A review of modern methods of data normalization in the tasks of multicriteria decision-making and multidimensional classification is presented. The invariant properties of linear normalization methods are determined. Two basic principles of normalization of multidimensional data are defined: preservation of dispositions of natural and normalized values on the measurement scale and the absence of a displacement in the areas of normalized values of various criteria relative to each other. A method is proposed for converting normalized values of cost criteria to profit criteria based on the reverse sorting algorithm (ReS-algorithm). The ReS-algorithm preserves the dispositions of the natural and normalized values of the attributes of the alternatives and eliminates the displacement the areas of normalized values of the cost criteria relative to the profit criteria, which ensures the equality of the contributions of various criteria to the performance indicator of the alternatives.

中文翻译：

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将成本标准的归一化值转换为 MCDM 任务中的收益标准的 ReS 算法

回顾了多标准决策和多维分类任务中的现代数据规范化方法。确定线性归一化方法的不变性质。定义了多维数据归一化的两个基本原则：在测量尺度上保留自然值和归一化值的分布，以及在各种标准的归一化值区域中不存在相对于彼此的位移。提出了一种基于反向排序算法（ReS-algorithm）将成本标准的标准化值转换为利润标准的方法。