Optimal granulation selection for multi-label data based on multi-granulation rough sets

Multi-label decision data serve as an important extension of decision data, where several labels associate with each object. In classical multi-granulation rough set models, granulation selection is always related to positive region. However, some positive region reducts are not appropriate for multi-label data due to the fact that the uncertainties implied by labels are not totally considered. To overcome this deficiency in this paper, we propose the optimal granulation selection in multi-granulation and multi-label decision table. First, two kinds of fine and coarse decision functions are introduced, which represent all certainly and all possibly associated labels for the objects in the same class from optimistic and pessimistic viewpoints, respectively. Some relevant propositions and theorems are also carefully examined. Based on granular significance, a novel approach of optimal granulation selection is discussed. Finally, a heuristic algorithm is designed and an illustrative example is given to show the effectiveness of this algorithm. The main contribution of this paper is to extend the attribute reduction of multi-label data based on rough set theory, and overcome the limitation of the positive region reducts, in which the uncertainties implied by labels are not totally considered.