RUI: Knowledge Processing with Interval Methods

摘要：基于区间方法的知识处理本研究探讨了基于区间方法的知识处理。现代技术已经从观测、实验和科学模拟中发展出大量数据集。然而，如何有效地处理这些数据集以有效地发现知识仍然是一个重大挑战。用区间方法处理知识有其内在的优点。首先，定性属性通常表示为数据属性的范围，而不是特定的点。通过将属性值分组到有意义的区间，可以忽略不重要的数量差异，从而增加对定性处理的关注。更重要的是，区间值属性比点包含更多的信息，表示可变性和不确定性。最后，在实际应用中，区间值计算结果比点值计算结果更有意义和实用。本研究涉及数据集区间表示、区间排序关系、区间矩阵分解与主成分分析、区间解的内逼近、区间值规则生成的理论与算法，以及用区间方法处理知识的便携式计算环境。这项研究扩展了目前关于区间值数据的知识。本研究的理论和算法结果应具有广泛的计算适用性，特别是在处理可变性和不确定性方面。此外，该研究项目提高了以本科为主的大学的教育质量，为阿肯色州培养了更多高质量的计算机科学毕业生，阿肯色州在STEM劳动力培训方面落后于全国。

Abstract - RUI: Knowledge processing with interval methodsThis research investigates knowledge processing with interval methods. Modern technologies have evolved collections of massive datasets from observations, experiments, and scientific simulation. However, it remains a significant challenge to effectively process these datasets to discover knowledge effectively and efficiently. Knowledge processing with interval methods has intrinsic merit. First, qualitative properties are often presented as ranges of data attributes rather than specific points. By grouping attribute values into meaningful intervals, insignificant quantitative differences can be ignored, allowing an increased focus on qualitative processing. More importantly, interval-valued attributes contain more information than points, representing variability and uncertainty. Finally, in practice, interval-valued computational results can be more meaningful and useful than point values. This study involves theories and algorithms for dataset interval representation, interval ordering relations, interval matrix decomposition and principal component analysis, inner approximation of interval solutions, interval-valued rule generation, and a portable computational environment for knowledge processing with interval methods. This research expands current knowledge on interval-valued data. The theoretical and algorithmic results of this research should have broad applicability to computing, especially for handling variability and uncertainty. In addition, this research project enhances the quality of education at a predominantly undergraduate institution and produce more high quality computer science graduates for Arkansas, a state which lags behind the nation in STEM workforce training.