In the complex multi-attribute large-group decision making (CMALGDM) problems where attribute values are interval-valued intuitionistic fuzzy numbers (IVIFNs), the number of decision attributes is often large and their correlation degrees are high, which increase the difficulty of decision making and thus influence the accuracy of the result. To solve this problem, this paper proposes the interval-valued intuitionistic fuzzy principal component analysis (IVIF-PCA) model. This model represents major information of original attributes, effectively reduces dimensions of attribute space, and synthesizes original attributes into several relatively independent principal components (PCs). The basic thought of this model is as follows: first, we use thoughts of ‘equivalency’ and ‘order invariance’ to transform IVIFN samples into interval number samples; subsequently, we use the ‘error theory’ to replace interval numbers with their middle points, and combine the middle points with the traditional PCA to obtain the PC scores of interval number samples; finally, we adopt the thought of ‘equivalency’ to obtain the PC scores of IVIFN samples. Moreover, based on the IVIF-PCA model, we give a decision making method for the CMALGDM problem. The feasibility and validity of the decision making method is investigated through a numerical example.
Complex multi-attribute large-group decision making (CMALGDM) Interval-valued intuitionistic fuzzy principal component analysis (IVIF-PCA) Error theory Score function Weighted arithmetic average operator
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We would like to thank the two anonymous reviewers for their constructive comments that have helped to improve the presentation and quality of the paper. This paper was supported by the National Natural Science Foundation of China (No. 71102072, No. 71271143, No. 71171141, and No. 71171202).
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