Pawlak’s classical Rough set theory has been used in analyzing complete information systems, where all available objects in the information systems have non-missing attribute values. However, classical rough set theory cannot cope with the incomplete information systems where some attribute values are missing. Subsequently, the attribute selection is one of the main problems in incomplete information systems. Only few studies were proposed to the attribute selection problem in incomplete information systems due to its complexities, specifically on attribute selection. The most popular approaches are based on the extensions of classical rough set theory where it is relaxed by non-symmetric similarity relation and limited tolerance relation. From these two approaches, limited tolerance relation is more favorable. However, the approach has it weaknesses from the issues of imprecise and accuracy to evaluate the significant of subsets of attributes in incomplete information systems. To overcome these issues, we propose a new limited tolerance relation in rough set using conditional entropy to handle flexibility and precisely data classification. The novelty of the approach is that, unlike previous approach that use limited tolerance relation, it takes into consideration the similarity precision between objects in incomplete information systems and therefore this is the first work that used similarity precision. We also compared the proposed approach with limited tolerance relation approach, and the results show that the proposed approach achieves higher accuracy in the process of attribute selection in incomplete information systems.
Rough set; Limited tolerance relation; Similarity precision; Incomplete information system.