Multigranulation Decision-theoretic Rough Set in Ordered Information System

The decision-theoretic rough set model based on Bayesian decision theory is a main development tendency in the research of rough sets. To extend the theory of decision-theoretic rough set, the article devotes this study to presenting multigranulation decision-theoretic rough set model in ordered information systems. This new multigranulation decision-theoretic rough set approach is characterized by introducing the basic set assignment function in an ordered information system. It is addressed about how to construct probabilistic rough set and multigranulation decision-theoretic rough set models in an ordered information system. Moreover, three kinds of multigranulation decision-theoretic rough set model are analyzed carefully in an ordered information system. In order to explain probabilistic rough set model and multigranulation decision-theoretic rough set models in an ordered information system, an illustrative example is considered, which is helpful for applying these theories to deal with practical issues.