24 201170068

1 4 2 6 2.1....................... 6 2.1.1................... 6 2.1.2................... 7 2.1.3................... 8 2.2..................... 8 2.3................. 9 2.3.1........... 12 2.3.2........... 12 2.4......................... 13 2.4.1................ 13 2.5.................. 13 2.5.1................ 15 2.5.2................ 18 2.5.3................. 20 2.5.4................ 21 2.6........................... 24 2.6.1................... 25 2.6.2................... 25 2.7.................... 26 2.7.1.................. 27 2.7.2................. 29 2.7.3................... 30 1

2 2.8................. 34 3 39 3.1 A B. 40 3.2 A B 42 4 44 5 51 52 55 56

2.1............. 10 2.2............ 10 2.3.................... 11 2.4................... 11 2.5 LETS....................... 24 2.6...................... 27 2.7............... 31 2.8.................. 34 3.1................... 40 3.2......................... 41 3.3.................. 42 3.4......................... 43 4.1.............. 45 3

1 [1][2] n n 4

5 2 ( ) 2 3 4 5

2 2.1.,,,,,. [3].... 2.1.1. [4]..,.,.,,.,, [5]. 6

7,., [5].,,.,,, [5].,,.,.,, 0,., [5]. 2.1.2,....

8. 2.1.3,.,,.,.. 2.2 1 [4]

9 [4] 3 [4] 2.3 2 1

10 Edy( ) Suica( ) 1 [6] 2.1: 2.2: IC 1 IC 1 IC

11 2 [4] 2.3: 2.4:

12 2.3.1 2.3.2 ( )

13 2.4,,,,,.,. 2.4.1,,,.,,,,..,,.,,.,,,.,,,., [7]. 2.5 1930, 1980. 1990,

14,,,. ( ) 1.,,,.,.,,. 2.,,.,.,,,,. ( ) 1.,,.,,. 2.

15,,,.,,.,,,,,,.,,. 2.5.1,,,, [3]. 1..,. 1886 1964,.,,.,,.

16 2.,.,,,.,,.,,. 3..,,.,,,,,,.,.,.,.,,,,,. 4..

17 5. ( ). 6. 1

18 2.5.2 1. 2. ( )

19

20 2.5.3,,, 3.,. [9] 0

21 [9],.,.,.,. [9]. 2.5.4, 2,000, 100.,, LETS.LETS,1983,,, [10].

22 LETS LETS,LETS, 4,.,LETS,,, LETS,.,LETS. LETS, LETS.LETS,,.,.,.,,, [10]. LETS,,..,LETS,.,,,,

23.,,.,,,.,.,.,,LETS,, [10].,,,,.,.,,,,, [10].,LETS,.

24 2.5: LETS 2.6 ( ),..,,., [11]. 2,1, 1.

25 2.6.1,.,.,,.,. 2.6.2,.,,, 2.

26 2.7, ( ) ( ) ( ) [12] [13]

27 n 2.7.1 2.6: (N, v) N = {1,, n} v N v N S S v(s) v

28 (N, v) x=(x 1,, x n ) n (i) x i = v(n) i=1 (ii) i N x i v({i}) (i) (ii) I [13] I = {x R n n x i = v(n), x i v({i}), i=1 i = 1, 2, n} (2.1) 2 x y 2 S y (i)x i > y i i S (ii) i S x i v(s) x y xdomy

29 [14] C(v) = {x R n i S x i v(s) S N} (2.2) i S x i v(s) S N 2.7.2 [17] N β S β δs δ s = 1 i N S β,s i i δs S β δ s v(s) v(n) S β δ s S δ s v(s)

30 v(n) 2.7.3 [18],,, [14]. u i 2 x=(x 1, x 2, x m ) y=(y 1, y 2, y m ) : λ(0 λ 1) u i (λx + (1 λ)y) λu i (x) + (1 λ)u i (y) x k y k (k = 1, 2,, m) u i (x) u i (y) [12] 2.7

31 2.7: ( ) 1000 1 1000 1 ( ) i N : N = (1,, n) : w i = (wi 1,, wi m, wi m+1 ) : i x = (x 1,, x m, x m+1 ) : n m+1 m+1

