An interval-valued intuitionistic fuzzy principal component analysis model-based method for complex multi-attribute large-group decision-making

The complex multi-attribute large-group decision-making problems that are based on interval-valued intuitionistic fuzzy information have become a common topic of research in the field of decision-making. Due to the complexity of this kind of problem, alternatives are usually described by multiple attributes that exhibit a high degree of interdependence or interactivity. In addition, decision makers tend to be derived from different interest groups, which cause the assumption of independence between the decision maker preferences in the same interest group to be violated. Because traditional aggregation operators are proposed based on the independence axiom, directly applying these operators to the information aggregation process in the complex multi-attribute large-group decision-making problem is not appropriate. Although these operators can obtain the overall evaluation value of each alternative, the results may be biased. Therefore, we draw the thought from the conventional principal component analysis model and propose the interval-valued intuitionistic fuzzy principal component analysis model. Based on this new model, we provide a decision-making method for the complex multi-attribute large-group decision-making problem. First, we treat the attributes and the decision makers as interval-valued intuitionistic fuzzy variables, and we transform these two types of variables into several independent variables using the proposed principal component analysis model. We then obtain each alternative's overall evaluation value by utilizing conventional information aggregation operators. Moreover, we obtain the optimal alternative(s) based on the ranks of the alternative overall evaluation values. An illustrative example is provided to demonstrate the proposed technique and evaluate its feasibility and validity.