Probability Covering-based Rough Set And L-fuzzy Variable Precision Covering-based Rough Set

The covering-based rough set model is considered as a generalization of the rough set model. This thesis studies probability covering-based rough set and L-fuzzy variable precision covering-based rough set. This thesis mainly includes three parts.The first, we discuss about probabilistic covering-based rough set and theoretic-decision covering-based rough set. Here, we give out some kind of uncertainty mea-sures in covering-based rough set and the degree of covering-based rough membership. Through out the degree of covering-based rough membership, we define ?,?-fuzzy prob-abilistic covering-based rough set. A similar idea can be applied into three-way deci-sions theory to obtain covering-based three-way decisions which is the main work of this study. In the framework of three-way decisions, three-way decisions based on coverings are first studied by applying the approach of decision-theoretic rough set. Then, we apply the Bayesian decision procedure theory into covering decision systems.The second, we mainly studies fuzzy variable precision rough approximation op-erators based on fuzzy coverings of a universe of discourse. We built two pairs (TI, IT) lower/upper fuzzy variable precision rough approximation operators and (II, TT) lower/upper fuzzy variable precision rough approximation operators on U. After that, we investigate their basic properties, such as topology properties, dual properties. Be-sides, we also set two pairs (TI,IT) lower/upper fuzzy variable precision rough ap-proximation operators and (II, TT) lower/upper fuzzy variable precision rough ap-proximation operators on U based on a family of R-foresets and R-aftersets, which are degenerated into the fuzzy-neighborhood-oriented fuzzy variable precision rough approximation operators. Finally, we find out an equivalent condition between the fuzzy-neighborhood-oriented fuzzy variable precision rough approximation operators and fuzzy variable precision rough approximation operators.The third, we construct L-fuzzy covering variable precision rough set (L-FCVPRs) and mainly study some properties of type I and type ? L-fuzzy covering lower and upper approximation operators of L-fuzzy sets on X. Topology properties of type I and type ? L-fuzzy covering lower and upper approximation operators are also discussed through a fuzzy interior operator and fuzzy closure operator. Also, we investigate the dual properties and comparison between L-fuzzy covering variable precision rough approximation operators.