Lattice for Rough Intervals

This paper deals with the rough interval approach on lattice theory. In the interval-set model, a pair of sets is referred to as the lower and upper bounds which de¯ne a family of sets. A signi¯cant di®erence between these concepts lies in the de¯nition and interpretation of their extended set-theoretic operators. The operators in the rough-set model are not truth-functional, while the operators in the interval-set model are truth-functional. We have showed that the collection of all rough intervals in an approx- imation space forms a distributive lattice. Some important results are also proved. Finally, an example is considered to illustrated the paper.