9 1: $O$,,, ( ), BT $2W6$ 22,, BT [7] BT, 12, $\xi_{1}=$ $(x_{11}, x_{12}, \ldots,x_{112}),$ $\xi_{2}=(x_{21}, x_{22}, \ldots, x_{212})$ $i$ $

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1 $\iota$ (Kiyoto Kawai), (Kazuyuki Sekitani) Systems engineering, Shizuoka University 3 10, $2N6$ $2m7$,, 53 [1, 2, 3, 4] [9, 10, 11, 12], [8] [6],, ( ) ( ), $\ovalbox{\tt\small REJECT}\backslash ^{9}$, 2006 \not\subset 12,, Data Envelopment $Analy_{8}is$ (DEA) [13] 12 Bradley-Terry(BT) [$\eta$, $Aa$, DEA,, $2m7$ 1, [5] DEA 2 BT 21,, ,,,, 1, ,, 3,,, 1 1 1, 1,,

$\ovalbox{\tt\small REJECT}\backslash ^{9}$, 2006 \not\subset 12,, Data Envelopment $Analy_{8}is$

2 9 1: $O$,,, ( ), BT $2W6$ 22,, BT [7] BT, 12, $\xi_{1}=$ $(x_{11}, x_{12}, \ldots,x_{112}),$ $\xi_{2}=(x_{21}, x_{22}, \ldots, x_{212})$ $i$ $j$ j, $i$ $j$ $q_{1j}$ $p_{ij}= \frac{x_{2i}}{x_{2i}+x_{1j}},q_{lj}=\frac{x_{1i}}{x_{2j}+x_{1i}}$ $(i\neq j)$ (1),, ( ), $i$ $j$,,, ( ) $r_{\{j}$, $i$ $j$ $8_{ij(=r4_{J^{-r_{ji})}}}$ $(r:j, s_{*j})$ , 579, 2 293, /, $B$ ) $-$

$\frac{x_{2i}}{x_{2i}+x_{1j}},q_{lj}=\frac{x_{1i}}{x_{2j}+x_{1i}}$ $(i\neq j)$ (1),, ( ), $i$ $j$,,,$

3 $\epsilon_{1}$ $r_{1\dot{f}}$ $\backslash$ 10 $\varpi$ 2: $2006$ : $\vdash$ 12 $\ovalbox{\tt\small REJECT} S$ $\ovalbox{\tt\small REJECT}_{J\backslash I}$ $\ovalbox{\tt\small REJECT}_{\text{ }\backslash \mathfrak{l}}$ $(s_{ji})$ : : $\ovalbox{\tt\small REJECT}\backslash$ $/c$ $1$ ) $-\cdot-(t_{lj})$ $\frac{\text{ }}{\text{ }*\text{ } }$ $\neg$ $\cdot t-\cdot-$ $ $ $ \infty$ $u82440$ SO $ u$ $5605u $ $*$ $*$ $\ovalbox{\tt\small REJECT}$ $ u0\ovalbox{\tt\small REJECT}\ovalbox{\tt\small REJECT}$ $r\iota j$ 2 (2) $tf$ $P:j$ $Pr(r_{tj})=(\begin{array}{l}n_{ij}r_{tj}\end{array})p_{1j }r(1-p_{lj})^{n}u-r_{j}$ (2), $\{r_{lj}\}$ (1) 1 $\sum_{\iota\approx 1}^{12}\sum_{j\prime i}^{12}\frac{(r_{jj}-n_{1j_{\overline{\alpha_{1}}+oe_{1f}}^{x_{aarrow)^{2}}}}}{n_{i\dot{g}}\frac{l}{x_{ll}}aarrow}+\frac{(\epsilon_{ji}-n_{j:}}{n_{j1}\frac{x_{13}}{xa+ae\iota g}}$ (3) (3) $\xi_{2}$ (3) $ij$, (3),, $x_{1},x_{2}$ $x_{11}=x_{12}=\cdots=x_{112}=x_{1}$, $H_{0}$ : (4) $x_{21}=x_{22}=\cdots=x_{212}=x_{2}$, $H0$, $\xi_{1}=x_{1},\xi_{2}=x_{2}$ (3), $x_{1},x_{2}$ $H_{0}$, $x_{1},$ $x_{2}$ $x_{1}$ (4) $x_{2}$ $( \sum_{1=1}^{12}\sum_{j\neq i}^{12}\frac{r_{i\dot{g}}^{2}}{n_{1j}})\frac{x_{1}}{x_{2}}+(\sum_{i=1}^{12}\sum_{j\neq i}^{1l}\frac{\epsilon_{j1}^{2}}{n_{1j}})\frac{x_{2}}{x_{1}}$ (5)

