Uni e si y o New Mexico
Explo a ion o Neu osophic b-semi-open and b-semi-closed Se s
Sudeep Dey1and Gau am Chand a Ray2,∗
1Depa men o Ma hema ics, Science College, Kok ajha , Assam, India; sudeep.dey[email p o ec ed]
2Depa men o Ma hema ics, Cen al Ins i u e o Technology Kok ajha , Assam, India;
[email p o ec ed]
∗Co espondence: [email p o ec ed]
Abs ac .In his w i e-up, we in oduce and de elop he concep s o neu osophic b-semi-open se s and neu-
osophic b-semi-closed se s, examining hei p ope ies and beha iou s unde a ious opological ope a ions.
Addi ionally, we explo e hei in e ac ions wi h o he es ablished classes o open se s wi hin neu osophic opo-
logical spaces. The no ions o neu osophic b-semi-in e io and neu osophic b-semi-closu e a e also p esen ed,
and hei nume ous p ope ies a e ho oughly in es iga ed.
Keywo ds: Neu osophic b-semi-open se ; Neu osophic b-semi-closed se ; Neu osophic b-semi-in e io ;
Neu osophic b-semi-closu e.)
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1. In oduc ion
The e m “ uzzy se ” was coined by L.A. Zadeh [25] in 1965, and a mo e gene alized e sion
known as he in ui ionis ic uzzy se was in oduced by K. A anasso [1] in 1986. Following
hese de elopmen s, Flo en in Sma andache [18, 19] u he ex ended he concep , gi ing ise
o he neu osophic se . A neu osophic se is cha ac e ized by h ee membe ship unc ions:
u h-membe ship, alsi y-membe ship, and inde e minacy-membe ship unc ions. No ably,
all h ee neu osophic componen s emain unbiased o one ano he . The in oduc ion o neu-
osophy spa ked global in e es , leading esea che s [20–22, 24] o con ibu e signi ican ly o
i s ad ancemen . Neu osophic heo y o e s a mo e gene al and sui able app oach o add ess-
ing eal-li e p oblems. Nume ous p ac ical-based wo ks [2, 7, 9] ha e been ca ied ou in a
neu osophic en i onmen .
In 2012, Salama & Alblowi [22] p oposed he concep o a neu osophic opological space,
a gene aliza ion o in ui ionis ic uzzy opological space de eloped by D.Coke [4] in 1997.
Subsequen ly, a ious concep s ela ed o neu osophic opological spaces we e de eloped by
S.Dey, G.C.Ray, Explo a ion o NBSO and NBSC Se s
Neu osophic Se s and Sys ems, Vol. 97, 2026
di e en esea che s [6, 12, 16, 17, 21, 23]. These included he in oduc ion o a ious ypes o
open and closed se s [3,5,10,11,13–15] connec ed o neu osophic opological spaces.
In 2018, Ebenanja e al. [8], desc ibed he concep o neu osophic b-open se s and in es i-
ga ed some p ope ies. In his a icle, we p esen a new ype o open se called neu osophic
b-semi-open se and examine some o i s undamen al p ope ies. Addi ionally, we de ine
and s udy neu osophic b-semi-in e io and neu osophic b-semi-closu e o a neu osophic se ,
explo ing some p ope ies associa ed wi h hese concep s.
2. P elimina ies
2.1. De ini ion: [18]
Le Xbe he uni e se o discou se. A neu osophic se Ao e Xis de ined as A=
{⟨x, TA(x),IA(x),FA(x)⟩:x∈X}, whe e he unc ions TA,IA,FAa e eal s anda d o non-
s anda d subse s o ]−0,1+[, i.e., TA:X→]−0,1+[,IA:X→]−0,1+[,FA:X→]−0,1+[
and −0≤ TA(x) + IA(x) + FA(x)≤3+.
The neu osophic se Ais cha ac e ized by he u h-membe ship unc ion TA,
inde e minacy-membe ship unc ion IA, alsi y-membe ship unc ion FA.
2.2. De ini ion: [24]
Le Xbe he uni e se o discou se. A single- alued neu osophic se Ao e Xis de ined as
A={⟨x, TA(x),IA(x),FA(x)⟩:x∈X}, whe e TA,IA,FAa e unc ions om X o [0,1] and
0≤ TA(x) + IA(x) + FA(x)≤3.
