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Grey
1.
1
2.
2
3.
DENG
• • • 3
4.
• • 5
5.
•
• • ⊗∈[a,∞] • ⊗∈(−∞,a) • ⊗∈[a,a] • 6
6.
⊗1 ∈ [a,
b], a〈b; ⊗ ∈ [c, d ], c〈d; 2 ⊗ + ⊗2∈[a + c,b + d ]; 1 − ⊗ = [−b,−a]; ⊗1 − ⊗2 = ⊗1 + (− ⊗2 ) ∈ [a − d, b − 7 c];
7.
• ab〉 o
⊗-1 ∈ [1/b,1/a]; • ⊗1 ⋅ ⊗2 ∈ [min{ac, ad , bc, bd}, max{ac, ad , bc, bd}]; • K ∈ℜ + K ⋅⊗∈[Ka, Kb] 8
8.
• 9
9.
ξ∈ (o,1)
• ɣoi ɣ (Xo , Xi ) k ɣ (xo (k), xi (k)) ɣoi (k) 10
10.
•
• 3 • 4 • 5 • 6 • 7 • 8 • 11
11.
(g/cm3)
(Mpa) (GPA) [530, 580] [10, 20] [6, 9] [180,200] [25,35] [380, 420] [10, 15] [1.2,4.2] [80,100] [5,15] [330, 380] [1, 5] [1, 4] [3400,3600] [67,78] [470, 530] [1, 2] [0.5, 3] [3900,4100] [345,355] [220, 280] [9, 12] [0.5,2] [3500,3700] [115,125] 12
12.
• •
Wl ∊ [0.10,0.10], • w2 ∊[0.20,0.20], • w3 ∊[0.20,0.20], • w4 ∊[0.30, 0.30], • w5 ∊[0.40,0.40] 13
13.
•
Stiffness Tensile strength Density Elongation at break Max temp • • • • • • • • ||Ai|| 355 4100 9 20 580 ||x||=max(max(|a1-|,|a1+|), max(|a2-|,|a2+|),…, max(|a3-|,|a3+|) 14
14.
•
Stiffness Tensile Density Elongation Max temp strength at break • • • 4 • 5 • 6 • 7 • Wi [0.1,0.1] [0.2,0.2] [0.2,0.2] [0.3,0.3] 8 [0.4,0.4] X3,2 X3,2 [ =[0.8293,0.8781] ||x||=max(max(180,200),) max(80,100, max(3400,3600),max(3900,4100), max(3500,3700) 15
15.
•
G1 G2 G3 G4 G5 • A1 • A2 • 4 A3 • 5 A4 • 6 A5 • 7 Wi [0.1,0.1] [0.2,0.2] [0.2,0.2] [0.3,0.3] [0.4,0.4] • 8 X3,2 [0.8293*0.2,0.8781*0.2 =[0.1658,0.1756] X3,2 16
16.
•
G1 G2 G3 G4 G5 • A1 • A2 • 4 A3 • 5 A4 • 6 A5 • 7 U0 [0.0972,0.1] [0. 9 ,0.2] [0.133,0.2] [0.15,0.225] [0.365,0.4] • 8 17
17.
•
• • • 4 • 5 • 6 • 7 • 8 X3,2 =(ro2 - -0.1658)+(0.2-0.1756) 0.0488 ∆3,2 r3,2)= 18
18.
•
• • • 4 ɣ(xo(k),x1(k)) 0.5383 0.3614 1.0000 1.000 1.0000 • 5 ɣ(xo(k),x2(k)) 0.5233 0.3554 0.4918 0.7372 0.4959 • 6 • 7 ɣ(xo(k),x3(k)) 0.5734 0.8116 0.4853 0.3688 0.4327 • 8 ɣ(xo(k),x4(k)) 1.0000 1.0000 0.4514 0.3418 0.7348 ɣ(xo(k),x5(k)) (0.6187) 0.8436 0.4309, 0.6091 0.3333 19 ɣ(xo(2),x3(2))= (0+0.5*(0.4207))/(0.0488+(0.5)*(0.4207))=0.8116
19.
•
• • • ɣ(xo,x1)=1/5 *(0.5383, 0.3614,1.0000,1.0000,1.0000)=0.7799 4 • 5 ɣ(xo,x1)=1/5 *(0.5233, 0.3554, 0.4918, 0.7372, 0.4959)= 0.5187 6 • • 7 ɣ(xo,x1)=1/5 *(0.5734, 0.8117, 0.4853, 0.3688, 0.4327)= • 0.5344 8 ɣ(xo,x1)=1/5 *(1.0000,1.0000, 0.4514, 0.3418, 0.7348)= 0.7056 20 ɣ(xo,x1)=1/5 *(0.6187, 0.8436, 0.4309, 0.6091,
20.
21
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