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.