A PCA-based fuzzy tensor evaluation model for multiple-criteria group decision making - Singh, Meenu; Pant, Millie; Kong, Lingping; Alijani, Zahra; Snášel, Václav (Applied soft computing, 2023)
Multiple-criteria group decision-making (MCGDM) problems mainly consist of multiple factors and multiple Decision Makers (DMs) or Users, for which dimension extension is necessary when considering all the entries of DMs together. Tensor, a generalized form of a matrix, displays a multi-way array item, which is the most suitable and practical way to represent high-dimensional data without losing any information. In this paper, we first reduce the dimension through Principal Component Analysis (PCA), which helps consider the most-informative criteria. Then, we reintroduced the tensor as a fuzzy-form tensor for the MCGDM problem because of user information uncertainty. We choose Interval-valued Neutrosophic Fuzzy numbers (IVNFNs) as the basis for the tensor form because of their ability to distinguish between truth, indeterminacy, and falsity in the data. Lastly, a Generalized Interval-valued Neutrosophic Fuzzy Weighted Geometric (GIVNFWG) operator is defined. Moreover, a generalized framework for fuzzy-form tensors for high-dimensional MCGDM problems is proposed. The feasibility and efficiency of this proposed process is illustrated for a real-world MCGDM problem of ranking the most efficient Third Party Reverse Logistics Partners (3PRLPs), i.e., recycled fiber-based paper mills for the packaging industry. The obtained results are according to the experts and are validated using sensitivity analysis. This analysis facilitates in assessing the impact on the overall ranking performance of 3PRLPs by considering various combinations of environment and technological sub-criteria. •We put forward a generalization of IVNF tensor numbers, namely, IVNF-tensor, as an extension of IVNFNs and developed an extend version of weighted geometric aggregation operator for evaluation process of IVNF-tensor.•We proposed a approach for MCGDM problems by using proposed IVNF-tensor and PCA method, where the PCA plays two roles in user’s weight determination and the criteria reduction. The aggregated values of IVNF-tensor by the proposed operator is used as priorities of the criteria and sub-criteria later in the MCDM method.•To handle the pairwise comparison data, we introduce an easy way of data transformation that converts the DM’s rating into IVNF numbers, which facilitate the tensor construction and data operations. It is ideal and practical way to have a fuzzy-form tensor in MCGDM.•We conduct the experiments on a real-world problem and make the most thorough sensitivity analysis of how the least important criteria ineffective to the final decision making. [Display omitted]