پایان نامه ارشد درمورد مقایسات زوجی

المللی) از عبارات کلامی و مقادیر فازی (اعداد مثلثی) به شرح جدول 4-10 استفاده شده است.

جدول 4-10 عبارات کلامی به کار رفته در تحقیق و مقادیر معادلشان
عبارت کلامی
مقدار فازی
بدون تأثیر
(0.300 ,0.100 ,0.000)
تأثیر خیلی کم
(0.500 ,0.300 ,0.100)
تأثیر کم
(0.700 ,0.500 ,0.300)
تأثیر زیاد
(0.900 ,0.700 ,0.500)
تأثیر خیلی زیاد
(1.000 ,0.900 ,0.700)

برای بررسی معیارها از نظر5 خبره استفاده شده است. نظرات و مقایسه زوجی هر خبره در “پیوست د” آورده شده است. در این ماتریس‌ها،x ̃_ij=(l_ij,m_ij,u_ij)ا اعداد فازی مثلثی میباشند و x ̃_ii=(i=1,2,3,…,n) به صورت عدد فازی (0,0,0) در نظر گرفته می‌شوند.
برای در نظر گرفتن نظر همه خبرگان، طبق فرمول 1 از نظرات میانگین حسابی می‌گیریم و ماتریس تجمیع شده نظرات را تشکیل می دهیم.
فرمول(1) z ̃=(x ̃^1⊕x ̃^2⊕x ̃^3⊕…^ ⊕x^p)/p
در این فرمولp تعداد خبرگان و x ̃^1، x ̃^2 ،x ̃^p به ترتیب ماتریس مقایسه زوجی خبره 1، خبره 2 و خبره p می‌باشد وz ̃ عدد فازی مثلثی به صورت z ̃_ij=(〖l_ 〗_ij^’,〖m_ 〗_ij^’,〖u_ 〗_ij^’)ااست. جدول زیر میانگین مقایسات زوجی را نشان می‌دهد.
جدول 4-11 میانگین نظر تمام خبرگان
C13
C12
C11
C10
C9
C8
C7
C6
C5
C4
C3
C2
C1

