Noravshan to‘plamlarning arifmetikasi
![2 Kirish
Noravshan to’plam kons е psiyasi, Zad е ning fikricha, haqiqiy dunyoning
tizimlarida, ayniqsa odamlarni o’z ichiga olgan gumanistik tizimlarda noo’rin sun'iy
aniqlikka erishishni talab qilgan tizimlarning klassik nazariyasiga oid mat е matik
usullardan qoniqmaslik [35] hisobiga tug’ilgan.
Noravshan to’plamlar nazariyasi 1975 yilda amaliyotda qo’llanilgan bo’lib,
bunda Mamdani va Assilian (Mamdani and Assilian)lar oddiy bug’ dvigat е lini
boshqarish maqsadida birinchi noravshan hisoblagichni qurganlar [101,129].
А va В – X dagi mos ravishda μA va μB tegishlilik funksiyali ikkita noravshan
to’plam bo’lsin. A va B noravshan to’plamlarning cheklangan ko’paytmasi amali
ularning tegishlilik funksiyalariga qarab, quyidagi tarzda aniqlanadi.
А va В – X dagi mos ravishda
μA va μB tegishlilik funksiyali ikkita noravshan
to’plam bo’lsin. A va B noravshan to’plamlarning algebraik yig’indisi amali ularning
tegishlilik funksiyalariga qarab, quyidagi tarzda aniqlanadi:
A=0.03/1+0.1/2+0.28/3+0.52/4+0.75/5+0.94/6+1/7+0.96/8+0.87/9+
+0.71/10+0.55/11+0.4/12+0.28/13+0.19/14+0.12/15+0.06/16+0.02/17,
B=0/1+0/2+0/3+0.02/4+0.06/5+0.12/6+0.17/7+0.25/8+0.35/9+0.5/10+
+0.68/11+0.82/12+0.95/13+1/14+0.95/15+0.62/16+0.35/17+
+0.17/18+0.06/19,
A^+¿B¿ =0.03/1+0.1/2+0.28/3+0.52/4+0.75/5+0.94/6+1.0/7+0.96/8+
+0.91/9+0.86/10+0.86/11+0.88/12+0.96/13+1.0/14+0.95/15+
+0.62/16+0.35/17+0.17/18+0.06/19.
(1.2.5-rasmga qarang ).
0 2 4 6 8 10 12 14 16 18 20 0
0.2
0.4
0.6
0.8
1
1.2
x
m(x)
1.2.5-rasm . Noravshan to’plamlarning algebraik yig’indisi](https://docx.uz/documents/465d5e55-5f17-486f-a24a-163be2b735b1/page_2.png?v=1)
![61.2.8.b-rasm. Simmetrik ayirma
A noravshan to’plamning m-darajasi quyidagiga teng:μAm(x)= [μA(x)]m, ∀ x∈ X ,∀ m ∈R+
,
bu yerda
R+ - musbat aniqlangan haqiqiy sonlar to’plami.
Noravshan to’plamlar konsentrasiyasi, kengaytmasi .
A quyidagi universumda noravshan to’plam bo’lsin:
A= {(x:μA(x))|x∈ X }
.
U holda
Con m konsentrasiyalash amali yordamida darajaga ko’tarish natijasida
hosil bo’ladigan noravshan to’plamlar
Con mA= {(x:(μA(x))m)|x∈ X }
A ning konsentrasiyalari, kengaytma amali yordamida ildiz olish
dil nA= {(x:n√μA(x))|x∈X }
esa A ning kengaytmalari deyiladi.
Natija .
[μA(x)]n≤ μA(x)≤n√μA(x) ifoda hamma x∈X larda haqiqiy bo’lsa va
n>1
bo’lsa, u holda Con nA⊂A⊂dil nA qism to’plamlarning munosabati ham haqiqiy
hisoblanadi.
Noravshan to’plamning konsentrasiyasi: n=2.
A=0.03/1+0.1/2+0.21/3+0.37/4+0.57/5+0.8/6 +0,96/7+1.0/8+0.94/9+
+0.7/10+ 0.42/11+0.27/12+0.17/13+0.09/14+0.03/15,
А2 = 0.0009/1+0.01/2+0.044/3+0.137/4+0.325/5+0.64/6+0.92/7+1.0/8+
+0.884/9+0.49/10+0.174/11+0.07/12+0/03/13+0/01/14+0/0009/15.
( 1.2.9-rasmga qarang ).](https://docx.uz/documents/465d5e55-5f17-486f-a24a-163be2b735b1/page_6.png?v=1)
![80 2 4 6 8 10 12 14 16 18 2000.20.40.60.8 11.2
xm
(x)
1.2.10-rasm . Noravshan to’plamlarning kengaytmasi
Noravshan to’plamlarni konsentrasiya va kengaytma amallaridan foydalangan
holda almashtirish misollari quyida keltirilgan [6].
А
=
∫ μA(x)/x
Juda А
=
∫ [μA(x)]
2/x
Juda juda А
=
∫ [μA(x)]
4/x
Bir muncha А
=
∫ √μA(x)/x
Ozgina А
=
∫ 4√μA(x)/x
А emas
=
∫(1−μA(x))/x
Uncha А emas
=
∫ (1−[μA(x)]
2)/x
Noravshan nuqtalar, noravshan oraliqlar, noravshan sohalar .](https://docx.uz/documents/465d5e55-5f17-486f-a24a-163be2b735b1/page_8.png?v=1)
Noravshan to‘plamlarning arifmetikasi