m
?
1,?ì1 ×¥
Q
n| o?ì ×
?1 ×
o9;μ
àμ
ü b
6| o1 ×2T
12
3
4
5
6
? 1 ×2T
ò
Q
ZE 1 ùs?phZ_YV
????¥
^?b
……
íE

312456 146325
ZE 2 9
¤s 1; 4? 2,3ò; 3? 4,5
ò; 2? 6; 1?b
2,3 4,5íE

132456 ?
3→2 4 →5
1
2
3
(1)
1
2
3
(2)
1
2
3
4
(1)
1
2
3
4
(2)
1
2
3
4
(3)
1
2
3
4
(4)
?ì1 ×¥2T ——é ×m
??W?μHM ?¥μ_m
3???
¥é ×m
Q {1 2 3}
{(1,2,3)}i

{1,2,3,4} {2,(1,3,4)} {(1,3,4),2}
4???
¥é ×m
Q
{(1,2),(3,4)}
{1,2,3,4}?
1
2
3
4
1
2
3
4
1
2
3
4
(1) (2) (3)
1
2
3
4
(4)
μ·B¥? ?
^? ? (1)
é ×m¥
3??
T
_ ?Ym —— ?B??i
Hμ
_
^?Mo ?Y ? (4)

e ? (2) (3) b
é ×m
¥?é
Ai? ?
^?
?i·B¥? ?
^?5?
??¥?
?
¨?D?¤s
¥
¨?Bá ? (1) b
T
eAes )1,,1,1(,null==
)¤s_
1~)1,1,2,2(
)1( T
Aes ==
=
0001
1000
1100
0110
A

=
Evv
Evv
a
ji
ji
ij
,0
,1
1
2
3
4
(4)
_ ?Yé ×m G=(V,E)¥
Q
?
#¤ ?
T
n
ssss ),,,(
21
null=
¤s_

)¤s_
2~)2,1,2,3(
)1()2( T
Ass ==
TT
ss )3,3,5,5(,)3,2,3,3(
)4()3(
==
eAAss
kkk
==
)1()(
TT
ss )8,5,8,9(,)5,3,6,8(
)6()5(
==
,
)(
→∞→
k
sk
nullnull
TT
ss )13,9,17,21(,)9,8,13,13(
)8()7(
==
eAAss
kkk
==
)1()(
_ ?Yé ×m¥
Q
?
? n(>3)???¥
_ ?Yé ×mi
??
r
P
#¤ ? A
@ A
r
>0 A?
í?
s
eA
k
k
k
=
∞→
λ
lim
í? A¥Kv+??1??
? λ??+?_
 s O
=
0001
1000
1100
0110
A
1 {1 2 4 3}
ssk
k
→∞→ )(,
)(
BBa
T
s )230.0,167.0,280.0,323.0(
,4.1
=

¨ s

1
2
3
4
(4)
{1,2,3,4}?
=
000100
100100
110000
001010
111000
111010
A
TT
TT
ss
ss
)16,25,21,32,28,38(,)9,12,7,16,10,15(
)3,4,3,9,5,8(,)1,2,2,3,3,4(
)4()3(
)2()1(
==
==
12
3
4
5
6
6| o1 ×2T
T
s )104.0,150.0,113.0,231.0,164.0,238.0(,232.2 ==λ
Q?1 {1 3 2 5 4 6}
2,
ü6"d¥
V?
+
-
+
-
+
+
+
+
-
-
+
v
2
v
1
v
3
v
4
v
6
v
7
v
5
è
÷ ?¨"d¥??
v
1

÷ ?¨
 v
2

÷Nì
v
3


3á
q v
4
—ìaé

v
5
—y<á′ v
6
—ü<
v
7
— | g9
b
"d¥í
í ——m¥??
{?|¥μ_m

íW¥?Y ——{Z_¥
?Y¥?Q
——
¥ +a–|
?| —— Z4
p Z??|?Y ——°¤?Y
{?|μ_m G
1
=(V,E)¥
#¤ ? A
V~??" E~"

+
=
Evv
vv
vv
a
ji
ji
ji
ij
?
1 ?
1 ?
0
,1
1
+
-
+
-
+
+
+
+
-
-
+
v
2
v
1
v
3
v
4
v
6
v
7
v
5

=
0000001
1000000
0100001
1000000
0010010
0000001
0001110
A
-
v
i
v
j
+

H
v
i
9F?á
/
H
v
j
9F h

{?|¥μ_m G
1
??
?

