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1 c Data Envelopment Analysis DEA IT DHARMA Ltd DEA-AR (Assurance Region) 1 DEA 1 1 [1] [2] 2. [2] (RF : Range factor) 47240Copyright c by ORSJ. Unauthorized reproduction of this article is prohibited.
2 RF RF RF 1 UZR (Ultimate Zone Rating) Defensive Runs Saved : DRS (1/5) 1 (1/7) 1 6 (1/10) 36 (6/7) 2 5 (1/8) 13 (2/13) 3 3 (1/6) 30 (3/7) 4 (1/7) 2 (1/4) 1 (1/19) 4 (2/21) 2 (2/19) 3 (1/21) 8 (3/19) 14 (7/21) (6/6) 24 (2/4) 1 19 (1/11) 14 (4/11) 2 7 (2/9) 7 (1/7) 3 21 (3/7) 44 (7/8) 8 (1/5) 2 (1/7) 2 (2/21) 4 (2/19) 1 (1/21) 5 (3/19) 5 (4/21) 1 (1/19) (a/b): 220 b a (DEA) DEA / / 2. / 3. / 4. / 5. / 6. / 7. / 8. / Copyright c by ORSJ. Unauthorized reproduction of this article is prohibited.41473
3 9. / x (x 0.194)/( ) DEA CCR [3] o F 1 n M 9G 1 x gh (=1): h g y jh: h j θ =max M u jy jo u jy jh G v gx gh 0 g=1 (h =1,...,n; h o ) G v gx go =1, u 2 2u j (j 2) g=1 v g 0(g =1,...,G), u j 0(j =1,...,M) 1 h o 1 3 (u 2 2 u j (j 2)) 2 1 (G =1) u jy jh 1 (h =1,...,n; h o), u j 0(j =1,...,M) v g i k S(i, k) DEA-AR SS I(i, k, j)= 1 : i k j 0: 6 6 Ce Pa 1: 2 :13 :24 :3 5: 6 :7 : A(i, j) =1: i j 0: A(i, j) S(i, k) [ DEA-AR ] I(i, k, j) k F 1 max I(i, k, j) S(i, k) i,k,j SS I(i, k, j) A(i, j) =c j; i,k c j =1(j 6),c 6 =3 3 1 I(i, k, j) =Q [Q =8,Q=9] i,k,j I(i, k, j) 1, I(i, k, j) {0, 1} k,j 4 I(i, k, j) A(i, j) =1; k i,j I(i, 6,j) A(i, j) =P [P =3,P =4] i,j 6 3 best9 DEA (DEA best9) Ce θ hih u j[j =1,...,M] i 4 h i 47442Copyright c by ORSJ. Unauthorized reproduction of this article is prohibited.
4 3 4 θ hi 2012 Ce11 best9 DEA best Ce12 best9 DEA best Pa11 best9 DEA best Pa12 best9 DEA best θ =0.611 u j[j =1,...,M] θ hh<θ hi h i θ hh>θ hi h i best9 DEA best9 θ hh>θ hi h i i h DEA best9 () Ce11 Ce DEA best9 Pa11 Pa best9 DEA best9 best DEA best best9 5 6 DEA 2011 best DEA best9 (u 2 2u j (j 2)) 2 best DEA best Copyright c by ORSJ. Unauthorized reproduction of this article is prohibited.43475
5 7 best9 DEAbest9 Ce11 Ce12 Pa11 Pa (62 ) DEA best DEA best DEA best DEA u j o 220 (u 2 2u j (j 2)) DEA best9 10 Pa11 Pa (a, b) u a/u b L ab U ab 2 L ab U ab DEA-AR (a, b) u a/u b L ab U ab DEA-AR M 47644Copyright c by ORSJ. Unauthorized reproduction of this article is prohibited.
6 n (DEA-AR) θ o =max M u jy jo u jy jh 1 (h =1,...,n; h o) u kl jk u j u ku jk ( j k) u j 0(j =1, 2,...,[M =9]) o θ o 3 F (1) DEA best best best (2) c 7 =1, I(i, 6,j) A(i, j) =4, I(i, k, j) =9 i,j i,k,j DEA best DEA best9 best [243] 2012 [252] (3) 108 (6) (6) 157 (5)* 75 2 (2)* 15 (6) (6) 184 (6)* 68 (1) 216 (3) 239 (6) 238 (1) 248 (4)* 54 (2) 231 (5)* 35 (4) 112 * 3 best9 () [] 10 DEA best9 best [207] 2012 [204] (6)* 3 (6)* 14 1 (3)* 26 (4) (2) 175 (6)* 5 3 (4) 142 (3)* 34 (6) 187 (6) 201 (6) 194 (6) 192 (1)* 7 (5) 101 (6) 129 (2)* 27 (5)* (1)* 54 + * 3 best 9 () [] best9 3 1 best9 best9 best DEA best9 best (DEA best9) (1) Copyright c by ORSJ. Unauthorized reproduction of this article is prohibited.45477
7 11 best9 SS0 3 3DEA 5, 6 8 9, 10 Ce Ce Pa Pa (2) (3) (4) (1) (2) DEA best9 best9 (4) SS 220 best9 SS best9 best UZR DRS [1] T. Ueda and H. Amatatsu, Determination of bounds in DEA assurance region method: Its application to evaluation of baseball players and chemical companies, Journal of the Operations Research Society of Japan, 52, , [2] [3] DEA Ce (5/6) RF DEA-AR (a, b) 47846Copyright c by ORSJ. Unauthorized reproduction of this article is prohibited.