The se o all single alued neu osophic se s o e Xis deno ed by N(X).
Th oughou his a icle, a neu osophic se (NS, o sho ) will mean a single alued neu-
osophic se .
2.3. De ini ion: [12]
Le A, B ∈ N(X). Then
(i) (Inclusion): I TA(x)≤ TB(x),IA(x)≥ IB(x),FA(x)≥ FB(x) o all x∈X hen Ais
said o be a neu osophic subse o Band which is deno ed by A⊆B.
(ii) (Equali y): I A⊆Band B⊆A hen A=B.
(iii) (In e sec ion): The in e sec ion o Aand B, deno ed by A∩B, is de ined as A∩B=
{⟨x, TA(x)∧ TB(x),IA(x)∨ IB(x),FA(x)∨ FB(x)⟩:x∈X}.
(i ) (Union): The union o Aand B, deno ed by A∪B, is de ined as A∪B={⟨x, TA(x)∨
TB(x),IA(x)∧ IB(x),FA(x)∧ FB(x)⟩:x∈X}.
( ) (Complemen ): The complemen o he NS A, deno ed by Ac, is de ined as Ac=
{⟨x, FA(x),1− IA(x),TA(x)⟩:x∈X}
S.Dey, G.C.Ray, Explo a ion o NBSO and NBSC Se s
Neu osophic Se s and Sys ems, Vol. 97, 2026 382
( i) (Uni e sal Se ): I TA(x) = 1,IA(x) = 0,FA(x) = 0 o all x∈X hen Ais said o be
neu osophic uni e sal se and which is deno ed by ˜
X.
( ii) (Emp y Se ): I TA(x) = 0,IA(x) = 1,FA(x) = 1 o all x∈X hen Ais said o be
neu osophic emp y se and which is deno ed by ˜
∅.
2.4. De ini ion: [22]
Le {Ai:i∈△} ⊆ N(X), whe e △is an index se . Then
(i) ∪i∈△Ai={⟨x, ∨i∈△TAi(x),∧i∈△IAi(x),∧i∈△FAi(x)⟩:x∈X}.
(ii) ∩i∈△Ai={⟨x, ∧i∈△TAi(x),∨i∈△IAi(x),∨i∈△FAi(x)⟩:x∈X}.
2.5. De ini ion: [12]
Le τ⊆ N(X). Then τis called a neu osophic opology on Xi
(i) ˜
∅and ˜
Xbelong o τ.
(ii) A bi a y union o neu osophic se s in τis in τ.
(iii) In e sec ion o any wo neu osophic se s in τis in τ.
I τis a neu osophic opology on X hen he pai (X, τ) is called a neu osophic opological
space (NTS, o sho ) o e X. The membe s o τa e called neu osophic τ-open se s (o
neu osophic open se s o open se s, o sho ) in X. I o a neu osophic se A,Ac∈τ hen
Ais said o be a neu osophic τ-closed se (o neu osophic closed se o closed se , o sho )
in X.
2.6. De ini ion: [12]
Le (X, τ) be a NTS and A∈ N(X). Then he neu osophic
(i) in e io o A, deno ed by in (A), is de ined as in (A) = ∪{G:G∈τand G⊆A}.
(ii) closu e o A, deno ed by cl(A), is de ined as cl(A) = ∩{G:Gis a neu osophic closed
se and G⊇A}.
2.7. De ini ion: [12]
Le (X, τ) be a NTS and A, B ∈ N (X). Then
(i) [cl(A)]c=in (Ac)
(ii) [cl(A)]c=in (Ac)
(iii) cl(A∪B) = cl(A)∪cl(B)
(i ) cl(A∩B)⊆cl(A)∩cl(B)
( ) in (A∪B)⊇in (A)∪in (B)
( i) in (A∩B) = in (A)∩in (B)
S.Dey, G.C.Ray, Explo a ion o NBSO and NBSC Se s
Neu osophic Se s and Sys ems, Vol. 97, 2026 383
2.8. De ini ion: [8]
Le (X, τ) be a NTS and Gbe a NS o e X. Then Gis called a
(i) neu osophic b-open (NBO, o sho ) se i G⊆[in (cl(G))] ∪[cl(in (G))].
(ii) neu osophic b-closed (NBC, o sho ) se i G⊇[in (cl(G))] ∩[cl(in (G))].