$t-\cdot-$ $02932672722802857472556887$ 5570 681678552555158163151149156153 2250 307233278303755175608086 6925770 $5605535\infty$ 154157162153160159 $u82440$ 2602512797387 SO 848584 5685736760$

4 $\frac{\sum_{\dot{g}\neq i}n_{1j_{\varpi_{1f}+\overline{x_{2}}}^{arrow x}}}{\sum_{j\neq:}n_{1j}}$ 11 (5) 2 $A=[ \sum_{t=1}^{12}\sum_{j\neq:_{n}}^{12_{\lrcorner_{\frac{i}{f}}}^{2}}^{0}$ $\sum_{1=1}^{12_{\sum_{0}}12_{a}^{r^{l}}}j\neq i\mathfrak{n}\ell d]$ $i$, A (, $a_{1j}$, (5) $i$ $[a_{1j}x_{j}^{*}/x:]$ $i$ (6) $( \sum_{-1}^{12}\sum_{j\neq i}^{12}\frac{r_{j}^{2}}{m_{j}})\frac{x_{1}^{*}}{x_{2}}=(\sum_{i-1}^{12}\sum_{jl}^{12}\frac{\epsilon_{j}^{2}}{n_{j}})\frac{xi}{xi}$ (6) 2 (6) $x_{1}^{*}=5709$, $x_{2}^{l}=2624$, (3) $=172473$ (7) $131(=12-(2-1))$, (3) 131 $H_{0}$ 5% , $H_{0}$, 131 1% , 1%,, 23 BT 12 $\epsilon_{1},\epsilon_{2}$ (2) $L$ $L$ $L= \prod_{t\approx 1}^{12}\prod_{i\prime j}(\begin{array}{l}n_{ij}r_{ij}\end{array})(\frac{1}{x_{2i}+x_{1j}})^{n_{j}}\prod_{\iota=1}^{12}x_{2l}^{u_{l}}\prod_{k=1}^{12}x_{1k}^{v_{k}}$ (8) $l$, $u\iota vk$,, $k$ $u_{l}=\sum_{j\neq l}r_{lj},$ $v_{k}= \sum_{j\neq k}s_{jk}$ $L$ $\xi_{1},\xi_{2}$ BT [7] 2 12 $\xi_{1}$ $\xi_{2}$ 3,, $i$ $(\xi_{1}, \xi_{2})$, $\epsilon_{1},\epsilon_{2}$ BT,, 3 BT f $109(=12x11-(24-1))$ 109 5% , 2 BT, % , 10% 3, 1 4

$i}^{12}\frac{r_{j}^{2}}{m_{j}})\frac{x_{1}^{*}}{x_{2}}=(\sum_{i-1}^{12}\sum_{jl}^{12}\frac{\epsilon_{j}^{2}}{n_{j}})\frac{xi}{xi}$ (6) 2 (6) $x_{1}^{*}=5709$, $x_{2}^{l}=2624$, (3) $=172473$ (7)$