(0.220,0.420,0.620)
(0.500,0.700,0.880)
(0.140,0.300,0.500)
(0.500,0.700,0.880)
(0.540,0.740,0.920)
(0.580,0.780,0.940)
(0.160,0.340,0.540)
(0.500,0.700,0.900)
(0.540,0.740,0.900)
(0.220,0.420,0.620)
(0.580,0.780,0.940)
(0.580,0.780,0.940)
(0.000,0.000,0.000)
C1
(0.260,0.460,0.660)
(0.580,0.780,0.940)
(0.240,0.420,0.620)
(0.460,0.660,0.820)
(0.100,0.260,0.460)
(0.300,0.500,0.700)
(0.500,0.700,0.880)
(0.660,0.860,0.980)
(0.500,0.700,0.880)
(0.540,0.740,0.920)
(0.460,0.660,0.840)
(0.000,0.000,0.000)
(0.460,0.660,0.840)
C2
(0.540,0.740,0.920)
(0.240,0.420,0.620)
(0.120,0.300,0.500)
(0.500,0.700,0.900)
(0.580,0.780,0.940)
(0.580,0.780,0.940)
(0.260,0.460,0.660)
(0.500,0.700,0.880)
(0.100,0.260,0.460)
(0.580,0.780,0.940)
(0.000,0.000,0.000)
(0.260,0.460,0.660)
(0.300,0.500,0.700)
C3
(0.120,0.300,0.500)
(0.540,0.740,0.920)
(0.660,0.860,0.980)
(0.500,0.700,0.900)
(0.200,0.380,0.580)
(0.120,0.300,0.500)
(0.500,0.700,0.900)
(0.500,0.700,0.900)
(0.540,0.740,0.920)
(0.000,0.000,0.000)
(0.620,0.820,0.960)
(0.580,0.780,0.940)
(0.080,0.260,0.460)
C4
(0.260,0.460,0.660)
(0.160,0.340,0.540)
(0.060,0.220,0.420)
(0.540,0.740,0.920)
(0.160,0.340,0.540)
(0.180,0.380,0.580)
(0.540,0.740,0.920)
(0.620,0.820,0.960)
(0.000,0.000,0.000)
(0.180,0.380,0.580)
(0.500,0.700,0.900)
(0.580,0.780,0.940)
(0.620,0.820,0.960)
C5
(0.080,0.260,0.460)
(0.140,0.300,0.500)
(0.580,0.780,0.940)
(0.580,0.780,0.940)
(0.500,0.700,0.880)
(0.220,0.420,0.620)
(0.540,0.740,0.920)
(0.000,0.000,0.000)
(0.540,0.740,0.900)
(0.580,0.780,0.940)
(0.660,0.860,0.980)
(0.620,0.820,0.960)
(0.580,0.780,0.940)
C6
(0.120,0.300,0.500)
(0.120,0.300,0.500)
(0.180,0.380,0.580)
(0.500,0.700,0.900)
(0.220,0.420,0.620)
(0.260,0.460,0.660)
(0.000,0.000,0.000)
(0.420,0.620,0.820)
(0.180,0.380,0.580)
(0.460,0.660,0.840)
(0.500,0.700,0.880)
(0.580,0.780,0.940)
(0.180,0.380,0.580)
C7
(0.240,0.420,0.620)
(0.200,0.380,0.580)
(0.120,0.300,0.500)
(0.080,0.260,0.460)
(0.620,0.820,0.960)
(0.000,0.000,0.000)
(0.160,0.340,0.540)
(0.460,0.660,0.860)
(0.180,0.380,0.580)
(0.580,0.780,0.940)
(0.540,0.740,0.920)
(0.620,0.820,0.960)
(0.540,0.740,0.920)
C8
(0.580,0.780,0.940)
(0.300,0.500,0.700)
(0.580,0.780,0.940)
(0.160,0.340,0.540)
(0.000,0.000,0.000)
(0.140,0.340,0.540)
(0.160,0.340,0.540)
(0.540,0.740,0.920)
(0.580,0.780,0.940)
(0.540,0.740,0.920)
(0.540,0.740,0.920)
(0.620,0.820,0.960)
(0.180,0.380,0.580)
C9
(0.500,0.700,0.900)
(0.580,0.780,0.940)
(0.500,0.700,0.900)
(0.000,0.000,0.000)
(0.540,0.740,0.920)
(0.580,0.780,0.940)
(0.160,0.340,0.540)
(0.140,0.340,0.540)
(0.500,0.700,0.880)
(0.540,0.740,0.920)
(0.540,0.740,0.920)
(0.540,0.740,0.920)
(0.540,0.740,0.920)
C10
(0.220,0.420,0.620)
(0.540,0.740,0.920)
(0.000,0.000,0.000)
(0.160,0.340,0.540)
(0.220,0.420,0.620)
(0.200,0.380,0.580)
(0.580,0.780,0.940)
(0.540,0.740,0.920)
(0.040,0.180,0.380)
(0.620,0.820,0.960)
(0.500,0.700,0.900)
(0.180,0.380,0.580)
(0.260,0.460,0.660)
C11
(0.140,0.340,0.540)
(0.000,0.000,0.000)
(0.540,0.740,0.920)
(0.540,0.740,0.920)
(0.540,0.740,0.920)
(0.260,0.460,0.660)
(0.460,0.660,0.860)
(0.580,0.780,0.940)
(0.220,0.420,0.620)
(0.580,0.780,0.940)
(0.580,0.780,0.940)
(0.540,0.740,0.920)
(0.540,0.740,0.920)
C12
(0.000,0.000,0.000)
(0.580,0.780,0.940)
(0.580,0.780,0.940)
(0.500,0.700,0.900)
(0.540,0.740,0.920)
(0.440,0.620,0.800)
(0.280,0.460,0.660)
(0.180,0.380,0.580)
(0.460,0.660,0.840)
(0.240,0.420,0.620)
(0.180,0.340,0.540)
(0.040,0.180,0.380)
(0.220,0.420,0.620)
C13

