Structured approximations as a basis for three-way decisions in rough set theory
Structured approximations as a basis for three-way decisions in rough set theory
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DOI：
10.1016/j.knosys.2018.11.022
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发表时间：
2019-02-01
影响因子：
8.8
通讯作者：
Yao, Yiyu
中科院分区：
文献类型：
--
作者：
Hu, Mengjun;Yao, Yiyu
粗糙集理论的一个主要应用是概念分析，用于根据对象的描述来确定对象是否是概念的实例。具有相同描述的对象形成等价类，等价类族用于定义粗糙集近似。当从近似中导出决策规则时，等价类的描述位于决策规则的左侧。因此，它是有用的，以保持近似的结构信息，即，在等价类方面的近似的组成。然而，现有的研究没有明确考虑结构信息。为了解决这个问题，我们在完整和不完整的信息表中引入结构化粗糙集近似，作为粗糙集三路决策的基础。在一个完整的表中，我们定义了一系列合取可定义的概念。结构化三向近似是由三组合取可定义的概念给出的三个结构化正、边界和负区域。通过采用可能世界语义，我们在不完备表中引入了合取可定义区间概念的概念，并利用它来构造结构化的三向近似。结构化近似的内部结构有助于粗糙集近似的合理语义，并直接和显式地与三路决策规则相关。(C)2018爱思唯尔B.V.保留所有权利。
A major application of rough set theory is concept analysis for deciding if an object is an instance of a concept based on its description. Objects with the same description form an equivalence class and the family of equivalence classes is used to define rough set approximations. When deriving the decision rules from approximations, the description of an equivalence class is the left-hand-side of a decision rule. Therefore, it is useful to retain structural information of approximations, that is, the composition of an approximation in terms of equivalence classes. However, existing studies do not explicitly consider the structural information. To address this issue, we introduce structured rough set approximations in both complete and incomplete information tables, which serve as a basis for three-way decisions with rough sets. In a complete table, we define a family of conjunctively definable concepts. The structured three-way approximations are three structured positive, boundary and negative regions given by three sets of conjunctively definable concepts. By adopting a possible-world semantics, we introduce the notion of conjunctively definable interval concepts in an incomplete table, which is used to construct the structured three-way approximations. The internal structure of structured approximations contributes to sound semantics of rough set approximations and is directly and explicitly related to three-way decision rules. (C) 2018 Elsevier B.V. All rights reserved.