logo

Noravshan to’plamlarning arifmetikasi

Загружено в:

08.08.2023

Скачано:

0

Размер:

189.0390625 KB
1Mavzu: Noravshan to’plamlarning arifmetikasi
Reja:
Kirish
1. Noravshan to’plamlarning algebraik yig’indisi
2. Noravshan to’plamlarning cheklangan yig’indisi
Foydalanilgan adabiyotlar 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  3А  va  В  –  X  dagi mos  ravishda μA  va  	μB  tegishlilik funksiyali ikkita noravshan
to’plam   bo’lsin.   A   va   B   noravshan   to’plamlarning   chegaralangan   yig’indisi     amali
ularning tegishlilik funksiyalariga qarab quyidagi tarzda aniqlanadi:
A=0.06/1+0.17/2+0.31/3+0.5/4+0.67/5+0.82/6+0.93/7+1.0/8+0.98/9+
     +0.89/10+0.75/11+0.6/12+0.45/13+0.33/14+0.23/15+0.14/16+
     +0.08/17+0.03/18,
B=0.03/4+0.08/5+0.15/6+0.26/7+0.4/8+0.55/9+0.7/10+0.85/11+
    +0.95/12+1/0/13+0.96/14+0.85/15+0.6/16+0.33/17+0.18/18+0.09/19,	
A	˙¿B
=0.06/1+0.17/2+0.31/3+0.53/4+0.75/5+0.97/6+1.0/7+1.0/8+1.0/9+
   +1.0/10+1.0/11+1.0/12+1.0/13+1.0/14+1.0/15+0.64/16+0.41/17+
   +0.21/18+0.09/19.
( 1.2.6-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)
1.2.6 -rasm. Noravshan to’plamlarning cheklangan yig’indisi 
A=0.03/1+0.15/2+0.5/3+0.77/4+0.93/5+1.0/6+0.96/7+0.85/8+0.71/9+
     +0.55/10+0.4/11+0.27/12+0.18/13+0.11/14+0.05/15+0.01/16,
B=0.04/5+0.1/6+0.17/7+0.28/8+0.4/9+0.55/10+0.71/11+0.89/12+0.98/13+
     +1.0/14+0.93/15+0.65/16+0.2/17+0.06/18+0.01/19,	
A¿¿B
=0/1+0/2+0/3+0/4+0/5+0.1/6+0.13/7+0.13/8+0.11/9+0.1/10+0.11/11+0.16/12+0.16/1
3+0.11/14+0/15+0/16+0/17+0/18+0/19.
( 1.2.7-rasmga qarang ) . 40	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)1.2.7 -rasm.   A va B noravshan to’plamlarning cheklangan ko’paytmasi  
Cheklangan va simmetrik ayirmalar.
Norvshan   to’plamlarning   cheklangan   ayirmasi  	
|−|   quyidagi   formula   bilan
aniqlanadi:	
∀	x∈X	,μA|−|B(x)=	max	(0,μA(x)−	μB(x))
.	
A|−|B
 elementlari  B  dan ko’ra  A  ga ko’proq tegishli bo’lgan noravshan to’plam.
Noravshan   to’plamlarning   simmetrik   ayirmasi   –   bu,   B   ga   qaraganda   A   ga
ko’proq tegishli bo’lgan 	
¿t  elementlarning noravshan to’plami:	
∀	x∈X	,μA∇B(x)=|μA(x)−	μB(x)|
.
A   va   B   noravshan   to’plamlarning   cheklangan   va   simmetrik   ayirmalariga
misollar :
A=0.08/1+0.23/2+0.45/3+0.7/4+0.86/5+0.96/6+1/0/7+0.98/8+
     +0.92/9+0.82/10+0.67/11+0.47/12+0.3/13+0.13/14,
B=0.03/6+0.08/7+0.18/8+0.34/9+0.55/10+0.7/11+0.84/12+0.94/13+
+0.99/14+1.0/15+0.96/16+0.82/17+0.6/18+0.2/19,	
A|−|B
=0.08/1+0.23/2+0.45/3+0.7/4+0.86/5+0.93/6+0.92/7+0.8/8+
     +0.58/9+0.27/10+0/11, 5А∇В=0.08/1+0.23/2+0.45/3+0.7/4+0.86/5+0.96/6+1.0/7+0.98/8+
       0.92/9+0.82/10+0.03/11+0.36/12+0.65/13+0.86/14+1.0/15+
       0.96/16+0.82/17+0.6/18+0.2/9.
(1.2.8. а  va 1.2.8.b-rasmlarga 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)
1.2.8. а -rasm. Cheklangan ayirma	
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) 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 ). 70	2	4	6	8	10	12	14	16	
0
0.2
0.4
0.6
0.8
1
1.2	
x	
m(x)1.2.9-rasm .  Noravshan to’plamlarning konsentrasiyasi 
Noravshan to’plamning kengaytmasi  n=2.
A=0.03/2+0.06/3+0.13/4+0.23/5+0.4/6+0.61/7+0.82/8+0.96/9+
     +1.0/10+0.94/11+0.74/12+0.51/13+0.33/14+0.23/15+0.16/16+0.1/17+
     +0.05/18+0.02/19,	
A1/2
=0.17/2+0.25/3+0.36/4+0.48/5+0.63/6+0.78/7+0.9/8+0.98/9+1.0/10+
 +0.97/11+0.86/12+0.72/13+0.57/14+0.48/15+0.4/16+0.3/17+
                 +0.22/18+0.15/19
   ( 1.2.10-rasmga qarang ). 80	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)1.2.10-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 . 9Foydalanilgan adabiyotlar
1. Muhamediyeva   D.T.   Noravshan     axborot   holatida   sust   shakllangan
jarayonlarni   modellashtirish.   Toshkent:   O’zR   FA     matematika   va   axborot
texnologiyalar   instituti,   2010.   37   ta   jadval,   87   ta   rasm,   155   ta   bibl.atama,   400
bet. 
2. Артикова С., Мухамедиева Д.Т.  Информатизация регулирования развития
экономики Республики // Известия ВУЗов. –Т., 2000. №3.
3. Артикова С., Мухамедиева Д.Т. Реализация моделей принятия решений с
учетом   информационных   ситуаций   //Узбекский   журнал   энергетики   и
информатики.-Т. ,2000. №3.
4. Ахмедов   Т.М.   Мухамедиева   Д.Т.   Шодмонова   У.А.   Рациональное
управление   распределением   и   использованием   ресурсов   в   условиях
рыночной   экономики.   Доклады   международной   конференции
«Устойчивое   экономическое   развитие   и   эффективное   управление
ресурсами   в   Центральной   Азии».   ТГЭУ   и   Ноттенгемский   Трент
Университет (Великобритания). Ташкент-Ноттенгем. 2001. –С.14-17.

