Rough Set Extension under Incomplete Information System with “?" Values

Classical rough set theory (RST) can't process incomplete information system (IIS) because it is based on an indiscernibility relation which is a kind of equivalent relation. In the literature a non-symmetric similarity relation based rough set model (NS-RSM) has been introduced as an extended model under IIS with “?" values directly. Unfortunately, in this model objects in the same similarity class are not necessarily similar to each other and may belong to different target classes. In this paper, a new inequivalent relation called Maximal Limited Consistent block relation (MLC) is proposed. The proposed MLC relation improves the lower approximation accuracy by finding the maximal limited blocks of indiscernible objects in IIS with “?" values. Maximal Limited Similarity rough set model (MLS) is introduced as an integration between our proposed relation (MLC) and NS-RSM. The resulted MLS model works efficiently under IIS with “?" values. Finally, an illustrative example is given to validate MLS model. Furthermore, approximation accuracy comparisons have been conducted among NS-RSM and MLS. The results of this work demonstrate that the MLS model outperform NS-RSM.