Interval Multi-attribute Large Group-decision Method Based On Clustering Algorithm

Due to the complexity of the economy,the scale of decision-making groups gradually expand,and there are more and more members involved in groups,as a result that the existing method of group decision making has been unable to meet the demand.With uncertainty and complexity of the decision problem,the evaluation of the decision-makers must consider multiple attributes,at the same time,because of the uncertainty and the ambiguity of human thinking,most evaluation information of policymakers are fuzzy numbers,especially interval number,but the researches on interval multi-attribute large group decision making are few.As for the multi-attribute large group decision making problem that the weights of attribute are completely known and the attribute values are interval type random variable,a large group decision making method is proposed.The main works of this paper is as follows:First of all,for the dependence on the initial clustering center of the traditional K-clustering algorithm,this paper proposed an improved K-clustering algorithm of optimal initial clustering center.In consideration of actual distribution of data sets,we selected clustering centers closing to the actual cluster centers,the result showed that after fewer iterations,the better results were obtained for higher rate of correct clustering and stable result.Secondly,we proposed the similarity measure of the interval data,this measure was proofed that it can satisfy the basic properties of the similarity through mathematical method,and it is fit for interval numbers for arbitrary distribution.On this basis,this paper combined the improved K-mean clustering algorithm to cluster analysis for interval multi-attribute large group decision making problem,the better clustering result can verify that the definition of similarity is effective.Thirdly,in order to choose the optimal number of clusters in the clustering process,we compared the effect of clustering in the case of different categories,both the greater similarity of the inter-class and the smaller the similarity of infra-class,the better the clustering effect.So we calculated the ratios of similarity of the inter-class and the similarity between classes for selecting corresponding number of maximum ratio.Finally,we considered the uncertainty of interval data,as well as group decision making with the greatest satisfaction for setting weights of class.So we put forward three factors closely related with weights: interval width,compactness of evaluation information of inter-class,the proportion of class members.Compared to the other method,this method is more scientific,more comprehensive.