As an important technology in artificial intelligence, Granular Computing 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 Granular Computing. By generating centroids (prototypes) and partition matrix, fuzzy clustering is a commonly encountered way of information granulation. As a reverse process of granulation, degranulation involves data reconstruction completed on a basis of the granular representatives (decoding information granules into numeric data). 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 process becomes. 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 reconstruction (degranulation), in this study, we develop an augmented scheme through modifying the partition matrix. By proposing the augmented scheme, we elaborate 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. 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. The results obtained on both synthetic and publicly available datasets are reported to show the enhancement of the data reconstruction performance thanks to the proposed method. It is pointed out that by using the proposed approach in some cases the reconstruction errors can be reduced close to zero by using the proposed approach.

粒计算作为人工智能中的一项重要技术，作为一种新的多学科范式出现，近年来备受关注。形成大量数值数据的抽象和有效表征的信息颗粒已被认为是颗粒计算的基本结构。通过生成质心（原型）和分区矩阵，模糊聚类是一种常见的信息粒度化方式。脱粒是粒化的逆过程，是在粒代表的基础上完成数据重构（将信息粒解码为数值数据）。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，造粒过程的性能变得更好。然而，现有的脱粒方法通常无法恢复原始数值数据，这是造成重构误差发生的重要原因之一。为了提高重建（脱粒）的质量，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，我们详细阐述了一系列新的造粒-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。通过修改分区矩阵，新的分区矩阵是通过一系列矩阵运算构建的。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。据报告，在合成数据集和公开可用数据集上获得的结果表明，由于所提出的方法，数据重建性能得到了增强。指出在某些情况下通过使用所提出的方法，可以通过使用所提出的方法将重构误差减小到接近于零。据报告，在合成数据集和公开可用数据集上获得的结果表明，由于所提出的方法，数据重建性能得到了增强。指出在某些情况下通过使用所提出的方法，可以通过使用所提出的方法将重构误差减小到接近于零。据报告，在合成数据集和公开可用数据集上获得的结果表明，由于所提出的方法，数据重建性能得到了增强。指出在某些情况下通过使用所提出的方法，可以通过使用所提出的方法将重构误差减小到接近于零。