A Method to Handle the Missing Values in Multi-Criteria Sorting Problems Based on Dominance Rough Sets

Abstract

The handling of missing attribute values remains a challenging and problematic issue in data analysis. Imputation techniques are key procedures used to deal with missing attribute values. However, although these methods are widely used, they cause data bias. Rough set theory, a unique mathematical tool for decision making under uncertainty, overcomes this problem by properly adjusting the relationships. Rough sets are often preferred in both classification and sorting problems. The aim of sorting problems is to sort the objects in the decision table (DT) from best to worst and/or to select the best one. For this purpose, it is necessary to obtain a pairwise comparison table (PCT) from the DT. However, in the presence of missing values, the transformation from DT to PCT is not feasible because there are no ranking methods in the literature for sorting problems based on rough sets. To address this limitation, this paper presents a way to transform from DT to PCT and introduces a generalization of the relation belonging to the do not care type of missing values in the dominance-based rough set approach (DRSA) to the decision support tool jRank. We also adapted the DomLem algorithm to enable it to work in PCT with missing values. We applied our method step by step to a decision table with 11 objects and investigated the effect of missing values. The experimental results showed that our proposed approach captures the semantics of 'do not care' type missing values.