There is a very important problem that has not attracted sufficient attention in academia, i.e., nonlinear field normalization citation counts at the paper level obtained using nonlinear field normalization methods cannot be added or averaged. Unfortunately, there are many cases adding or averaging the nonlinear normalized citation counts of individual papers that can be found in the academic literature, indicating that nonlinear field normalization methods have long been misused in academia. In this paper, we performed the following two research works. First, we analyzed why the nonlinear normalized citation counts of individual papers cannot be added or averaged from the perspective of theoretical analysis in mathematics: we provide mathematical proofs for the crucial steps of the analysis. Second, we systematically classified the existing main field normalization methods into linear and nonlinear field normalization methods. The above two research works provide a theoretical basis for the proper use of field normalization methods in the future, avoiding the continued misuse of nonlinear data. Furthermore, because our mathematical proof is applicable to all nonlinear data in the entire real number domain, our research works are also meaningful for the whole field of data and information science.

翻译：一个非常重要的问题没有在学术界引起足够重视,即非线性实地正常引用在使用非线性实地正常化方法获得的纸张水平上的非线性正常引用数无法增加或平均。不幸的是,许多案例增加了或平均了非线性正常引用个别论文数,这些案例可见于学术文献中,表明非线性实地正常化方法长期以来在学术界被滥用。在本文中,我们进行了以下两项研究工作。首先,我们从数学理论分析的角度分析了为什么不能增加或平均非线性正常引用个别论文数:我们为分析的关键步骤提供了数学证明。第二,我们系统地将现有的主要实地正常应用方法分类为线性和非线性实地正常化方法。上述两项研究工作为今后适当使用实地正常使用非线性方法提供了理论基础,避免继续滥用非线性数据。此外,由于我们的数学证据适用于整个实际数字领域的所有非线性数据,我们的研究工作对整个数据和信息科学领域也具有意义。</s>