A set-valued semantic approach for handling missing attribute values in incomplete information systems

Abstract

In order to handle incomplete information systems, numerous extended rough set theories have been introduced, primarily because the classical version of this theory is limited to complete information systems. Even though these approaches can deal with incompleteness, however they have an issue due to poor performance in terms of uncertainty measures. Thus, this paper aims to handle incomplete information while improving the performance of uncertainty measures based on a new semantic interpretation using set-valued terms. Firstly, the interpretation of missing attribute values is proposed based on the semantics of set-valued information systems. The transformation from an incomplete to a complete one leads to a new information system called the Possible Equivalent Value-Set Information System (PEVS). Based on this system, a rough set model constructed from the similarity relation of a set-valued information system is developed. Similarity precision, which measures the similarity between sets of attributes, is also defined. Secondly, δ-rough set model induced by similarity precision is discussed. Based on this model, δ-accuracy, δ-roughness, and δ-approximation accuracy are constructed to measure the uncertainty in PEVS. Experimental analysis is conducted on real-life datasets to compare the performance of the uncertainty measures between the proposed approach and other rough set approaches. The results show that the proposed approach is feasible in handling incomplete information while providing better uncertainty measures in terms of accuracy, roughness, and approximation accuracy.