不协调区间值决策系统中的α-上、下近似约简

doi:10.6040/j.issn.1671-9352.7.2021.216

摘要/Abstract

摘要： 研究了不协调区间值决策系统中基于α-容差关系的属性约简问题。针对一种常用的α-容差关系,给出了保持全部决策类的下近似不变的α-下近似约简和保持全部决策类的上近似不变的α-上近似约简的定义,证明了α-上近似约简与已有的α-广义决策约简和α-不确定性保持约简的等价性,以及α-下近似约简与已有的α-确定性保持约简的等价性。讨论了α-上近似约简和α-下近似约简之间的关系,并用例子加以验证。

关键词: 粗糙集, 不协调区间值决策系统, α-容差关系, α-上近似约简, α-下近似约简

Abstract: The focus is on the attribute reductions of inconsistent interval-valued decision systems based on α-tolerance relation. With respect to one kind of α-tolerance relations in inconsistent interval-valued decision systems, notions of α-lower and upper approximate reductions are defined, which keep the lower and upper approximations of all the decision classes unchanged, respectively. Subsequently, the equivalences among the α-upper approximate reduction and α-generalized decision reduction, α-uncertainty maintained reduction, and between α-lower approximate reduction and α-certainty maintained reduction are proved. Meanwhile, the relationships between α-lower approximate reduction and α-upper approximate reduction are discussed in detail, and verified by some examples.

Key words: rough set, inconsistent interval-valued decision system, α-tolerance relation, α-upper approximate reduction, α-lower approximate reduction

中图分类号:

TP18

张晓雨,李同军. 不协调区间值决策系统中的α-上、下近似约简[J]. 《山东大学学报(理学版)》, 2022, 57(5): 20-27.

ZHANG Xiao-yu, LI Tong-jun. α-lower and upper approximation reductions in inconsistent interval-valued decision systems[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2022, 57(5): 20-27.

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