=
0000005.1
1000000
05.100002.1
3.0000000
0010020
0000007.0
0002.18.05.00
W
F ?μ_m G
2
# 
#¤ ? W
?

?

H
v
i
9F 1?ê?á
/
H
v
j
9F w
ij
?ê
j
w
i
vv
ij
→?
¥+ è
j1 WA
v
7
0.3
1
1.5
1
1.5
1.2
0.8
-2
-2
-0.7
-0.5
v
1
v
2
v
3
v
4
v
5
v
6
F ?μ_m G
2
j
w
i
vv
ij
→?

V? 
Pulse Process)
ù??
í
í v
i
M? ¥"d¥MV?
v
i
(t) ~ v
i

H
t ¥ ′  p
i
(t) ~ v
i

H
t ¥ ?M
 (
 )
nullnull,2,1,0,,,2,1),1()()1( ==++=+ tnitptvtv
iii
∑∑
==
=+=+
n
i
n
i
iijjiijj
tpatptpwtp
11
)()1(),()1( 
))(,),(),(()()),(,),(),(()(
2121
tptptptptvtvtvtv
nn
nullnull ==
)1()()1( ++=+ tptvtv

V?
?
Wtptp )()1( =+
Atptp )()1( =+

÷ ?¨"d¥??
e?
V? ——
S
 p(0)?
?s
1 1 ?1 0¥
V?
? 7
S
H
÷ ?¨
μl ?9F??"d¥M
)0()0( pv =
)1()()1( ++=+ tptvtv
Atptp )()1( =+
!
÷ ?¨"d¥ p(t) v(t)
2
3
1
-10010-1 2-21-110-1
1-11-1010 3-32-21
1
-1
nullnull
nullnull
-1
1
0-11-1000 1 1-10000
t
4
p
3
p
5
p
6
p
7
p
2
p
4
v
3
v
2
v
1
v
5
v
6
v
7
v
0 100000
0
100 0000
1
p
e?
V? S¥×??
?i
H
S¥òí
í¥′

^?1μK (×? )
S?×?
H ??M V[ e?¥1"
P-M1×?
)1()()1( ++=+ tptvtv
Wtptp )()1( =+
′×?

×?
S
×? ~ ?i i,t,| p
i
(t) |μ?
S′×? ~ ?i i,t,| v
i
(t) |μ?
t
Wptp )0()( = S¥×?? | %? W¥+??
,W¥d
,+??1 λ
e?
V? S¥×??
S
× |λ | ≤ 1
S
× |λ | ≤ 1 O (1??
S′× S
×? O λ??? 1

=
0000001
1000000
0100001
1000000
0010010
0000001
0001110
A
?
÷ ?¨"d¥
#¤ ? A
)1()(
2352
λ?λ?λλ=λf
+?[
T
76)2(,2)1( =?= ff
)2,1(∈?λ
÷ ?¨"di 

?×? ¥e?
V?
e?
V?¥×??
?é¥
o>?m S
*
~{?|¥
μ_m
_ ?Y OiB?
ê?
μí
^
¥????b
+
-
+
-
+
+
+
+
-
-
+
v
2
v
1
v
3
v
4
v
6
v
7
v
5

^é~?í
^¥H

^?| ~?í
^¥òμ_H?| +1-1-e
a
k
~é1 k¥í
^?|
r~
P a
k
??? 0¥Kv?
S
*

×
)1,,2,1(?== rkaaa
r-krk
null
,1±=
r
a
? S
*

×?5 S
*
′× 1≠

=
r
1k
k
a
e?
V? S
*
¥×??
a
1
=0,a
2
= (-1)
v1v2
× (-1)
v2v1
=1
a
3
=(+1)
v1v3v5v1
+(-1)
v1v4v7v1
+(+1)
v1v3v2v1
=1,a
4
=0,a
5
=1,r=5
S
*

×
)1,,2,1(?== rkaaa
r-krk
null
,1±=
r
a
352
aaa≠
(-1)
v1v2
→(+1)
v1v2
(? ? ?¨M1K? ?¨ )? a
2
=-1

