A decision-making method based on a two-stage regularized generalized canonical correlation analysis for complex multi-attribute large-group decision making problems

Abstract

For complex multi-attribute large-group decision-making problems in the interval-valued intuitionistic fuzzy environment, decision attributes are correlated and stratified, and the correlations among them are not always consistent. This paper proposes a decision-making method: a two-stage regularized generalized canonical correlation analysis (RGCCA) based on multi-block analysis method. The proposed two-stage RGCCA method can well represent the different characteristics between the positive and negative attribute blocks, which makes the decision making process closer to actual. Since RGCCA can only handle single-valued information, this research also presents a novel transformation method of interval-valued intuitionistic fuzzy numbers to single-valued numbers. For the two-stage RGCCA model, in the first stage, all attributes are divided into the positive and negative attribute blocks according to the signs of the weight coefficients of block components. In the second stage, we conduct RGCCA based on multi-block analysis method for the two types of blocks, respectively. Finally, in terms of the estimated values of block components in the two types of blocks and weights of the two types of blocks (obtained by the maximizing deviation method), the evaluation value of each alternative is calculated and the ranking result of alternatives is given. An example is illustrated to verify the feasibility and the validity of the proposed method.