A group decision-making (GDM) process is a social cognition process, which is a sub-topic of cognitive computation. The normalization of attribute values plays an important role in multi-attribute decision-making (MADM) and GDM problems. However, this research finds that the existing normalization methods are not always reasonable for GDM problems. To solve the problem of attribute normalization in GDM systems, some new normalization models are developed in this paper. An integrative study contributes to cognitive MADM and GDM systems. In existing normalization models, there are some bounds, such as \(\text {Max}(u_{j}), \text {Min}(u_{j}),\sum (u_{j}),\text {and} \sqrt {\sum (u_{j})^{2}}\). They are limited to a single attribute vector u_j. The bound of new normalization method proposed in this work is related to one or more attribute vectors, in which the attribute values are graded in the same measure system. These related attribute vectors may be distributed to all decision matrices graded by this decision system. That is, the new bound in developed normalization model is an uniform bound, which is related to a decision system. For example, this uniform bound can be written as one of \(\text {Max}(.), \text {Min}(.), \sum (.),\sqrt {\sum (.)^{2}}\). Some illustrative examples are provided. A practical application to the evaluation of software reliability is introduced in order to illustrate the feasibility and practicability of methods introduced in this paper. Some experimental and computational comparisons are provided. The results show that new normalization methods are feasibility and practicability, and they are superior to the classical normalization methods. This work has provided some new normalization models. These new methods can adapt to all decision problems, including MADM and GDM problems. Some important limitations and future research are introduced.

群体决策（GDM）过程是一种社会认知过程，它是认知计算的子主题。属性值的规范化在多属性决策（MADM）和GDM问题中起着重要作用。然而，这项研究发现，现有的归一化方法对于GDM问题并不总是合理的。为了解决GDM系统中属性归一化的问题，本文开发了一些新的归一化模型。综合研究有助于认知MADM和GDM系统。在现有的归一化模型中，存在一些界限，例如\（\ text {Max}（u_ {j}），\ text {Min}（u_ {j}），\ sum（u_ {j}），\ text {和} \ sqrt {\ sum（u_ {j}）^ {2}} \）。它们仅限于单个属性向量u _j。在这项工作中提出的新规范化方法的范围与一个或多个属性向量有关，其中属性值在同一度量系统中分级。这些相关的属性向量可以分布到由该决策系统分级的所有决策矩阵。也就是说，已开发的归一化模型中的新边界是统一边界，与决策系统有关。例如，此统一边界可以写为\（\ text {Max}（。），\ text {Min}（。），\ sum（。），\ sqrt {\ sum（。）^ {2}中的一个} \）。提供了一些说明性示例。介绍了一种在软件可靠性评估中的实际应用，以说明本文介绍的方法的可行性和实用性。提供了一些实验和计算比较。结果表明，新的归一化方法具有可行性和实用性，优于经典的归一化方法。这项工作提供了一些新的规范化模型。这些新方法可以适应所有决策问题，包括MADM和GDM问题。介绍了一些重要的局限性和未来的研究。