2.9. Theo em: [8]
Le (X, τ) be an NTS and Gbe a NS o e X. Then
(i) Gis an NBO se i Gcis an NBC se .
(i) Gis an NBC se i Gcis an NBO se .
2.10. De ini ion: [8]
Le (X, τ) be an NTS and A∈ N(X). Then he neu osophic
(i) b-in e io o A, deno ed by bin (A), is de ined as bin (A) = ∪{G:Gis an NBO se in
Xand G⊆A}.
(ii) b-closu e o A, deno ed by bcl(A), is de ined as bcl(A) = ∩{G:Gis an NBC se in X
and G⊇A}.
2.11. De ini ion: [10]
Le (X, τ) and (Y, σ) be wo NTSs and A∈τ,B∈σ. Then (X, τ) is called neu osophic
p oduc ela ed o (Y, σ) i o any NSs C∈ N(X) and D∈ N(Y) whene e C⊈Acand
D⊈Bc⇒C×D⊆Acט
Y∪˜
X×Bc, he e exis A1∈τ,B1∈σsuch ha C⊆Ac
1o D⊆Bc
1
and Ac
1ט
Y∪˜
X×Bc
1=Acט
Y∪˜
X×Bc.
2.12. De ini ion: [10]
Le (X, τ) and (Y, σ) be wo NTSs such ha Xis neu osophic p oduc ela ed o Y. Then
o he NSs A∈ N (X) and B∈ N(Y), we ha e
(i) cl(A×B) = cl(A)×cl(B).
(ii) in (A×B) = in (A)×in (B).
3. Main Resul s
3.1. De ini ion:
Le (X, τ) be an NTS. A non-emp y NS A∈ N(X) is called a
(i) neu osophic b-semi-open se (NBSO se , o sho ) in Xi he e exis s an NBO se G
in Xsuch ha G⊆A⊆cl(G).
(ii) neu osophic b-semi-closed se (NBSC se , o sho ) in Xi he e exis s an NBC se
Gin Xsuch ha in (G)⊆A⊆G.
S.Dey, G.C.Ray, Explo a ion o NBSO and NBSC Se s
Neu osophic Se s and Sys ems, Vol. 97, 2026 384
The collec ion o all he neu osophic b-semi-open se s o he NTS (X, τ) will be deno ed
by NBSO(X).
3.2. Example:
Le X={a, b},τ={˜
∅,˜
X}. Ob iously (X, τ) is an NTS. Le us conside he NSs A=
{⟨a, 0.9,0,0⟩,⟨b, 0,1,1⟩}, B ={⟨a, 1,0,0⟩,⟨b, 0.7,0.6,0.4⟩}, C ={⟨a, 0,1,1⟩,⟨b, 0.4,0.4,0.7⟩}
and D={⟨a, 0,1,0.9⟩,⟨b, 1,0,0⟩} o e X. Now cl(A) = ˜
X⇒in (cl(A)) = ˜
Xwhich gi es
A⊆in (cl(A)), i.e. A⊆in (cl(A)) ∪cl(in (A)). The e o e Ais an NBO se . Clea ly
A⊆B⊆cl(A). The e o e Bis an NBSO se in X. Clea ly Dis an NBC se as Ac=D. Now
in (D) = ˜
∅and C⊆D. The e o e in (D)⊆C⊆Dand so, Cis an NBSC se in X.
3.3. P oposi ion:
(i) E e y NBO se in an NTS is an NBSO se .
(ii) E e y NBC se in an NTS is an NBSC se .
P oo : (i) Le (X, τ) be an NTS and Abe an NBO se in X. Since A⊆A⊆cl(A).
The e o e Ais an NBSO se .
(ii) Le (X, τ) be an NTS and Abe an NBC se in X. Then Acis an NBO se and so, Ac
is an NBSO se [by (i)]. The e o e, he e exis s an NBO se Bsuch ha B⊆Ac⊆cl(B)⇒
[cl(B)]c⊆A⊆Bc⇒in (Bc)⊆A⊆Bc⇒Ais an NBSC se as Bcis an NBC se .
3.4. P oposi ion:
(i) E e y neu osophic open se in an NTS is an NBSO se .
(ii) E e y neu osophic closed se in an NTS is an NBSC se .
