A multiple-valued logic approach for multigranulation rough set model.

Rough sets have often been studied under a three-valued logic framework. In this paper, we attempt to extend the previous study in two ways. Firstly, we extend the previous study from single-granulation to multigranulation. Secondly, we study multigranulation rough set theory from the viewpoint of three-way decision. More precisely, we embody the idea of three-way decision theory in the definition of multigranulation rough set theory. This leads to an axiomatic definition of decision-oriented aggregation operators on 3={0,12,1}, which are quite different from those conjunctions proposed so far. Moreover, considering that a multigranulation rough set also divides the universe into five disjoint subsets, we present a five-valued semantics for multigranulation rough set model, and a kind of non-deterministic matrices is thus given.