Interval-valued Pythagorean fuzzy linguistic TODIM based on PCA and its application for emergency decision

Nowadays the emergency decision has become a hot topic in the field of decision-making with interval-valued Pythagorean fuzzy linguistic (IVPFL) information. Moreover, with the increase of attributes and decision makers, the complexity of the operation is a great challenge for making decision. How to overcome multicollinearity is a crucial link in the emergency decision modeling process. In this paper, we treat the attributes and DMs as IVPFL variables and construct the IVPFL principal component analysis (IVPFL-PCA) model to overcome the multicollinearity. Then, a novel TODIM (abbreviation for interactive and multicriterial decision-making in Portuguese) method is proposed to tackle the IVPFL information under several new variables that are independent of each other (i.e., the PCs) and the reasonable weights of PCs obtained based on the IVPFL-PCA model. Finally, a case study on earthquake emergency decision is presented to show the applicability of the proposed approach and some comparisons are presented to illustrate its superiorities.