P oo : (i) Le (X, τ) be an NTS and A∈τ. Then A=in (A). Now A⊆cl(A)⇒in (A)⊆
in (cl(A)) ⇒A⊆in (cl(A)) ⇒A⊆in (cl(A)) ∪cl(in (A)) ⇒Ais an NBO se . Thus o
A∈τ, he e exis s an NBO se Asuch ha A⊆A⊆cl(A). The e o e Ais an NBSO se .
Hence p o ed.
(ii) Le (X, τ) be an NTS and Abe a neu osophic closed se . Then Acis a neu osophic
open se and so, Acis an NBSO se [by (i)]. Then he e exis s an NBO se Bsuch ha
B⊆Ac⊆cl(B)⇒[cl(B)]c⊆A⊆Bc⇒in (Bc)⊆A⊆Bc⇒Ais an NBSC se as Bcis an
NBC se . Hence p o ed.
3.5. Rema k:
Con e ses o he p oposi ions 3.4(i) and 3.4(ii) a e no ue. We es ablish by he ollowing
example.
S.Dey, G.C.Ray, Explo a ion o NBSO and NBSC Se s
Neu osophic Se s and Sys ems, Vol. 97, 2026 385
Le X={a, b},τ={˜
∅,˜
X}. Ob iously (X, τ) is an NTS. Le us conside he NSs A=
{⟨a, 1,0,0⟩,⟨b, 0,1,1⟩} and B={⟨a, 0,1,1⟩,⟨b, 1,0,0⟩} o e X. Now in (cl(A)) = in (˜
X) = ˜
X
which gi es A⊆in (cl(A)), i.e. A⊆in (cl(A)) ∪cl(in (A)). The e o e Ais an NBO se and
so by 3.3(i), Ais an NBSO se . Clea ly Ais no a neu osophic open se . Thus an NBSO se
may no be a neu osophic open se .
Again Bis no a neu osophic closed se as Bc=Ais no a neu osophic open se . As A
is an NBO se , so by 2.9, Ac=Bis an NBC se and he e o e by 3.3(ii), Bis an NBSC se .
Thus an NBSC se may no be a neu osophic closed se .
3.6. P oposi ion:
Le (X, τ) be an NTS and G∈ N(X). Then Gis an NBSO se i Gcis an NBSC se .
P oo : Necessa y pa : Gis an NBSO se ⇒ he e exis s an NBO se Hsuch ha H⊆
G⊆cl(H)⇒[cl(H)]c⊆Gc⊆Hc⇒in (Hc)⊆Gc⊆Hc⇒Gcis an NBSC se as Hcis an
NBC se .
Su icien pa : Gcis an NBSC se ⇒ he e exis s an NBC se Hsuch ha in (H)⊆Gc⊆
H⇒Hc⊆G⊆[in (H)]c⇒Hc⊆G⊆cl(Hc)⇒Gis an NBSO se as Hcis an NBO se .
3.7. P oposi ion:
In an NTS, union o an a bi a y collec ion o NBSO se s is an NBSO se .
P oo : Le (X, τ) be an NTS and {Gλ:λ∈△}be an a bi a y collec ion o NBSO se s in
X, whe e △is an index se . Since Gλis an NBSO se , so he e exis s an NBO se Hλ o each
Gλ,λ∈△such ha Hλ⊆Gλ⊆cl(Hλ). Now Hλ⊆Gλ⊆cl(Hλ) o each λ∈△⇒ ∪λ∈△Hλ⊆
∪λ∈△Gλ⊆ ∪λ∈△cl(Hλ)⇒ ∪λ∈△Hλ⊆ ∪λ∈△Gλ⊆cl(∪λ∈△Hλ). Since a bi a y union o NBO
se s is an NBO se , so ∪λ∈△Hλis an NBO se . Thus he e exis s an NBO se ∪λ∈△Hλsuch
ha ∪λ∈△Hλ⊆ ∪λ∈△Gλ⊆cl(∪λ∈△Hλ). The e o e ∪λ∈△Gλis an NBSO se . Hence p o ed.
3.8. P oposi ion:
(i) In an NTS, union o a neu osophic open se and an NBSO se is an NBSO se .
(ii) In an NTS, union o an NBO se and an NBSO se is an NBSO se .
P oo : Ve y ob ious.
3.9. P oposi ion:
In an NTS, in e sec ion o an a bi a y collec ion o NBSC se s is an NBSC se .