5 $ $ 4 $ $ : \mp, $(x_{1})$ $(x_{2})$ $(x_{1})$ $(x_{2})$ $27\mathfrak{X}$ % $ $4u$ 2$6m$ :,, $(x_{1})$ $(x_{2})$ )1 4,,,,, 2 2,,, 4 3,, 4, 2 4, 4 2, 2, 2, 2, 2,, 1, 2,, 2 4 1, , 1

$5686 2524 5$4u$ 2$6m$ 6360 2537 5111 2634 4:,, $(x_{1})$ $(x_{2})$ 1 2 3 5 6 1 2$

6 $\gamma$ $\gamma$ 13 (05), 2, , $2W6$, 12, 3 1,, 2,,,, DEA, DEA, ( ), ( ),, DEA DEA, 1, 1,, $\gamma$,, $k$ $x_{1k}$, $x_{2k}$, $2N6$ $y_{k}$ $k$ $x_{k}$ $(x_{1k}, x_{2k})$ $\gamma$, $P(\gamma)$ (9) $P(\gamma)\equiv\{(x,y) j\approx 1j\approx 11212\}$ (9) (9), (, )

$$x_{2k}$, $2N6$ $y_{k}$ $k$ $x_{k}$ $(x_{1k}, x_{2k})$ $\gamma$,$

7 14?, (10) $k$ max $\{\phi y_{k} (x_{k},\phi y_{k})\in P(\gamma)\}$ (10) $k$ $\phi^{*}$ (10) (10), $1/\phi^{*}$ DEA, $1/\phi^{*}$ $k$ $P(\gamma)$ $\gamma$, 6 5, $\gamma=630$, $\gamma=664$ 6; A $2\alpha)6$ $617614$ $1/\phi^{*}$ 5, (1), (1), (987), (979), (948), (842), (808), (786) (754), (736), (6%), (667), ,,, 1, 1, 2, $-$ $622603$

$623 647 2003 A 599 2004 685 597 2005 617 $2\alpha)6$ $617614$ $1/\phi^{*}$ 5, (1), (1), (987),$

8 $\gamma$ , 3, 5 ( ), 5, $\gamma=630$ 664, 633, 975,,,, 5 1, $k$ $\{j \phi^{*}y_{k}=\sum_{=\dot{f}1}^{12}y_{j}\lambda_{j},$ $oe_{k} \geq\sum_{j=1}^{12}x_{j}\lambda_{j},$ $\lambda_{j}>0\}$ (11), 10,, ( ),, , 1, $ \supset$, 617, ,,, 5 $2\infty 6$ 5, 6,,,? (10) $\phi$, $k$ $\max\{d_{1}+d_{2} (x_{k}-d, \phi^{*}y_{k})\in P(\gamma)\}$ (12), $d$ $(d_{1}, d_{2})$ $k$ (12),,, (12) $d_{1}+h$ $d_{1}$ $d_{2}$ (12) 7, 5 4,,,, $\{\lambda(0363, W39)+(1-\lambda)(0378,0) 0\leq\lambda\leq 1\}$,,, $\gamma=630$ 5 $\gamma=630$, 7 7 (,,,,,, ), 1 DEA

$(10) $\phi$, $k$ $\max\{d_{1}+d_{2} (x_{k}-d, \phi^{*}y_{k})\in P(\gamma)\}$ (12), $d$ $(d_{1}, d_{2})$ $k$ (12),,, (12) $d_{1}+h$ $d_{1}$$