8 1 (a/b) Ce11 32 (5/6) 29 (7/7) 37 (4/6) 45 (1/5) 44 (5/6) 6 (6/20) 7 (7/20) 10 (10/20) 19 (2/6) 21 (1/7) 14 (3/6) 3 (3/5) 6 (1/6) 42 (12/20) 45 (15/20) 40 (10/20) 11 (3/6) 17 (4/7) 32 (4/6) 15 (1/5) 27 (2/6) 30 (12/20) 33 (14/20) 31 (13/20) 27 (1/6) 20 (7/7) 9 (3/6) 19 (1/5) 4 (4/6) 39 (10/20) 43 (14/20) 42 (13/20) RF 14 (5/6) 1 (1/7) 22 (6/6) 30 (4/5) 25 (6/6) 29 (1/20) 35 (5/20) 32 (2/20) (2/6) Ce12 34 (4/9) 30 (6/7) 41 (1/8) 60 (6/8) 56 (7/7) 17 (16/24) 19 (18/24) 13 (13/24) 28 (5/9) 32 (2/7) 23 (8/8) 3 (3/8) 7 (1/7) 47 (8/24) 44 (5/24) 51 (12/24) 9 (1/9) 21 (5/7) 14 (2/8) 49 (2/8) 20 (1/7) 42 (16/24) 31 (12/24) 36 (14/24) 32 (2/9) 16 (2/7) 7 (2/8) 23 (2/8) 1 (1/7) 43 (5/24) 37 (1/24) 47 (8/24) RF 11 (5/9) 1 (1/7) 12 (1/8) 35 (3/8) 23 (3/7) 34 (1/24) 45 (7/24) 37 (2/24) (6/9) Pa11 21 (1/9) 18 (2/7) 41 (3/7) 55 (4/6) 47 (2/6) 6 (6/22) 20 (18/22) 9 (9/22) 32 (8/9) 36 (6/7) 17 (5/7) 1 (1/6) 10 (4/6) 48 (13/22) 40 (5/22) 45 (10/22) 1 (1/9) 10 (1/7) 22 (1/7) 52 (2/6) 40 (2/6) 1 (1/22) 48 (22/22) 1 (1/22) 40 (7/9) 13 (1/7) 7 (3/7) 17 (1/6) 1 (1/6) 49 (15/22) 48 (14/22) 34 (5/22) RF 9 (3/9) 5 (5/7) 17 (3/7) 30 (1/6) 21 (1/6) 31 (1/22) 37 (3/22) 40 (6/22) (3/9) Pa12 34 (8/9) 19 (2/6) 36 (1/5) 50 (3/5) 40 (1/7) 7 (7/20) 16 (16/20) 2 (2/20) 19 (2/9) 32 (5/6) 17 (5/5) 2 (2/5) 13 (7/7) 46 (14/20) 40 (8/20) 50 (18/20) 7 (3/9) 5 (1/6) 22 (1/5) 48 (2/5) 47 (6/7) 21 (9/20) 40 (16/20) 20 (8/20) 26 (2/9) 13 (1/6) 9 (5/5) 21 (3/5) 4 (3/7) 44 (12/20) 46 (14/20) 45 (13/20) RF 9 (3/9) 3 (3/6) 13 (1/5) 31 (3/5) 21 (2/7) 27 (2/20) 35 (5/20) 33 (4/20) (6/9) (a/b) : 60 b a u a/u b L ab U ab (m =) Copyright c by ORSJ. Unauthorized reproduction of this article is prohibited.47479
9 k t k 7 t 7 1 t k t k i j k t k i j f ij =log e t k ln t k [1] N M j μ j μ N N μ j = f ij/n, μ = f ij/(nm) i=1 i=1 D B D W D T D B = μ j μ /M N D W = { f ij μ j /N }/M i=1 N D T = f ij μ /(NM) i=1 = D B + D W D T t k =10 kd B + D W C 2 D B + D W = C 2 D B D W t k v v +(s 1 s 2)=0,s 1 0, s 2 0 (A1) C(1 b) s 1 0, C b s 2 0, b {0, 1} (A2) C: (A3) (s 1 + s 2) v (A2) s 1 s 2 =0s 1 s 2b D B + D W = C 2 D B t k F 2 t k F 2 max (s 1j + s 2j)/M D B N N : μ = f ij/(nm), μ j = f ij/n i=1 i=1 μ j μ + s 1j s 2j =0; j =1, 2,...,M μ j μ = s 1j + s 2j[ (A1)] (s 1j + s 2j)/M D B =0 D B M C 2(1 b j) s 1j 0, M C 2 b j s 2j 0, b j {0, 1} [ (A2) MC 2 (A3) C ] f ij μ j + t (1) ij t (2) ij =0 f ij μ j = t (1) ij + t (2) ij N i=1 (t (1) ij + t (2) ij )/(NM) D W =0 D W t (1) ij 0, t (2) ij 0: i =1,...,N; j =1,...,M D B + D W = C 2 : ln(t k) ln(t k+1) C 0 : k =1,...,m; t m+1 =1 s 1j,s 2j,t (1) ij,t (2) ij (i =1,...,N; j =1,...,M), t k(k =1,...,m+1),D W,D B N =10, M =9, m =6, C 0 = (ln 9)/20 ln t 1 =ln9 ln t 7 =0 (ln 9)/6 C 0 k t k 4 j μ j = 10 fij/10 5 i= (t 1) 5 2 (t 2) 4 3 (t 3) Copyright c by ORSJ. Unauthorized reproduction of this article is prohibited.
