In this study, inequality distance hyperplane multiclass support vector machines (IDH-MSVM) algorithm is proposed on the basis of multiclassification support vector machine (MSVM) which was proposed by J. Weston and C. Watkins in 1999. It only needs to solve a single objective optimization problem to deal with multiclassification problems. For original MSVM, the hyperplane distance refers to the classification interval between classical margin and hyperplane, which is equality. However, the IDH-MSVM introduces parameters to adjust distance between every classification hyperplane and classical margin, which makes the hyperplane distance inequality. The effectiveness of the proposed method is experimented on UCI standard data sets and compared with several multiclassification algorithms. Experimental results show that this method has a better classification effect on multiclassification data.

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.

Interval numbers multiple attribute decision-making (MADM) is an important branch of uncertainty decision theory, and the decision result largely depends on the selection of the aggregation operator. In this paper, we analyze the ordered weighted average (OWA) operator, which is an averaging aggregation operator. The OWA operator provides an aggregation method between the minimum and maximum operators. Moreover, we further analyze some of extensions about OWA operator, and pay special attention to the Bonferroni means and OWA (BON-OWA) operator. Note that the BON-OWA operator only aggregate the input arguments which are exact numbers. Under normal circumstances, decision makers is difficult to provide a clear evaluation value for attribute and most of them are described by vague information. When the decision information is an interval numbers, the BON-OWA operator cannot describe decision result accurately. Under these environments, we proposed the interval numbers BON-OWA (IBr,q-OWA) operator to deal with the vague decision information in this paper. Then we consider their main properties, such as idempotence, monotonicity, and boundedness and prove them. Besides, a wide range of special aggregation operators are found in changing parameter values, such as the square mean and max operator, and so on. We also compare the ranking method of the interval numbers based on Boolean matrix. As a result, the combination of IBr,q-OWA operator makes the decision result more scientific. Finally, a new approach for decision-making problem is developed based on the IBr,q-OWA operator, which shows the effectiveness in practical examples.