Semiring on Roughsets

The Zero Divisor Graph of a Rough Semiring

“…Theorem 2.1. [6] (T, ∆, ∇) is a rough Semiring. In the following section, Zero Divisor and Zero Divisor graphs of a rough semiring is studied.…”

“…, RS({x 1 } ∪ {x 2 })} be the set of all rough sets and from [6] (T, ∆, ∇) be the Rough semiring then the zero divisors of the rough semiring T is denoted by Z(T ) where Z(T ) = {RS(X 1 ), RS(X 2 ), RS(X 3 ), RS(X 1 ∪ X 2 ), RS(X 1 ∪ X 3 ), RS(X 2 ∪ X 3 ), RS({x 1 }), RS({x 1 } ∪ X 2 ), RS({x 1 } ∪ X 3 ), RS({x 2 }), RS(X 1 ∪ {x 2 }), RS({x 2 } ∪ X 3 ), RS({x 1 } ∪ {x 2 })} Remark 3.9. The diameter of a rough zero divisor graph ≤ 3 and the rough zero divisor graph is connected.…”

“…Manimaran et al [2] studied the notion of regular rough ∇ monoid under Praba∇ in 2014. Praba et al [6] dealt semiring on the set of all rough sets also the authors discussed rough ideals on semirings in 2014. Zadeh [7] introduced the concept of fuzzy sets in his paper.…”

Domination Number of Rough Ideal based Rough Edge Cayley Graph

“…The concept of semiring on rough sets were discussed by B. Praba, et.al [7]. The concept of ideals on Rough sets have also been discussed by A.…”

Diabetes Disease Analysis Using Rough Soft Set

“…The authors Ghosh and Samanta [3] described some basic properties of rough sets and rough soft groups in 2013. Manimaran et al [4,5,6,13] discussed a rough set approach for medical diagnosis, an algorithm for deduction of time to detect alzheimer's disease and the concept of rough semiring on the set of all rough sets in 2015 also a review of medical diagnosis is given by the same authors in fuzzy environment in 2016. In 2018, the same authors [7] described an analysis for skin disease using IF set.…”