Karar Analizi Topsis Yöntemi - I 1 2011-2012 BAHAR YARIYILI PROJE 1 080203036 EMRAH UZUMER 080203010 080203021 SAMET SARIKAYA 26 MART 2012 2 3 1. 4 2. 5 3. .10 4. 5. 18 6. 3 Preference By Similarity To An Ideal 4 ol 5 TOPSIS (Technique for Order Preference by Similarity to Ideal Solution) Yoon ve Hwang m n m m n n i j a a a a a a a a a A ... . . . . . . ... ... 2 1 2 22 21 1 12 11 i j A m k k j i j i j a a r 1 2 (1.1) ( i j r 6 edilir: m n m m n n i j r r r r r r r r r R ... . . . . . . ... ... 2 1 2 22 21 1 12 11 i w n i i w 1 1). i w m n n m m n n n n i j r w r w r w r w r w r w r w r w r w V ... . . . . . . ... ... 2 2 1 1 2 22 2 21 1 1 12 2 11 1 * A A ' * min ( ), (max J j v J j v A i j i i j i (1.2) t * * 2 * 1 * ,..., , n v v v A 7 ' max ( ), (min J j v J j v A i j i i j i (1.3) n v v v A ,..., , 2 1 J fayda (maksimizasyon), ' J elemandan : * i S i S * i S i S n j j i j i v v S 1 2 * * ) ( (1.4) n j j i j i v v S 1 2 ) ( (1.5) Burada hesaplanacak * i S ve i S * i C ve * * i i i i S S S C (1.6) 8 Burada * i C 1 0 * i C 1 * i C 0 * i C 7 : * i C 20 , 0 1 w , 15 , 0 2 w , 40 , 0 3 w ve 25 , 0 4 w 10 30 10 30 30 20 30 10 30 15 20 25 A 4 3 x ) boyutlu Standart Karar Matrisi (R) 11 r 6202 , 0 30 10 25 25 2 2 2 11 r i j r 2294 , 0 7682 , 0 2673 , 0 7442 , 0 6883 , 0 5122 , 0 8018 , 0 2481 , 0 6883 , 0 3841 , 0 5345 , 0 6202 , 0 R 0574 , 0 3073 , 0 0401 , 0 1489 , 0 1721 , 0 2049 , 0 1203 , 0 0496 , 0 1721 , 0 1537 , 0 0802 , 0 1241 , 0 V * A ) ve negatif ideal ( A * A A 4 3 2 1 * max , max , max , max i i i i i i i i v v v v A 9 1721 , 0 ; 3073 , 0 ; 1203 , 0 ; 1489 , 0 * A 4 3 2 1 min ; min ; min ; min i i i i i i i i v v v v A 0574 , 0 ; 1537 , 0 ; 0401 , 0 ; 0496 , 0 A 1606 , 0 * 1 S , 1428 , 0 * 2 S ve 1400 , 0 * 3 S 2 2 2 2 * 1 ) 1721 , 0 1721 , 0 ( ) 3073 , 0 1537 , 0 ( ) 1203 , 0 0802 , 0 ( ) 1489 . 0 1241 , 0 ( S 1428 , 0 1 S , 1490 , 0 2 S ve 1830 , 0 3 S 4707 , 0 1428 , 0 1606 , 0 1428 , 0 * 1 C 5106 , 0 1490 , 0 1428 , 0 1490 , 0 * 2 C 5666 , 0 1830 , 0 1400 , 0 1830 , 0 * 3 C 3 A , 2 A ve 1 A 10 Eleren ve Ersoy, 2007 rler, Demireli, 2010 me probleminde topsis kulla a 11 Yazarlar Problem tipi Eleren ve Ersoy, (2007) -- -- Demireli,(2010) belirleme Topsis -- Topsis AHP Topsis ANP 12 Bu uygulama, ( ,2010). tercihlerinde etkili olan bilimi ile ilgi olan TOPSIS (Technique for Order Preference by Similarity to Ideal Solution) ve AHP "fiyat" ve da biraz daha fazla 13 Kriterlerin bi ikili ka Tablo 2. Tablo 3. 14 . LAMDA max PW elde edilir. 8,907103911 8,058784948 8,329746282 8,145709547 8,267512168 8,108286726 8,554920053 8,766391556 LAMDA max 8,392307 3 , 7 2 5 0 5 6 5 5 1 0 , 3 5 8 2 7 5 1 8 0 , 7 8 8 7 0 4 3 3 3 0 , 5 3 1 3 4 7 3 7 7 0 , 1 7 8 3 7 1 5 5 9 0 , 2 4 6 4 0 6 1 8 1 , 1 5 8 3 5 8 4 1 3 1 , 6 6 6 0 3 3 2 5 A*PW/PW= A*PW = 15 Tablo 3.Karar Matrisi Standart Karar m yararlanarak ve Tablo 4.Standard Karar Matrisi -4 : - - 16 Tablo 5. Standart Karar Matrisi * i S i S bulunur. Tablo 6 S * 0 , 0 2 2 5 4 6 0 , 0 1 5 4 6 9 0 , 0 0 5 8 5 4 0 , 0 0 1 1 9 4 17 Tablo 7 S ' 0 , 0 0 0 2 7 0 , 0 0 1 6 8 5 0 , 0 0 6 1 6 8 0 , 0 2 1 8 1 5 * * i i i i S S S C 0 < Ci* < 1 C1*=0,011834 0 < C1* < 1 C2*=0,098251 0 < C2* < 1 C3*=0,513049 0 < C3* < 1 C4*=0,948118 0 < C4* < 1 B C4, C3, C2, C1 18 Bu edilmesi gereken nokta 19 6. Ahp ve Topsis , 2011. Demireli, E., , 5, 1,101-112, 2010 . Engin, T., Teknik , 2005 . 1986- -14 ,2008. Eleren ve Ersoy, Vizyoner Dergisi , 2007. , 2007. Afyon , 2011 .