P oo : Le (X, τ) be an NTS and {Gλ:λ∈△}be an a bi a y collec ion o NBSC se s in
X, whe e △is an index se . Then Gc
λis an NBSO se o each λ∈△⇒ ∪λ∈△Gc
λis an NBSO
se [by 3.7] ⇒(∩λ∈△Gλ)cis an NBSO se ⇒ ∩λ∈△Gλis an NBSC se [by 3.6]. Hence p o ed.
S.Dey, G.C.Ray, Explo a ion o NBSO and NBSC Se s
Neu osophic Se s and Sys ems, Vol. 97, 2026 386
3.10. P oposi ion:
(i) In an NTS, in e sec ion o a neu osophic closed se and an NBSC se is an NBSC se .
(ii) In an NTS, in e sec ion o an NBC se and an NBSC se is an NBSC se .
P oo : Ve y ob ious.
3.11. P oposi ion:
Le (X, τ) be an NTS and G∈ N(X). Then Gis an NBSO se i G⊆cl(bin (G)).
P oo : Necessa y pa : Since Gis an NBSO se , so he e exis s an NBO se Hsuch ha
H⊆G⊆cl(H). Ob iously H⊆bin (G) which implies cl(H)⊆cl(bin (G)). The e o e
G⊆cl(bin (G)).
Su icien pa : Gi en G⊆cl(bin (G)). Since bin (G)⊆G, so bin (G)⊆G⊆cl(bin (G)).
As bin (G) is an NBO se , so Gis an NBSO se .
3.12. P oposi ion:
Le (X, τ) be an NTS and G∈ N(X). Then Gis an NBSC se i G⊇in (bcl(G)).
P oo : Gis an NBSC se ⇔Gcis an NBSO se ⇔Gc⊆cl(bin (Gc))[by 3.11] ⇔Gc⊆
cl[(bcl(G))c]⇔Gc⊆[in (bcl(A))]c⇔G⊇in (bcl(A)).
3.13. P oposi ion:
Le Gbe an NBSO se in an NTS (X, τ). I K∈ N(X) is such ha bin (G)⊆K⊆bcl(G)
hen Kis an NBSO se in X.
P oo : Since Gis an NBSO se , so he e exis s an NBO se Hsuch ha H⊆G⊆cl(H).
Ob iously H⊆bin (G)⊆G⊆bcl(G). Again G⊆cl(H)⇒bcl(G)⊆bcl(cl(H)) ⊆cl(cl(H)) =
cl(H). Thus, H⊆bin (G)⊆K⊆bcl(G)⊆cl(H). The e o e, H⊆K⊆cl(H), which ensu es
ha Kis an NBSO se in X.
3.14. P oposi ion:
Le Gbe an NBSC se in an NTS (X, τ). I K∈ N(X) is such ha bin (G)⊆K⊆bcl(G)
hen Kis an NBSC se in X.
P oo : Gis an NBSC se ⇔Gcis an NBSO se . Now bin (G)⊆K⊆bcl(G)⇔[bin (G)]c⊇
Kc⊇[bcl(G)]c⇔bin (Gc)⊆Kc⊆bcl(Gc)⇔Kcis an NBSO se [by 3.13] ⇔Kis an NBSC
se in X.
S.Dey, G.C.Ray, Explo a ion o NBSO and NBSC Se s
Neu osophic Se s and Sys ems, Vol. 97, 2026 387
3.15. De ini ion:
Le (X, τ) be an NTS and A∈ N(X). Then he neu osophic b-semi-in e io o A, deno ed
by NBSin (A), is de ined as NBSin (A) = ∪{G:Gis an NBSO se in Xand G⊆A}.
3.16. P oposi ion:
Le (X, τ) be an NTS and A, B ∈ N (X). Then he ollowing hold.
(i) NBSin (A) is an NBSO se .
(ii) NBSin (A)⊆A
(iii) Ais an NBSO se i A=NBSin (A).
(i ) NBSin (˜
∅) = ˜
∅
( ) NBSin (˜
X) = ˜
X
( i) NBSin (NBSin (A)) = NBSin (A)
P oo :
(i) Since NBSin (A) is he union o NBSO se s, so by 3.7, NBSin (A) is an NBSO se .
(ii) Since NBSin (A) is he union o all NBSO se s con ained in A, so NBSin (A)⊆A.
