Multi-Class LR-Fuzzy Decision-Theoretic Rough Sets Based On Covering

Rough set theory is an important mathematical tool to deal with insufficient and incomplete information. As a promotion of probabilistic rough set model, decision-theoretic rough set is more beneficial to reduce decision risk because of introducing into loss function, so it has been widely applied in the actual decision. On the other hand, in the classical rough set theory, people research deeply the covering rough set model in recent years because equivalence relation or partition is so strict that it may limit the application of generalized. In this paper, we establish covering multi-class decision-theoretic rough set model by covering probabilistic rough set and decision-theoretic rough set.Firstly, considering the importance of loss function in decision-theoretic rough set, we provide covering-based multi-class decision-theoretic rough set model when loss function is an LR-fuzzy number, i.e., covering multi-class LR-fuzzy decision-theoretic rough set model; according to Bayes decision, the thresholds and decision rules are obtained on the basis of giving the expected loss function; meanwhile, we discuss the relationship between the thresholds and the risk attitude of decision maker and show the corresponding decision rules with decision makers of different attitude.Covering-based multi-class interval-valued decision-theoretic rough set model is discussed by using a certain ranking method and a degree of possibility ranking method, respectively. In the certain ranking method, the decision rules under a certain risk attitude of decision maker are derived by converting an interval into single. In the degree of possibility ranking method, we construct a preference com-plementary matrix and summarize all the combinations and their prerequisites by the flexibility of interval and the preference between interval values, and we obtain decision rules. Finally, a numerical example is given.