The Zero Divisor Graph of a Rough Semiring

Abstract

In this paper, we define the dominant set, zero divisor of the rough semiring (T, ∆, ∇). Also We prove that RS(X) is not a zero divisor for a dominant set X ⊆ U where U is the finite universal set on the set of all rough sets for the given information system together with the operations praba ∆ and praba ∇. We illustrate these concepts through examples.

Wiener Index of Rough Co-Zero Divisor Graph of a Rough Semiring

“…For any approximation space I = (U, R), the set of all Rough sets T was proved to be a lattice called Rough lattice having praba∆ and praba∇ as its least upper bound and greatest lower bound. Hence (T,∆,∇) is a semiring called rough semiring [9]. Theorem 2.1.…”

“…Let = { ( )| ⊆ } be the rough lattice [9] associated with the information system and * = − { (∅), ( )}. Moreover let = { ( )| ∈ ( )} be the rough ideal [5] on * .…”

“…In 201 [5]; [8][9][10] considered an approximation space = ( , ) where is nonempty finite set of objects and is an arbitrary equivalence relation on . With respect to the two operations ∆ and ∇ the set of all Rough sets on is proved to be a Semiring called namely Rough Semiring.…”

A Characterization of the Annihilators of a Rough Semiring

“…In [1], authors discussed the ideals of a commutative rough semiring and a characterization for the ideals of a rough semiring in terms of the principal ideals of the rough monoid for a given information system. Zero divisor graph of this rough lattice is constructed [8]. In [9], authors introduced the rough fuzzy ideals of a semiring and rough fuzzy prime ideals of a semiring.…”