Abstract Rough set model with double quantification satisfies the requirement of quantitative information in practical applications, it has better fault tolerance than probabilistic rough set model considering only relative quantification and graded rough set model considering only absolute quantification. In this paper, two kinds of consistency levels are introduced from the perspective of double quantification in an ordered information system, namely relative quantitative consistency level and absolute quantitative consistency level. The single-quantitative variable consistency dominance-based rough set models based on these two kinds of quantitative consistency levels and their basic properties with the relevant three-way decision rules are discussed respectively in an ordered information system. Moreover, two kinds of double-quantitative variable consistency dominance-based rough set models and their basic properties with the relevant decision rules based on these two kinds of quantitative consistency levels are introduced. A consistency analysis of decision making in a practical case study is used to illustrate and interpret the double-quantitative variable consistency rough set models and the related decision rules in the ordered information system. The obvious shortcomings of dominance-based rough set approach (DRSA) without quantitative information are compared to explain the advantages of the quantitative variable consistency dominance-based rough sets with the two consistency levels in the practical case study.

中文翻译：

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基于双定量变量一致性优势的粗糙集方法

摘要 双重量化的粗糙集模型满足了实际应用中对量化信息的要求，比只考虑相对量化的概率粗糙集模型和只考虑绝对量化的分级粗糙集模型具有更好的容错性。本文从有序信息系统中双重量化的角度介绍了两种一致性水平，即相对定量一致性水平和绝对定量一致性水平。在有序信息系统中分别讨论了基于这两种定量一致性水平及其基本性质和相关三向决策规则的基于单定量变量一致性优势的粗糙集模型。而且，介绍了两种基于双定量变量一致性优势的粗糙集模型及其基本性质以及基于这两种定量一致性水平的相关决策规则。以实际案例研究中的决策一致性分析为例，对有序信息系统中的双量化变量一致性粗糙集模型及相关决策规则进行说明和解释。通过比较没有定量信息的基于优势的粗糙集方法（DRSA）的明显缺点，在实际案例研究中解释了具有两个一致性级别的定量变量一致性基于优势的粗糙集的优势。