More results on rough sets via neighborhoods of graphs with finite path

Abstract

Abstract Rough set theory had been proposed by Pawlak in the early of 1982. The theory is a new mathematical tool to deal with vagueness and imperfect knowledge. In this paper, we study neighborhoods for vertices of graphs with length that at most 2 edges. A new binary relation induced from a simple graph is defined and more properties of star definability which based on reflexive and transitive relation will be discussed. So, we investigate N-star lower and N-star upper approximations, for every subset B of a set of vertices V of a graph G. The relationship between the star set and independent set will be discussed.