S
*

?×? v
1
~ ?¨
,v
2
~Nì
v
7
+
-
+
-
+
+
+
+
-
-
+
v
2
v
1
v
3
v
4
v
6
v
5
)1()(
2352
+= λλλλλfA¥+?[
T
O1??1
2/)31(,,1,0,0
≤?
±?±=
λ
λ ii
S
*

×?
S
*

× |λ | ≤ 1 O (1??
? S
*

×?5 S
*
′× 1≠

=
r
1k
k
a
}1,0,1,1,0{},,,,{
54321
=aaaaa
S
*

×
)1,2,1(?== rkaaa
r-krk
null
,1±=
r
a
1,1,
5353
=?= aaaa
-
+
-
+
+
+
+
+
-
-
+
v
2
v
1
v
3
v
4
v
6
v
7
v
5
+
S
*
′?×?
S
*
′
×?
(+1)
v3v5
→(-1)
v3v5
v
3


3á
q
v
5
—y<á′
(-1)
v3v5
′Q Z4
p
÷ ?¨"d¥′??×?$
Discussions
3,rm¥ ?s

JYd ? |Tü
 ?JYT ? 7í
JdT ? 5íYdT ? 4í
? |T ? 11íb??
|?? ? 1íb
ù ? |T
H ?s
¥ ?$
è
:JYd ? |s
¥1
),,(
321
xxxx =
11
321
=++ xxx
4
5
7
32
31
21
≥+
≥+
≥+
xx
xx
xx
3?·B
(5 3 3)
(4 4 3)
(5 4 2)
……
1,,
321
≥xxx
},,2,1{ nI null="
(1) ShapleyT|
@
Lf
0" )(svIs?∈?
φ
φ
=+≥
=
212121
),()()(
0)(
sssvsvssv
v
∪∪
[ I,v] ~n |T| v~+?f
),,,(
21 n
xxxx null=
~n |V v(I)¤?¥s
¥
@
v(s)~ 0"
s¥ ?
)(
1
Ivx
n
i
i
=

=
niivx
i
,,2,1),( null=≥
ShapleyT|
 ?ZE
Shapley′
!
)!1()!(
)(
n
ssn
sw

=
niisvsvswx
i
Ss
i
null,2,1)],\()()[( =?=


s?~0" s?¥í
í
" S
i
~c i¥
μ0"
)]\()([ isvsv?
~ i T s ¥o
Dp
)( si∈
)( sw
~s? %?¥o
Dp¥ ?×
? | (I={1,2,3})ü
?J¥s
¥ x
1
¥9
1/3 1/6 1/6 1/3
)]1\()()[( svsvsw?
)( sw
s
)1\()( svsv?
)1\(sv
)(sv
1
S
1 1 2 1 3 I
∪∪
1 7 5 11
0 1 1 4
1 6 4 7
1/3 1 2/3 7/3
)]1\()()[(
1
1
svsvswx
Ss
=


1 2 2 3
?
V¤ x
2
=23/6,x
3
=17/6
x
1
=13/3
T|¥?¨ è 1 ê
£) ?n¨¥ ?s?
20km 38km

@
?ì?1 ?ê?
Uim
1
2
3
Q
1
=5
Q
3
=5
Q
2
=3

£) ?
?
@
Q~ê

 L~5?é
yìn¨ P
1
=73Q
0.712
5?n¨ P
2
=0.66Q
0.51
L
?ì? V??y) ?ì
 óyì (¨5?|ê

?
3ì?
a/3ì? )