1Mavzu: Noravshan to’plamlarning arifmetikasi Reja: Kirish 1. Noravshan to’plamlarning algebraik yig’indisi 2. Noravshan to’plamlarning cheklangan yig’indisi Foydalanilgan adabiyotlar

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

3А va В – X dagi mos ravishda μA va μB tegishlilik funksiyali ikkita noravshan to’plam bo’lsin. A va B noravshan to’plamlarning chegaralangan yig’indisi amali ularning tegishlilik funksiyalariga qarab quyidagi tarzda aniqlanadi: A=0.06/1+0.17/2+0.31/3+0.5/4+0.67/5+0.82/6+0.93/7+1.0/8+0.98/9+ +0.89/10+0.75/11+0.6/12+0.45/13+0.33/14+0.23/15+0.14/16+ +0.08/17+0.03/18, B=0.03/4+0.08/5+0.15/6+0.26/7+0.4/8+0.55/9+0.7/10+0.85/11+ +0.95/12+1/0/13+0.96/14+0.85/15+0.6/16+0.33/17+0.18/18+0.09/19, A ˙¿B =0.06/1+0.17/2+0.31/3+0.53/4+0.75/5+0.97/6+1.0/7+1.0/8+1.0/9+ +1.0/10+1.0/11+1.0/12+1.0/13+1.0/14+1.0/15+0.64/16+0.41/17+ +0.21/18+0.09/19. ( 1.2.6-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) 1.2.6 -rasm. Noravshan to’plamlarning cheklangan yig’indisi A=0.03/1+0.15/2+0.5/3+0.77/4+0.93/5+1.0/6+0.96/7+0.85/8+0.71/9+ +0.55/10+0.4/11+0.27/12+0.18/13+0.11/14+0.05/15+0.01/16, B=0.04/5+0.1/6+0.17/7+0.28/8+0.4/9+0.55/10+0.71/11+0.89/12+0.98/13+ +1.0/14+0.93/15+0.65/16+0.2/17+0.06/18+0.01/19, A¿¿B =0/1+0/2+0/3+0/4+0/5+0.1/6+0.13/7+0.13/8+0.11/9+0.1/10+0.11/11+0.16/12+0.16/1 3+0.11/14+0/15+0/16+0/17+0/18+0/19. ( 1.2.7-rasmga qarang ) .

40 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)1.2.7 -rasm. A va B noravshan to’plamlarning cheklangan ko’paytmasi Cheklangan va simmetrik ayirmalar. Norvshan to’plamlarning cheklangan ayirmasi |−| quyidagi formula bilan aniqlanadi: ∀ x∈X ,μA|−|B(x)= max (0,μA(x)− μB(x)) . A|−|B elementlari B dan ko’ra A ga ko’proq tegishli bo’lgan noravshan to’plam. Noravshan to’plamlarning simmetrik ayirmasi – bu, B ga qaraganda A ga ko’proq tegishli bo’lgan ¿t elementlarning noravshan to’plami: ∀ x∈X ,μA∇B(x)=|μA(x)− μB(x)| . A va B noravshan to’plamlarning cheklangan va simmetrik ayirmalariga misollar : A=0.08/1+0.23/2+0.45/3+0.7/4+0.86/5+0.96/6+1/0/7+0.98/8+ +0.92/9+0.82/10+0.67/11+0.47/12+0.3/13+0.13/14, B=0.03/6+0.08/7+0.18/8+0.34/9+0.55/10+0.7/11+0.84/12+0.94/13+ +0.99/14+1.0/15+0.96/16+0.82/17+0.6/18+0.2/19, A|−|B =0.08/1+0.23/2+0.45/3+0.7/4+0.86/5+0.93/6+0.92/7+0.8/8+ +0.58/9+0.27/10+0/11,

5А∇В=0.08/1+0.23/2+0.45/3+0.7/4+0.86/5+0.96/6+1.0/7+0.98/8+ 0.92/9+0.82/10+0.03/11+0.36/12+0.65/13+0.86/14+1.0/15+ 0.96/16+0.82/17+0.6/18+0.2/9. (1.2.8. а va 1.2.8.b-rasmlarga 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) 1.2.8. а -rasm. Cheklangan ayirma 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)