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Rough approximations based on bisimulations

机译：基于双仿真的粗略近似

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摘要

In recent years, rough set theory initiated by Pawlak has been intensively investigated. When the classical rough sets based on equivalence relations have been extended to generalized rough sets based on binary relations, the lower and upper rough approximations, which are the core concepts of rough set theory, have been generalized in several different ways. A common feature of these generalized approximations is that they use only "one step" information of the underlying relation to discern objects. By "one step" in a binary relation we mean that the ordered pair of the starting and end points of the step belongs to the relation. Motivated by a rich notion, bisimulation, appearing in various areas of computer science, we introduce a kind of lower and upper rough approximations for generalized rough sets in this paper. Our lower and upper approximations are based on bisimulations, in particular, bisimilarity, which is the largest bisimulation. Roughly speaking, bisimilar objects are regarded as indiscernible. We present some basic properties of the new lower and upper rough approximations and illustrate our motivation and the applicability of our results by examples. Moreover, we make a detailed comparison between the rough approximations based on the underlying relation and the rough approximations based on bisimilarity. In particular, we provide a necessary and sufficient condition for the consistency of the two kinds of rough approximations. (C) 2016 Elsevier Inc. All rights reserved.
机译：近年来，对Pawlak提出的粗糙集理论进行了深入研究。当将基于等价关系的经典粗糙集扩展到基于二元关系的广义粗糙集时，作为粗糙集理论的核心概念的上下粗糙逼近已经以几种不同的方式得到了概括。这些广义近似的一个共同特征是，它们仅使用与识别对象之间潜在关系的“一步”信息。所谓二元关系中的“一个步骤”，是指该步骤的起点和终点的有序对属于该关系。受计算机科学各个领域中出现的丰富概念，双仿真的启发，我们为广义粗糙集引入了一种上下粗近似。我们的上下近似基于双模拟，特别是双相似性，这是最大的双模拟。粗略地说，双相似的物体被认为是不可识别的。我们介绍了新的上下近似值的一些基本性质，并通过示例说明了我们的动机和结果的适用性。此外，我们在基于基础关系的粗略近似与基于双相似性的粗略近似之间进行了详细的比较。特别地，我们提供了两种粗略近似的一致性的充要条件。 （C）2016 Elsevier Inc.保留所有权利。

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  • 来源
    《高分子論文集》 |2017年第2期|49-62|共14页
  • 作者

    Zhu Ping; Xie Huiyang; Wen Qiaoyan;

  • 作者单位

    Beijing Univ Posts & Telecommun, Sch Sci, Beijing 100876, Peoples R China|Beijing Univ Posts & Telecommun, State Key Lab Networking & Switching Technol, Beijing 100876, Peoples R China;

    Beijing Forestry Univ, Coll Sci, Beijing 100083, Peoples R China;

    Beijing Univ Posts & Telecommun, State Key Lab Networking & Switching Technol, Beijing 100876, Peoples R China;

  • 收录信息 美国《科学引文索引》(SCI);
  • 原文格式 PDF
  • 正文语种 eng
  • 中图分类
  • 关键词

    Rough set; Generalized approximation space; Bisimulation; Bisimilarity; Labeled transition system;

    机译：粗糙集广义逼近空间双仿真双相似度标签过渡系统;

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