On an Integration of Vague-Rough Sets Based on Vague Logical Operations

By defining a partial ordering relation on vague domain of unit interval, a definition of vague sets on a lattice V(I) is given in this paper. Applying the classical extension principle, the corresponding vague logical operators defined on V(I), are constructed with fuzzy logical operators on unit interval. The representations for a general model of vague rough approximation in a vague approximation space, as well as rough vague sets a transitional form from rough sets to vague rough sets, are presented via introduction of vague logical operations. Some basic properties of vague rough sets are discussed in this context.