9 16 7; $m\alpha d_{1}+2$ $ $ $\text{ _{}0}\text{ _{}9}\max$ $\frac{m\alpha d_{2}}{\text{ }}0378$ $ \ovalbox{\tt\small REJECT}$ 4 41,,, 2007 $P(\gamma)$, 2007 $\alpha_{g}$, $\alpha_{g}$ $\alpha_{g}$, $d=$ $d_{l}$ (, [ ), $d=(d_{1}, d_{2})$, 2006 $x_{g}=(x_{1g}, x_{2g})$, $x_{g}+d=(x_{1g}+d_{1}, x_{2g}+d_{2})$ $P(\gamma)$, $x_{g}+d$ $\alpha_{g}$ $(x_{g}+d, \alpha_{g})\in P(\gamma)$,, $d$ $\beta\in[0, \infty$ ) (13) nin $\{d_{1}+\beta d_{2} (x_{g}+d,\alpha_{g})\in P(\gamma)\}$ (13) $\beta$ ( ) $\beta>1$, $\beta<1$, $ \beta-1 $, $y=\alpha_{g}$ $P(\gamma)$ 2 2, $\alpha_{g}$ 206 $(x_{h},y_{h})$ $y=\alpha_{g}$ $P(\gamma)$ 2, 1 $(x_{h}, y_{h})$ $y=\alpha_{g}$ $\alpha_{g}/y_{h}(x_{h}, y_{h})$ $x$ $\alpha_{g}/y_{h}x_{h}$, $(x_{s},ys)$, $y=\alpha_{g}$ $P(\gamma)$ $\alpha_{g}/y_{s}(x_{9},ys)$, $a_{g}/y_{s}x_{s}$ 6, 5 614, $\alpha_{g}=0614$ (13) $f$, $\beta^{*}=03686$ $\beta\in[0, \beta^{t}$ ), $x_{g}+d^{*}$, $\beta\in[0,\beta^{*}$ ), $d_{1}^{*}<0,$ $d_{2}^{l}>0$, $x_{1g}$ $x_{2g}$ $\alpha_{g}$

$(x_{g}+d, \alpha_{g})\in P(\gamma)$,, $d$ $\beta\in[0, \infty$ ) (13) nin $\{d_{1}+\beta d_{2} (x_{g}+d,\alpha_{g})\in P(\gamma)\}$ (13) $\beta$ ( ) $\beta>1$, $\beta<1$, $ \beta-1 $, $y=\alpha_{g}$

10 17 2: $y=a_{k}$ $P(\gamma)$, $\beta=\beta^{*}$ $XQ+X$ $\beta=\beta^{*}$, $x_{1g}$ $X2G$,, $\beta>\beta$, $x_{g}+d^{*}$, $\beta>\beta^{*}$, $d_{1}^{*}>0$ $d_{2}^{*}>0$,, $\alpha_{g}$, $(\beta)$ $\alpha_{g}=0614$ $\beta$, $\alpha c=0614$,, ( ) ( ), $\beta\in[0, \beta^{*}]$,,, $\alpha_{g}=0614$, $a_{g}=0614$, $a_{g}$, $a_{g}$ $\frac{a_{g}}{0597}x572\geq 5915$ (14) (14) $a_{g}\geq 06174$, 6174,, 42 2\omega 07, $2W7$ , MLB ,,,,

$\alpha c=0614$,, ( ) ( ), $\beta\in[0, \beta^{*}]$,,, $\alpha_{g}=0614$, $a_{g}=0614$, $a_{g}$, $a_{g}$

11 $\text{ ^{}1}J\text{ ^{}t}j$ 18 8: / / $\overline{k}lhffi$ $t$ ) y t $\wedge$ $71s/\backslash \backslash$, $\aleph$ $\aleph$ NUt $*$ $M\overline{LB}ff$ $MLBMLBp$ $/p$ } $1$ $i$ } l \Re $i$ $6$ $f_{\overline{fl\xi@\re r_{ij}*\backslash f\mathfrak{w}\re \text{ }}}$ $/\backslash ( ) 4g\acute $\backslash \not\in n\neq$ 9: 2\alpha \cdot$ $\ovalbox{\tt\small REJECT}_{\text{ }}\overline{\text{ }}$ $\ovalbox{\tt\small REJECT}$ $)$ $\sim$ $T $ $) $\ovalbox{\tt\small \epsilon_{1j}\frac{\ovalbox{\tt\small REJECT} \text{ }}{\text{ }*\cdot\dagger REJECT}_{\text{ }}($ j-7/\backslash \cdot 1j-r}$ $\ovalbox{\tt\small REJECT}$ $\ovalbox{\tt\small REJECT} 6 $26P$ ( ) $7^{ffl\Re)}$ ( ) $\varpi\backslash ffi\re$ ) $\ovalbox{\tt\small REJECT}$ ( ) 5268 b ( ) ( ) ( ) ( ) $30$ $31$ $00$ $40$ $00$ $00$ $31$ $00$ $03$ $00$ $22$ $\ovalbox{\tt\small REJECT}\ovalbox{\tt\small REJECT}((*l$ ) $01$ ) (\approx 1 3 &*) ( 200&07 23, , 155, , 9 2, 5, 23, 5, 18, 5, 18, 5, 18, 2 9, 2 9,,,,,

