This paper presents a possibility of using of the rough sets theory for a reduction of attributes (criteria, data, information) of objects in multi-attributes decision analysis in a public administration system. It is investigated one natural dimension of reducing data which is to identify equivalence classes, i.e. objects that indiscernible using the available attributes, using approximation s...

Rough set is approximate representation of a crisp set. Rough set theory provides an approach to approximation of sets that leads to useful forms of granular computing. Several applications have revealed the need to extend the traditional rough set approach. A special place among various extensions is taken by the approach that replaces the relation based on equivalence with a tolerance relatio...

For further studying the theory of multigranulation rough sets (MGRS), we attempt to investigate a new theory on multigranulation rough sets from the topological view in this paper. We firstly explore multigranulation topological rough space and its topological properties by giving some new definitions and theorems. Then, topological granularity and topological entropy are proposed to character...

Rough sets are efficient for data pre-processing in data mining. Matroids are based on linear algebra and graph theory, and have a variety of applications in many fields. Both rough sets and matroids are closely related to lattices. For a serial and transitive relation on a universe, the collection of all the regular sets of the generalized rough set is a lattice. In this paper, we use the latt...

The paper presents a transition from the crisp rough set theory to a fuzzy one, called Alpha Rough Set Theory or, in short, a-RST. All basic concepts or rough set theory are extended, i.e., information system, indiscernibility, dependency, reduction, core, de®nability, approximations and boundary. The resulted theory takes into account fuzzy data and allows the approximation of fuzzy concepts. ...

Rough set theory is an important approach to granular computing. Type-1 fuzzy set theory permits the gradual assessment of the memberships of elements in a set. Hybridization of these assessments results in a fuzzy rough set theory. Type-2 fuzzy sets possess many advantages over type-1 fuzzy sets because their membership functions are themselves fuzzy, which makes it possible to model and minim...

Multi–granulation is an improvement of the classical rough set theory since it uses a family of binary relations instead of of a single indiscernibility relation for the constructing of approximation. In this paper, the multi–granulation rough set approach is further generalized into fuzzy environment. A family of fuzzy T–similarity relations are used to define the optimistic and pessimistic fu...