Double-quantitative variable consistency dominance-based rough set approach

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.