On Granular Rough Computing with Missing Values

Granular Computing as a paradigm in Approximate Reasoning is concerned with granulation of available knowledge into granules that consists of entities similar with respect to a chosen measure in information content and with computing on such granules. Thus, operators acting on entities in a considered universe should factor through granular structures giving values similar to values of same operators in non– granular environment. Within rough set theory, proposed 25 years ago by ZdzisÃlaw Pawlak and developed thence by many authors, granulation is also a vital area of research. The first author developed a calculus with granules as well as a granulation technique based on similarity measures called rough inclusions along with a hypothesis that granules induced in data set universe of objects should lead to new objects representing them, and such granular counterparts should preserve information content in data. In this work, this hypothesis is tested with missing values in data and results confirm the hypothesis in this context.