10 μ 2 = {5ln(t 1)+4ln(t 2)+ln(t 3)} /10 = 2.10 μ j 1 μ j h j k t k =exp(f hj) [ln t k = f hj] t a b r ab L ab U ab 1 h 2 4 r r 24 =7.78 2/6.97 4= L 24 =0.90 U 24 =1.55 (a, b) L abu ab 0.4 (max k μ k) >μ j j (max k μ k)= = [] 0.4 L abu ab DEA-AR F 2 t k t 1 t 2 t 3 t 4 t 5 t j μ j Copyright c by ORSJ. Unauthorized reproduction of this article is prohibited.49481
11 6 1 h j exp(f hj) h 2 4 r h r Copyright c by ORSJ. Unauthorized reproduction of this article is prohibited.
(2018 2Q C) [ ] R 2 2 P = (a, b), Q = (c, d) Q P QP = ( ) a c b d (a c, b d) P = (a, b) O P ( ) a p = b P = (a, b) p = ( ) a b R 2 {( ) } R 2 x = x, y
![(2018 2Q C) [ ] R 2 2 P = (a, b), Q = (c, d) Q P QP = ( ) a c b d (a c, b d) P = (a, b) O P ( ) a p = b P = (a, b) p = ( ) a b R 2 {( ) } R 2 x = x, y](/thumbs/101/151465237.jpg "(2018 2Q C) [ ] R 2 2 P = (a, b), Q = (c, d) Q P QP = ( ) a c b d (a c, b d) P = (a, b) O P ( ) a p = b P = (a, b) p = ( ) a b R 2 {( ) } R 2 x = x, y")
(2018 2Q C) [ ] R 2 2 P = (a, b), Q = (c, d) Q P QP = a c b d (a c, b d) P = (a, b) O P a p = b P = (a, b) p = a b R 2 { } R 2 x = x, y R y 2 a p =, c q = b d p + a + c q = b + d q p P q a p = c R c b
LINEAR ALGEBRA I Hiroshi SUZUKI Department of Mathematics International Christian University
LINEAR ALGEBRA I Hiroshi SUZUKI Department of Mathematics International Christian University 2002 2 2 2 2 22 2 3 3 3 3 3 4 4 5 5 6 6 7 7 8 8 9 Cramer 9 0 0 E-mail:hsuzuki@icuacjp 0 3x + y + 2z 4 x + y
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(2016 2Q H) [ ] R 2 2 P = (a, b), Q = (c, d) Q P QP = ( ) a c b d (a c, b d) P = (a, b) O P ( ) a p = b P = (a, b) p = ( ) a b R 2 {( ) } R 2 x = x, y
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(2016 2Q H) [ ] R 2 2 P = (a, b), Q = (c, d) Q P QP = a c b d (a c, b d) P = (a, b) O P a p = b P = (a, b) p = a b R 2 { } R 2 x = x, y R y 2 a p =, c q = b d p + a + c q = b + d q p P q a p = c R c b
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6 6.. [, b] [, d] ij P ij ξ ij, η ij f Sf,, {P ij } Sf,, {P ij } k m i j m fξ ij, η ij i i j j i j i m i j k i i j j m i i j j k i i j j kb d {P ij } lim Sf,, {P ij} kb d f, k [, b] [, d] f, d kb d 6..
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X G P G (X) G BG [X, BG] S 2 2 2 S 2 2 S 2 = { (x 1, x 2, x 3 ) R 3 x 2 1 + x 2 2 + x 2 3 = 1 } R 3 S 2 S 2 v x S 2 x x v(x) T x S 2 T x S 2 S 2 x T x S 2 = { ξ R 3 x ξ } R 3 T x S 2 S 2 x x T x S 2
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