Generalized Rough Digraphs and Related Topologies

Abstract

The primary objective of this paper, is to introduce eight types of topologies on a finite digraphs and state the implication between these topologies. Also we used supra open digraphs to introduce a new types for approximation rough digraphs.

Supra Rough Membership Relations and Supra Fuzzy Digraphs on Related Topologies

“…Let D = (V(D), E(D)) be a finite digraph. The J-degree of , where , for all J {O, I, , , <O>, <I>, < >, < >}is defined by (a) , ( [3] Let D = (V(D), E(D)) be a finite digraph and : V(D) P(V(D)) be a mapping which assigns for all V(D) its J-degree in P(V(D)). The pair (D, ) is namable as a J-degree space (concisely J-DS).…”

“…The pair (D, ) is namable as a J-degree space (concisely J-DS). Theorem 2.3 [3] If is a J-DS, then the a family , for each , , for all J {O, I, , , <O>, <I>, < >, < >} is a topology on D. Definition 2.4 [3]…”