Limited Tolerance Relation with Affinity-Degree Approach to Improve Accuracy of Approximation in Incomplete Information Systems

Information systems (IS) can be analyzed using various approaches to support the decision-making process. While many datasets contain complete information, others are incomplete. One widely used approach for studying information systems is using rough set theory, introduced by Pawlak in 1982. Pawlak’s classical rough set theory (RST), while excellent for analyzing complete datasets, struggles with incomplete information systems (IIS) in which some attribute values are missing or unknown, which are common in real-world scenarios. Thus, RST’s inability to handle missing attribute values limits its use in real-world scenarios where information is often imperfect. To manage incomplete information systems, several techniques, extensions of RST, are employed, including tolerance relations, non-symmetric similarity/affinity relations, and limited tolerance relations. The limited tolerance relation is typically preferred, yet disregarding the affinity degree between objects may lead to a loss of information. Moreover, the limited tolerance has weaknesses that prevent optimal data classification. This paper introduces a new limited-tolerance relation approach for incomplete information systems, designed to account for the degree of affinity among objects. The proposed approach improved classification accuracy by providing a more precise approximation of object relationships within incomplete information systems (IIS). By integrating the affinity-degree, the new limited tolerance relation demonstrates greater precision and improves the accuracy of approximation and classification of objects in IIS, which is worthy of attention.