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Properties of approximation operators over 1-neighborhood systems from the perspective of special granules

机译：从特殊颗粒的角度来看，近似运算符的特性

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摘要

As generalizations of Pawlak-neighborhood systems, 1-neighborhood systems with symmetry or transitivity are closely related to both partition spaces and covering spaces. In this article, we analyze the properties of a single covering-based approximation operator on symmetric or transitive 1-neighborhood systems. We also investigate the relationships between different covering-based approximation operators on them. Theoretically, we illuminate some necessary and sufficient conditions for 1-neighborhood systems being symmetric, transitive, or partitions with one or two approximation operators. To reduce potential computation complexity owing to these equivalent characterizations, objects dealt by approximation operators in this work are three particular kinds of granules, namely, points of universes, elements of 1-neighborhood systems, and cores of 1-neighborhood systems. As experimental results indicate, this study outdoes some related works in terms of computational efficiency, establishing the advantages of computing on these granules. Furthermore, our research has resulted in a solution to a problem posed by Yun et al. (Axiomatization and conditions for neighborhoods in a covering to form a partition.). (C) 2019 Elsevier Inc. All rights reserved.
机译：作为Pawlak邻域系统的概括，具有对称性或传递率的1个邻域系统与分区空间和覆盖空间密切相关。在本文中，我们在对称或传递1邻域系统上分析单个覆盖的近似运算符的性质。我们还研究了基于覆盖的近似运算符对它们之间的关系。从理论上讲，我们向1个邻域系统进行对称，传递或具有一个或两个近似运算符的分区的一些必要和充分条件。为了减少由于这些等同的特征而来的潜在计算复杂性，在这项工作中通过近似运算符处理的物体是三种特定种类的颗粒，即宇宙的点，1个邻域系统的元素，1个邻域系统的核心。随着实验结果表明，本研究在计算效率方面超越了一些相关的作品，建立了在这些颗粒上计算的优势。此外，我们的研究导致了云等人提出的问题的解决方案。 （覆盖物中邻域的公理化和条件，以形成分区。）。）。 （c）2019 Elsevier Inc.保留所有权利。

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