Interval-valued Pythagorean fuzzy linguistic KPCA model based on TOPSIS and its application for emergency group decision making

This paper investigates the emergency group decision-making problem based on interval-valued Pythagorean fuzzy language sets (IVPFLSs). The frequent occurrence of emergency events can bring huge economic damage to human beings. To reduce the loss, it is very important to make reasonable emergency decisions effectively and timely. In the emergency decision making (EDM), these problems are few studied, such as high dimension problem, data nonlinearity, and correlation. For EDM problems, the advantage of IVPFLSs is that it can reasonably express the evaluation information given by decision makers (DMs) through both qualitative and quantitative aspects. However, if the dimension and nonlinear relationship of the decision data keep growing, and the traditional decision-making methods will fail. The distance measure between decision data is necessary to calculate in the process of dimensionality reduction, and the current research does not propose the definition of IVPFLSs distance measure. On the basis of this, this paper first uses the attributes and DMs as variables to define the standard Euclidean distance measure between IVPFLSs. For nonlinear features, we construct the interval-valued Pythagorean fuzzy language kernel principal component analysis (IVPFL-KPCA) model to reduce the dimensionality. What is more, we also obtain the reasonable weight vectors of the attribute and DMs from cumulative contribution rate. For low-dimensional decision data, according to the technique for order performance by similarity to ideal solution method, the best emergency plan is selected for the information variables after dimensionality reduction. In sum, the IVPFL-KPCA model not only avoids multicollinearity and nonlinear separability between decision data, but also obtains reasonable weights. It further improves the efficiency of decision-making operations and reduces the difficulty of the algorithm. Finally, an example of earthquake emergency plan is shown to demonstrate the feasibility and practicability of the proposed method. Besides, we also compare it with the existing methods, which proves the effectiveness of the method.