As an important technology in artificial intelligence Granular Computing (GrC) has emerged as a new multi-disciplinary paradigm and received much attention in recent years. Information granules forming an abstract and efficient characterization of large volumes of numeric data have been considered as the fundamental constructs of GrC. By generating prototypes and partition matrix, fuzzy clustering is a commonly encountered way of information granulation. Degranulation involves data reconstruction completed on a basis of the granular representatives. Previous studies have shown that there is a relationship between the reconstruction error and the performance of the granulation process. Typically, the lower the degranulation error is, the better performance of granulation is. However, the existing methods of degranulation usually cannot restore the original numeric data, which is one of the important reasons behind the occurrence of the reconstruction error. To enhance the quality of degranulation, in this study, we develop an augmented scheme through modifying the partition matrix. By proposing the augmented scheme, we dwell on a novel collection of granulation-degranulation mechanisms. In the constructed approach, the prototypes can be expressed as the product of the dataset matrix and the partition matrix. Then, in the degranulation process, the reconstructed numeric data can be decomposed into the product of the partition matrix and the matrix of prototypes. Both the granulation and degranulation are regarded as generalized rotation between the data subspace and the prototype subspace with the partition matrix and the fuzzification factor. By modifying the partition matrix, the new partition matrix is constructed through a series of matrix operations. We offer a thorough analysis of the developed scheme. The experimental results are in agreement with the underlying conceptual framework

中文翻译：

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粒度计算：通过改进的分区矩阵进行脱粒的增强方案

作为人工智能中的一项重要技术，粒计算（GrC）作为一种新的多学科范式出现，近年来备受关注。形成大量数字数据的抽象和有效表征的信息颗粒已被认为是 GrC 的基本结构。通过生成原型和分区矩阵，模糊聚类是一种常见的信息粒化方法。去颗粒是在颗粒代表的基础上完成的数据重构。先前的研究表明，重建误差与造粒过程的性能之间存在关系。通常，脱粒误差越低，造粒性能越好。然而，现有的脱粒方法通常不能恢复原始数值数据，这是造成重构误差发生的重要原因之一。为了提高脱粒质量，在本研究中，我们通过修改分区矩阵开发了一种增强方案。通过提出增强方案，我们专注于一系列新的造粒-脱粒机制。在构造方法中，原型可以表示为数据集矩阵和分区矩阵的乘积。然后，在脱粒过程中，重构的数值数据可以分解为划分矩阵和原型矩阵的乘积。颗粒化和去颗粒化都被认为是数据子空间和原型子空间之间具有分区矩阵和模糊化因子的广义旋转。通过修改分区矩阵，通过一系列矩阵运算构造新的分区矩阵。我们对开发的方案进行了彻底的分析。实验结果与基础概念框架一致