Òåîðåìà Äþáóà-Ïðàéäà Ïóñòü A, B íå÷åòêèå ÷èñëà, è îïåðàöèè ñëîæåíèÿ, óìíîæåíèÿ, âû÷èòàíèÿ è äåëåíèÿ îïðåäåëåíû ïî ïðèíöèïó ðàñøèðåíèÿ. Òîãäà: 1. A + B , A − B , A · B , A/B íå÷åòêèå ÷èñëà; Òåîðåìà Äþáóà-Ïðàéäà Ïóñòü A, B íå÷åòêèå ÷èñëà, è îïåðàöèè ñëîæåíèÿ, óìíîæåíèÿ, âû÷èòàíèÿ è äåëåíèÿ îïðåäåëåíû ïî ïðèíöèïó ðàñøèðåíèÿ. Òîãäà: 1. A + B , A − B , A · B , A/B íå÷åòêèå ÷èñëà; 2. Âûïîëíÿåòñÿ dA + Be = dAe + dBe dA − Be = dAe − dBe dA · Be = dAe · dBe dA/Be = dAe/dBe. Òåîðåìà Äþáóà-Ïðàéäà Ïóñòü A, B íå÷åòêèå ÷èñëà, è îïåðàöèè ñëîæåíèÿ, óìíîæåíèÿ, âû÷èòàíèÿ è äåëåíèÿ îïðåäåëåíû ïî ïðèíöèïó ðàñøèðåíèÿ. Òîãäà: 1. A + B , A − B , A · B , A/B íå÷åòêèå ÷èñëà; 2. Âûïîëíÿåòñÿ dA + Be = dAe + dBe dA − Be = dAe − dBe dA · Be = dAe · dBe dA/Be = dAe/dBe. Z |A| = µA (a)ada a∈R Íå÷åòêèå îïåðàöèè 2 2,005 µ 1 2 x Íå÷åòêèå îïåðàöèè 2 2,005 4 4,000 µ 1 2 4 x Íå÷åòêèå îïåðàöèè 4 4,000 2+2 4,004 µ 1 4 x Íå÷åòêèå îïåðàöèè µ 4 4,000 2+2 4,004 2·2 4,620 1 4 x Íå÷åòêèå îïåðàöèè 4 4,000 2+2 4,004 µ 2·2 4,620 1 8/2 5,456 4 x Íå÷åòêèå îïåðàöèè µA (x) = exp x−dAe K K = 1 T (x, y ) = xy S(x, y ) = max(x, y ) µ 2 4 4,000 2+2 4,004 2·2 4,620 x Íå÷åòêèå îïåðàöèè µA (x) = exp x−dAe K K = 0.3 T (x, y ) = xy S(x, y ) = max(x, y ) µ 2 4 4,000 2+2 4,005 2·2 4,059 x Íå÷åòêèå îïåðàöèè µA (x) = exp x−dAe K K = 1 T (x, y ) = xy S(x, y ) = max(x, y ) µ 2 4 4,000 2+2 4,004 2·2 4,620 x Íå÷åòêèå îïåðàöèè µA (x) = exp x−dAe K K = 3 T (x, y ) = xy S(x, y ) = max(x, y ) µ 2 4 4,131 2+2 4,372 2·2 4,977 x Íå÷åòêèå îïåðàöèè µA (x) = exp x−dAe K K = 1 T (x, y ) = xy S(x, y ) = max(x, y ) µ 2 4 4,000 2+2 4,004 2·2 4,620 x Íå÷åòêèå îïåðàöèè µA (x) = 2 x−dAe max 0, 1 − K K = 1 T (x, y ) = xy S(x, y ) = max(x, y ) µ 4 4,000 2+2 4,005 2·2 4,392 x Íå÷åòêèå îïåðàöèè µA (x) = exp x−dAe K K = 1 T (x, y ) = xy S(x, y ) = max(x, y ) µ 2 4 4,000 2+2 4,004 2·2 4,620 x Íå÷åòêèå îïåðàöèè µA (x) = exp x−dAe K K = 1 T (x, y ) = min(x, y ) S(x, y ) = max(x, y ) µ 2 4 4,000 2+2 4,012 2·2 4,783 x Íå÷åòêèå îïåðàöèè µA (x) = exp x−dAe K K = 1 T (x, y ) = xy S(x, y ) = max(x, y ) µ 2 4 4,000 2+2 4,004 2·2 4,620 x Íå÷åòêèå îïåðàöèè µA (x) = exp x−dAe K K = 1 T (x, y ) = xy S(x, y ) = x + y − xy µ 2 4 4,000 2+2 4,074 2·2 4,979 x Ðàçìûâàíèå 6 6,000 µ x Ðàçìûâàíèå 6 6,000 3+3 6,001 µ x Ðàçìûâàíèå 6 6,000 3+3 6,001 2 + 2 + 2 6,003 µ x Ðàçìûâàíèå 6 6,000 3+3 6,001 2 + 2 + 2 6,003 1+. . .+1 5,961 µ x Ðàçìûâàíèå 6 6,000 3+3 6,001 2 + 2 + 2 6,003 1+. . .+1 5,961 2·3 6,411 µ x Ðàçìûâàíèå 6 6,000 3+3 6,001 2 + 2 + 2 6,003 1+. . .+1 5,961 µ 2·3 6,411 6·1 5,415 x Ðàçìûâàíèå A+B B a+b f (a, b) = b µC (c) = max µA (a)µB (b) C= a,b f (a,b)=c µ x