$}}$ $\ovalbox{\tt\small REJECT}$ $)$ $\sim$ 232026242526617158700 5 4 9 5 101018251421027 68 $T $ 8 9 9 9 12120 2742293835 $) $\ovalbox{\tt\small \epsilon_{1j}\frac{\ovalbox{\tt\small REJECT} \text{$

12 19, 2, MLB $G=(\overline{x}_{1G},\overline{x}_{2G})$ 9 2 $(\overline{x}_{1g},\overline{x}_{2g})=(5923,2642)$ (15) 0$W8$, 0149, , $\overline{x}_{g}$, 1 630, $\gamma=630$ (16) max (16) $\{a (\overline{x}_{g},a)\in P(\gamma)\}$ (16) , , : 608, $0973(=$ 0592/0608), 592 5, ( B,,, ) 0948, , 3, $2W7$, $2m7$ e $2W6$ 2, 0948 $2\infty 6$ 3,,, 5 $/\backslash 2006 ^{l}$ ( 2) 12,, (9) , ( 1 7) , ( 5)

$$2W7$, $2m7$ e 3 0973 $2W6$ 2, 0948 $2\infty 6$ 3,,, 5 $/\backslash 2006 ^{l}$ ( 2) 12,, (9) 5 1 2006, ( 1 7) 2 2006, ($

13 ,,,,,, ( 5) ( 2) $\cdot$ ( 6, 10), 2007 * ( 5, 10) 1,, DEA, 2,,,, (C) No [1], : : (HBJ, 1988) [2] : \sim (, 2000) [3] : (,2006) [4], : (, 1989) [5],,, (2006) 12/07, [6], :,, 537 (205) $\eta$ [ : 5, (, 1991) [8] :,, 49 (2004) [9], : $DEA/OERA$, 7 (1997) pp41-51 [10] :, 38 (1987) [11] :, 47 $(2W2) $ [12] : $DEA$ [13] :, (, 1993), 38 (1993)

$157-168 [6], :,, 537 (205) 23-25 $\eta$ [ : 5, (, 1991) [8] :,, 49 (2004) 380-389 [9], : $DEA/OERA$, 7$

42 1 ( ) 7 ( ) $\mathrm{s}17$ $-\supset$ 2 $(1610?\sim 1624)$ 8 (1622) (3 ), 4 (1627?) 5 (1628) ( ) 6 (1629) ( ) 8 (1631) (2 ) $\text{ }$ ( ) $\text{

$42 1 ( ) 7 ( ) $\mathrm{s}17$ $-\supset$ 2 $(1610?\sim 1624)$ 8 (1622) (3 ), 4 (1627?) 5 (1628) ( ) 6 (1629) ( ) 8 (1631) (2 ) $\text{ }$ ( ) $\text{$ 26 [\copyright 0 $\perp$ $\perp$ 1064 1998 41-62 41 REJECT}$ $=\underline{\not\equiv!}\xi*$ $\iota_{arrow}^{-}\approx 1,$ $\ovalbox{\tt\small ffl $\mathrm{y}