. This method overcomes the traditional TOPSIS's shortcoming of excavating the inherent law of the data difficultly. An example shows its validity. Based on principal component analysis method (PCA) and gray correlation clustering analysis, presents an index integration method. In the process of analyzing and evaluating multiple index problems, first we analyze these indexes using grey correlation clustering analysis method, in order to classify them into several classes which can be defined. Then we analyze these classes based on PCA to get principal component set of every class. Finally we integrate all indexes based on the weight of every class. This method not only includes the information of all indexes, but allows for the relations among these index classes. An example shows this method is easy andnational. Introducing the grey system theory, this paper presents a new grey correlation technique for order preference by similarity to ideal solution (GC-TOPSIS) to develop traditional TOPSIS. First, we decide the weight of every decision-making index using AHP and entropy method. Second, according to grey correlation analysis method, we establish GC-TOPSIS by using grey correlation degree as decision-making unit. Finally, through a supplier selection problem we prove its validity and feasibility. In this paper, we analyzed the disadvantage of traditional TOPSIS, and presented a new decision-making method based on grey correlation degree and TOPSIS. This method established a new kind of relative similarity degree by combining the Euclidean distance with grey correlation degree. The new similarity degree reflects the distance and the different shape between a selected scheme and the ideal solution and negative ideal solution. Its implication is clearer.