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,

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