£) ?¥ 5 ?Z?
1??yì
230)3(,160)2(,230573)1(
712.0
===?= CCC
620)3()2()1(
1
=++= CCCD
9g'
35020566.0)35(73)2,1(
51.0712.0
=++?=C
2 1,2T
580)3()2,1(
2
=+= CCD
9 g'
36538366.0)53(73)3,2(
51.0712.0
=++?=C
3 2,3T
595)3,2()1(
3
=+= CCD
9g'
46358566.0)55(73)3,1(
51.0712.0
=++?=C
4 1,3T
T?
LC460)3()1( =+> CC
55638)35(66.0
20566.0)535(73)3,2,1(
51.0
51.0712.0
5
=?++
+++?==CD
5 ?ì
T9g'
D
5
Kl,? óyì
yìn d
1
=73×(5+3+5)
0.712
=453
1→25?n d
2
=0.66 ×5
0.51
×20=30
2→35?n d
3
=0.66 ×(5+3)
0.51
×38=73
D
5
{
D
5
?s?$
230)3(
160)2(
230)1(
=
=
=
C
C
C
ì 3yp d
1
? 5:3:5s?,d
2
,d
3
?ì 1,2?μ
ì 2yp d
3
?ì 1,2? 5:3s?,d
2
?ì 1?μ
ì 19
ì 3s? d
1
×5/13=174<C(3),
ì 2s? d
1
×3/13+d
3
×3/8 =132<C(2),
ì 1s? d
1
×5/13+d
3
×5/8+ d
2
=250>C(1)
?
]
i
ShapleyT|
}3,2,1{=I"
+?f
v(s)~ ó (" s)yì1??yì??¥g'
0)3()2()1(,0)( ==== vvvv φ
40350160230)2,1()2()1()21( =?+=?+= CCCv ∪
64556230160230)3,2,1()3()2()1()(
0)31(
25365230160)3,2()3()2()32(
=?++=?++=
=
=?+=?+=
CCCCIv
v
CCCv


),,(
321
xxxx =
~ ?ìV??g' v(I)?¤?¥s

9
ì 1V??g'?¤?¥s
¥ x
1
)]1\()()[( svsvsw?
)( sw
s
)1\()( svsv?
)1\(sv
)(sv
s 1 1 2 1 3 I
∪∪
0 40 0 64
0 0 0 25
0 40 0 39
1 2 2 3
1/3 1/6 1/6 1/3
0 6.7 0 13
x
1
=19.7,
ì 1 C(1)-x
1
=210.4,ì 2 C(2)-x
2
=127.8,ì 3 C(3)-x
3
=217.8
?ì9g' 556?¥s?
x
2
=32.1,x
3
=12.2 x
2
Kv ?3
d$
T|¥?¨ è 2
Yv8?¥ ?×
90 |¥v8? 3?
YF? |
sY1 40,30,20 |b
v8V %
H3V?
¥!?
DZ VYVb
?
?
Y¥??]
Hg!?
DQ
D¨ Shapley
T|9

Yv8?¥ ?×b
1)()32()31()21(
,0)3()2()1(,0)(
====
====
Ivvvv
vvvv
∪∪∪
φ
ù ? 3
|
Mμv3/1
321
=== xxx ?×
v8 I={1,2,3}GQ}V 3?
Y
=
?5
¥???V
?l +?f
0
45,1
)(
s
sv
ShapleyT|l2
a??a ?μ ?$b
?? 31??
μT¥ ?'1?l I={1,2,…n}¥

0" (
2
n
-1? )¥+?f

L=
èS??b
? n??êí ?ê ?,Yè??? iZ??í ?¥g' y
i
nZ
]í ?¥g' Y,#? iZ??F
H ? n-1Z¥g' z
i
(i=1,2,…n),
??
]í ?
HòZs?¥n¨b
i
ij
j
zyiIv?=


)\(

v(s) (???,íE¨ ShapleyT| p3
??l+?f
1T¥ ? (??¥g' )5μ
,)(),,2,1(0)(
1
YyIvniiv
n
i
i
===

=
null
p3T|¥ 
eZE
!o??
~)\( iIvb
i
=
í i?F
H n-1ZT¥ ?
~)(IvB=#
?8T¥ ?
),,(
1 n
bbb null=:
0),,,,(
21
≥=
in
xxxxxB null¥s
¥ pòZ ?
è,JYd ? |Tü
 ?JYT ? 7í
JdT ? 5íYdT ? 4í ? |
T ? 11íbù ? |T
H ?s
¥ ?$
),,(),7,5,4(11
321
xxxxbB === p'X?

