Fuzzy probabilistic rough sets and their corresponding three way decisions
The concept of probabilistic rough sets, as a main subject of this paper, is intimately connected with the concept of decision theoretic rough sets. This paper investigates fuzzy and interval valued fuzzy probabilistic rough sets within frameworks of fuzzy and interval valued fuzzy probabilistic approximation spaces, respectively. Four types of fuzzy probabilistic rough sets as well as interval valued fuzzy probabilistic rough sets are established in terms of different constraints on parameters. To find a suitable way of explaining and determining these parameters in each model, three way decisions are studied based on Bayesian minimum risk decision procedure, i.e. the decision theoretic rough set approach. The proposed models in this paper broaden applications of probabilistic rough sets due to their abilities of directly dealing with real valued and interval valued data.
Knowl. Based Syst.