با تشکیل ماتریس تجمیع نظرات شایسته است تمامی نظرات با استفاده از فرمول های2 و 3 نزمالیزه شوند.
فرمول(2) H ̃_ij=z ̃_ij/r=((〖l_ 〗_ij^’)/r,(〖m_ 〗_ij^’)/r,(〖u_ 〗_ij^’)/r)=(〖l_ 〗_ij^”,〖m_ 〗_ij^”,〖u_ 〗_ij^”)
کهr از رابطه زیر به‌دست می‌آید:
فرمول(3) r=max_(1≤i≤n) (∑_(j=1)^n▒u_ij )
جدول 4-12 ماتریس نرمالیزه شده
C13
C12
C11
C10
C9
C8
C7
C6
C5
C4
C3
C2
C1

(0.021,0.041,0.061)
(0.049,0.068,0.086)
(0.014,0.029,0.049)
(0.049,0.068,0.086)
(0.053,0.072,0.090)
(0.057,0.076,0.092)
(0.016,0.033,0.053)
(0.049,0.068,0.088)
(0.053,0.072,0.088)
(0.021,0.041,0.061)
(0.057,0.076,0.092)
(0.057,0.076,0.092)
(0.000,0.000,0.000)
C1
(0.025,0.045,0.064)
(0.057,0.076,0.092)
(0.023,0.041,0.061)
(0.045,0.064,0.080)
(0.010,0.025,0.045)
(0.029,0.049,0.068)
(0.049,0.068,0.086)
(0.064,0.084,0.096)
(0.049,0.068,0.086)
(0.053,0.072,0.090)
(0.045,0.064,0.082)
(0.000,0.000,0.000)
(0.045,0.064,0.082)
C2
(0.053,0.072,0.090)
(0.023,0.041,0.061)
(0.012,0.029,0.049)
(0.049,0.068,0.088)
(0.057,0.076,0.092)
(0.057,0.076,0.092)
(0.025,0.045,0.064)
(0.049,0.068,0.086)
(0.010,0.025,0.045)
(0.057,0.076,0.092)
(0.000,0.000,0.000)
(0.025,0.045,0.064)
(0.029,0.049,0.068)
C3
(0.012,0.029,0.049)
(0.053,0.072,0.090)
(0.064,0.084,0.096)
(0.049,0.068,0.088)
(0.020,0.037,0.057)
(0.012,0.029,0.049)
(0.049,0.068,0.088)
(0.049,0.068,0.088)
(0.053,0.072,0.090)
(0.000,0.000,0.000)
(0.061,0.080,0.094)
(0.057,0.076,0.092)
(0.008,0.025,0.045)
C4
(0.025,0.045,0.064)
(0.016,0.033,0.053)
(0.006,0.021,0.041)
(0.053,0.072,0.090)
(0.016,0.033,0.053)
(0.018,0.037,0.057)
(0.053,0.072,0.090)
(0.061,0.080,0.094)
(0.000,0.000,0.000)
(0.018,0.037,0.057)
(0.049,0.068,0.088)
(0.057,0.076,0.092)
(0.061,0.080,0.094)
C5
(0.008,0.025,0.045)
(0.014,0.029,0.049)
(0.057,0.076,0.092)
(0.057,0.076,0.092)
(0.049,0.068,0.086)
(0.021,0.041,0.061)
(0.053,0.072,0.090)
(0.000,0.000,0.000)
(0.053,0.072,0.088)
(0.057,0.076,0.092)
(0.064,0.084,0.096)
(0.061,0.080,0.094)
(0.057,0.076,0.092)
C6
(0.012,0.029,0.049)
(0.012,0.029,0.049)
(0.018,0.037,0.057)
(0.049,0.068,0.088)
(0.021,0.041,0.061)
(0.025,0.045,0.064)
(0.000,0.000,0.000)
(0.041,0.061,0.080)
(0.018,0.037,0.057)
(0.045,0.064,0.082)
(0.049,0.068,0.086)
(0.057,0.076,0.092)
(0.018,0.037,0.057)
C7
(0.023,0.041,0.061)
(0.020,0.037,0.057)
(0.012,0.029,0.049)
(0.008,0.025,0.045)
(0.061,0.080,0.094)
(0.000,0.000,0.000)
(0.016,0.033,0.053)
(0.045,0.064,0.084)
(0.018,0.037,0.057)
(0.057,0.076,0.092)
(0.053,0.072,0.090)
(0.061,0.080,0.094)
(0.053,0.072,0.090)
C8
(0.057,0.076,0.092)
(0.029,0.049,0.068)
(0.057,0.076,0.092)
(0.016,0.033,0.053)
(0.000,0.000,0.000)
(0.014,0.033,0.053)
(0.016,0.033,0.053)
(0.053,0.072,0.090)
(0.057,0.076,0.092)
(0.053,0.072,0.090)
(0.053,0.072,0.090)
(0.061,0.080,0.094)
(0.018,0.037,0.057)
C9
(0.049,0.068,0.088)
(0.057,0.076,0.092)
(0.049,0.068,0.088)
(0.000,0.000,0.000)
(0.053,0.072,0.090)
(0.057,0.076,0.092)
(0.016,0.033,0.053)
(0.014,0.033,0.053)
(0.049,0.068,0.086)
(0.053,0.072,0.090)
(0.053,0.072,0.090)
(0.053,0.072,0.090)
(0.053,0.072,0.090)
C10
(0.021,0.041,0.061)
(0.053,0.072,0.090)
(0.000,0.000,0.000)
(0.016,0.033,0.053)
(0.021,0.041,0.061)
(0.020,0.037,0.057)
(0.057,0.076,0.092)
(0.053,0.072,0.090)
(0.004,0.018,0.037)
(0.061,0.080,0.094)
(0.049,0.068,0.088)
(0.018,0.037,0.057)
(0.025,0.045,0.064)
C11
(0.014,0.033,0.053)
(0.000,0.000,0.000)
(0.053,0.072,0.090)
(0.053,0.072,0.090)
(0.053,0.072,0.090)
(0.025,0.045,0.064)
(0.045,0.064,0.084)
(0.057,0.076,0.092)
(0.021,0.041,0.061)
(0.057,0.076,0.092)
(0.057,0.076,0.092)
(0.053,0.072,0.090)
(0.053,0.072,0.090)
C12
(0.000,0.000,0.000)
(0.057,0.076,0.092)
(0.057,0.076,0.092)
(0.049,0.068,0.088)
(0.053,0.072,0.090)
(0.043,0.061,0.078)
(0.027,0.045,0.064)
(0.018,0.037,0.057)
(0.045,0.064,0.082)
(0.023,0.041,0.061)
(0.018,0.033,0.053)
(0.004,0.018,0.037)
(0.021,0.041,0.061)
C13

