Multigranulation Decision-theoretic Rough Set Based on Incomplete Interval-valued Information Systems

Abstract

Most of the previous results about decision-theoretic rough set do not take a variety of decision maker’s attitude into consideration, which is vulnerable environmental impact in reality. To solve such problems, a strategy is firstly introduced into multigranulation decision-theoretic rough set by the definition of decision function. Firstly, the equivalence classes are replaced with maximal consistent classes to establish the decision-theoretic rough set in an incomplete interval-valued information system. Then, based on the definition of decision function, the Sigmoid-multigranulation decision-theoretic rough set model and generalized multigranulation decision-theoretic rough set model are proposed and some properties of two models are studied in an incomplete interval-valued information system. Finally, the relation is illustrated between generalized multigranulation decision-theoretic rough set model and other related rough set models. This study suggests potential application areas and new research trends concerning decision-theoretic rough set.