id	author	title	date	pages	extension	mime	words	sentence	flesch	summary	cache	txt
ejpam-5392	Hosny, M.; Al-shami, Tareq	Employing a Generalization of Open Sets Defined by Ideals to Initiate Novel Rough Approximation Spaces with a Chemical Application	2024	28	.pdf	application/pdf	11430	819	82	1 Ask the the expert(s) to give a relation L over X; 2 Choose a λ type; 3 for every y ∈ X do 4 compute Gλ(y) 5 end 6 Construct a topology ϑλ = {V ⊆ X : ∀y ∈ V,Gλ(y) ⊆ V } on X; 7 Initiate C1 = {clλ(V ) : V ∈ ϑλ}; 8 Construct a θ-topology ϑθλ = {V ∈ ϑλ : intθλ(V ) Math, 17 (4) (2024), 3436-3463 3452 (i) V is αλ-exact ⇒ V is Sλ-exact ⇒ V is βλ-exact ⇒ δβλ-exact ⇒ V is L-θβλ-exact. (ii) V is Pλ-exact ⇒ V is βλ-exact ⇒ V is δβλ-exact ⇒ V is L-θβλ-exact. (iii) V is αλ-exact ⇒ V is Sλ-exact ⇒ V is βλ-exact ⇒ V is ∧ βλ -exact ⇒ V is L-θβλ- exact. (iv) V is Pλ-exact ⇒ V is βλ-exact ⇒ V is ∧ βλ -exact ⇒ V is L-θβλ-exact. (v) V is λ-exact ⇒ V is L-θβλ-exact. (vi) V is L-θβλ-rough ⇒ V is δβλ-rough ⇒ V is βλ-rough ⇒ V is Sλ-rough ⇒ V is αλ-rough. (vii) V is L-θβλ-rough ⇒ V is δβλ-rough ⇒ V is βλ-rough ⇒ V is Pλ-rough. (viii) V is L-θβλ-rough ⇒ V is ∧ βλ -rough ⇒ V is βλ-rough ⇒ V is Sλ-rough ⇒ V is αλ-rough. (ix) V is L-θβλ-rough ⇒ V is ∧ βλ -rough ⇒ V is βλ-rough ⇒ V is Pλ-rough. (x) V is L-θβλ-rough ⇒ V is λ-rough.	cache/ejpam-5392.pdf	txt/ejpam-5392.txt