بعد از محاسبه ماتریس های فوق، ماتریس روابط کل فازی با توجه به فرمول‌های 4 تا 7 به‌دست می‌آید.
فرمول(4) T=lim┬(k→+∞)⁡〖(H ̃^1⊕H ̃^2⊕…⊕H ̃^k)〗⁡
که هر درایه آن عدد فازی به صورت t ̃_ij=(〖l_ 〗_ij^t,〖m_ 〗_ij^t,〖u_ 〗_ij^t) است و به صورت زیر محاسبه می‌شود:
فرمول(5) [〖l_ 〗_ij^t]=H_l×〖(I-H_l)〗^(-1)
فرمول(6) [〖m_ 〗_ij^t]=H_m×〖(I-H_m)〗^(-1 )
فرمول(7) 〖〖[u〗_ 〗_ij^t]=H_u×〖(I-H_u)〗^(-1)
در این فرمول‌ها I ماتریس یکه و H_l، H_mو H_u هر کدام ماتریس nnهستند که درایه‌های آن‌را به ترتیب عدد پایین، عدد میانی و عدد بالاییِ اعداد فازیِ مثلثیِ ماتریسِ H تشکیل می‌دهد.4-17 نشان دهنده ماتریس tمی باشد.
جدول4-13 ماتریس روابط