(iii) Suppose ha Ais an NBSO se . Since A⊆Aand Ais an NBSO se , so A⊆
NBSin (A). Again NBSin (A)⊆A[by (ii)]. The e o e A=NBSin (A). Con e sely i
A=NBSin (A) hen Ais an NBSO se as NBSin (A) is NBSO se [by (i)]. Hence p o ed.
(i ) Since e e y neu osophic open se is an NBSO se , so ˜
∅is an NBSO se and he e o e
by (iii), NBSin (˜
∅) = ˜
∅.
( ) Since e e y neu osophic open se is an NBSO se , so ˜
Xis an NBSO se and he e o e
by (iii), NBSin (˜
X) = ˜
X.
( i) Since by (i), NBSin (A) is an NBSO se , so by (iii), NBSin (NBSin (A)) =
NBSin (A).
3.17. P oposi ion:
Le (X, τ) be an NTS and A, B ∈ N (X). Then he ollowing hold.
(i) A⊆B⇒NBSin (A)⊆NBSin (B)
(ii) NBSin (A∪B)⊇NBSin (A)∪NBSin (B).
(iii) NBSin (A∩B)⊆NBSin (A)∩NBSin (B).
P oo :
(i) Since A⊆Band NBSin (A)⊆A, so NBSin (A)⊆B. Since NBSin (A) is an NBSO
se such ha NBSin (A)⊆Band since NBSin (B) is he la ges NBSO se con ained in B,
so NBSin (A)⊆NBSin (B).
S.Dey, G.C.Ray, Explo a ion o NBSO and NBSC Se s
Neu osophic Se s and Sys ems, Vol. 97, 2026 388
(ii) A⊆A∪B⇒NBSin (A)⊆NBSin (A∪B). Simila ly NBSin (B)⊆NBSin (A∪B).
The e o e NBSin (A∪B)⊇NBSin (A)∪NBSin (B).
(iii) A∩B⊆A⇒NBSin (A∩B)⊆NBSin (A). Simila ly NBSin (A∩B)⊆NBSin (B).
The e o e NBSin (A∩B)⊆NBSin (A)∩NBSin (B).
3.18. De ini ion:
Le (X, τ) be an NTS and A∈ N (X). Then he neu osophic b-semi-closu e o A, deno ed
by NBScl(A), is de ined as NBScl(A) = ∩{G:Gis an NBSC se in Xand G⊇A}.
3.19. P oposi ion:
Le (X, τ) be an NTS and A∈ N (X). Then he ollowing hold.
(i) NBScl(A) is an NBSC se .
(ii) A⊆NBScl(A).
(iii) Ais an NBSC se i A=NBScl(A).
(i ) NBScl(˜
∅) = ˜
∅
( ) NBScl(˜
X) = ˜
X
( i) NBScl(NBScl(A)) = NBScl(A)
P oo :
(i) As NBScl(A) is he in e sec ion o NBSC se s, so by 3.9, NBScl(A) is an NBSC se .
(ii) As NBScl(A) is he in e sec ion o all NBSC se s con aining A, so A⊆NBScl(A).
(iii) Suppose ha Ais an NBSC se . Since A⊇Aand Ais an NBSC se , so NBScl(A)⊆A.
Again A⊆NBScl(A) [by (ii)]. The e o e A=NBScl(A). Con e sely i A=NBScl(A) hen
Ais an NBSC se as NBScl(A) is an NBSC se [by (i)]. Hence p o ed.
(i ) Since e e y neu osophic closed se is an NBSC se , so ˜
∅is an NBSC se and he e o e
by (iii), NBScl(˜
∅) = ˜
∅.
( ) Since e e y neu osophic closed se is an NBSC se , so ˜
Xis an NBSC se and he e o e
by (iii), NBScl(˜
X) = ˜
X.
( i) Since by (i), NBScl(A) is an NBSC se , so by (iii), NBScl(NBScl(A)) = NBScl(A).
3.20. P oposi ion:
Le (X, τ) be an NTS and A, B ∈ N (X). Then he ollowing hold.
(i) A⊆B⇒NBScl(A)⊆NBScl(B)
(ii) NBScl(A∪B)⊇NBScl(A)∪NBScl(B).
(iii) NBScl(A∩B)⊆NBScl(A)∩NBScl(B).
P oo :
S.Dey, G.C.Ray, Explo a ion o NBSO and NBSC Se s
Neu osophic Se s and Sys ems, Vol. 97, 2026 389