2x
3
=≥?
0
0
,nullAbAx
TT
1
1
≥?
≥?
=



nni
i
i
bxx
bxx
Bx
null
11
[ n-1ZT¥ ?1/K

?
T
T
bxA = p3

=
iii
bb
n
x
1
1
~ x
i
¥/K
|
:? ?
ü (s


i
xB
11),7,5,4(,== Bb è
,3),1,3,4( =?=
∑ i
xBx
)2,4,5()1,1,1( =+=xx
n
B
bb
n
xB
n
xx
iiiii
+?=?+=
∑∑
1
)(
1

3 Nash3
),,(
1 n
ddd null=:
1C?

H¥ˉ
?
N$
o (
1ps
¥ ?8T¥ ? B
ii
i
i
i
i
dx
Bxts
dxxma

=


..
)(

?

+= )(
1
iii
dB
n
dx
0=
i
d
ü (s
¥ ? B
i
i
xd = 3 Nash3? 2x
3

4Kl  ?3
¥
K1,xxxx
n
),,(
1
null=
ii
i
i
ii
xx
Bxts
xxnmi

=


..
)(
2

?

= )(
1
Bx
n
xx
iii
n
B
bb
n
x
iii
+?=

1
ii
bBx?= ?
7
? i Z¥H=rm
4Kl  ?3
2x
3
11),7,5,4(,== Bb è
,6),4,6,7( =?=

Bxx
i
)2,4,5()2,2,2( =?=xx

5
i3
d
i
~C? (K?? )
e
i
~ ?X? (Kú? )
ii
ii
i
de
dx
u
=
i
)(
iiiii
ii
i
i
deudx
de
dB
u
+=
=
∑∑

Bxts
unmixma
i
i
i
=

..
)(

?
ii
i
i
xexd ==,
5?
i¥3? 2x
3
¥1 ès
¥??


=
ii
i
i
i
xxB
x
x
x ~
iii
xed ==,0

6 Raiffi3
Dx
3 x=(5,4,2)1?
:)1 ¥s
¥$
é?ZT ?¥s
¥
 Bnx?
jj
xbBnjj =  ?1ZT
H¥e ?í?D?,1)(
jini
n
x
xx
x
x
j
ii
j
j
≠=
+==,,,1,
)1(2
,
2
null
Z?sZ
üs5? 11 nnjx
j
¤?
ü ( |,,,2,1 nj null 11),7,5,4(,== Bb è
)4,6,7(),1,3,4( == xx


++
=
ij
j
i
ii
x
n
x
n
x
n
n
x ]
)1(2
1
2
[
11
)
12
5
2,
12
11
3,
3
2
4
=x
p3T|¥ 6?ZE
Vs1 ? ?
ShapleyT|
A
?
B
?
!
)!1()!(
)(
n
ssn
sw

=
niisvsvswx
i
Ss
i
,,2,1)],\()()[( null=?=


)(),\( IvBiIvb
i
==o3
Issv ∈),(31

x
3
)(
1

+=
iii
xB
n
xx
/K~
i
x
Nash3

+= )(
1
iii
dB
n
dx
C ~
i
d
Kl  ?3

= )(
1
Bx
n
xx
iii
K~
i
x
i3
)(
iiiii
ii
i
i
deudx
de
dB
u
+=
=
∑∑

d
i
~C,e
i
~ ?X
ii
i
i
xexd ==,
ii
bBx?=
,
1
bAx
=
B ? 4?ZEM]
èμB'Z (J )= ?Z (Y,d ),??'ZDà

B ?ZT
H? ? 10í? ?s
¥? ?$
Raiffi3C
?
)(),\( IvBiIvb
i
==o3
Z?sZ
üs5?
K
? 11, nnjxj
j
)67.1,67.1,67.6().( =xShapleyA
10)(),10,10,0(),\(,==== IvBbiIvbB
i
)0,0,10(,=?= xbBx
ii
)0,0,10(
1
==
T
T
bAx
)83.0,83.0,34.8(=x


++
=
ij
j
i
ii
x
n
x
n
x
n
n
xRaiffiC ]
)1(2
1
2
[
11
).(
)0,0,10(=x
p3T|¥ ? ?ZEl2
A ?? ? 31?9
ˉb
B ?9
e?L? ?3 V¨?òZ
L
?Mμ?v¥ f ? B? ?
a
ê <?b
C ? I
n
s
¥¥
/K?
|

Shapley¥
±XB??
 1 D?b
Discussions