32 x=(x 1,, x m, x m+1 ) i U i (x) U i (x 1, x m, x m+1 ) = u i (x 1,, x m ) + x m+1 (2.3) (2.3) i, S S S i x i =(x 1 i,, xm i, xm+1 i ) i S x j i w j i, j = 1,..., m + 1 (2.4) i S S U i (x i ) = i S i S u i (x 1,..., x m ) + i S x m+1 i (2.5) S S v(s) { v(s) = max u i (x 1 i,..., x m i ) + } x m+1 (x i ) i S i S i S s.t. i S x j i w j i, j = 1,..., m + 1 (2.6) i S v(s) = max u i (x 1 i,..., x m i ) + (x i ) i S i S i S s.t. i S x m+1 x j i w j i, j = 1,..., m + 1 (2.7) i S

33 (2.7) v(s) v(s) = max u i (x 1 i,..., x m i ) (x i ) i S s.t. i S i S x j i w j i, j = 1,..., m + 1 (2.8) i S (N, v),(n, v ) v, v α, β 1, β 2,, β n S N v (S) = αv(s) + i S βi α

34 2.8 [1][2] 2.8 ( ) 2 2.8:

35 n x 1 x n V = {x 1, x 2,, x n } S : A R : B A S V A (S), R V A (R) B S V B (S), R V B (R) V At A V Bt B A B B A. F A (V A (S), V A(R)), F B (V B (S), V B (R)) V A (S) V A (R) V B (S) V B (R) F A (V A (S), V A(R)) > 0 F B (V B (S), V B (R)) > 0 V A (t + 1) = V At + ( V A (S) + V A (R)) V B (t + 1) = V Bt + (+V B (S) V B (R))

36 A V A (R) V A (S) = (a 1, a 2,, a n ) F A (V A (S), V A (R)) = B V B (S) V B (R) = (b 1, b 2,, b n ) n i=1 a i F B (V B (S), V B (R)) = 1 A B S A B B A R n i=1 b i

37 A +5 +4 +3 +2 +1-1 -2-3 -4-5 B +5 +4 +3 +2 +1-1 -2-3 -4-5

38 n=5 5 ( ). A S ( ) 3 B R. A S V A (S) V A (S) = (2, 2, 0, 3, 0) V A (R) V A (R) = (0, 2, 1, 0, 0) A V A (R) V A (S) = (0, 2, 1, 0, 0) (2, 2, 0, 3, 0) = ( 2, 0, 1, 3, 0) (a 1, a 2, a 3, a 4, a 5 ) = ( 2, 0, 1, 3, 0) F A (V A(S), V A(R)) = Σa i (i = 1 n) = 2 0 B F B (V B (S), V B (R)) 0 V A (t + 1) V B (t + 1) V A (t + 1) = V At + ( V A (S) + V A (R)) V B (t + 1) = V Bt + (+V B (S) V B (R))

3 39

40 3.1 A B 3.1: 3.1 1. A B 2. 3.2 a b b a

41 3.2: S A (A )a R B (B )b a S V a (S) b R V b (R) a R V a (R) b S V b (S) V a (t + 1) a V b (t + 1) b

42 3.2 A B 3.3:

43 1. A B 2. 3.4:

4 S S 4.1 44

45 4.1: A 100 100 B 200 200 A B

46 i N : N = (1,, n) : w i = (wi 1,..., wi m+n ) : i x = (x 1 i,..., x m+n i ) : x = (x m+3 i,..., x m+n i ) : n m + n m + 1 m + 2 (m + 3,..., m + n) m + 3 m + 4 x i U i U i (x 1,..., x m+n ) = u i (x 1,..., x m+n ) +x m+1 + p i (x m+2 ) +q i (x m+3,..., x m+n ) (4.1) (4.1)

47 U i u i p i q i : i : i : i : i (4.1) i (4.2) p(x m+2 ) = λx m+2 (4.2) (4.3) q i (x m+3,..., x m+n ) = µx T (4.3) x T x S N S N S S S i x i = (x 1 i,..., xm+n i )

48 i S x j i w j i, j = 1,..., m + n (4.4) i S i S x j i < i S w j i i S x j i = i S w j i S (4.5) U i (x 1,..., x m+n ) = u i (x 1,..., x m ) i S i S + x m+1 + p(x m+2 ) i S i S + i S q i (x m+3,..., x m+n ) (4.5) S S v(s) v(s) = max (x i ) i S + i S p(x m+2 ) + i S { u i (x 1,..., x m ) + i S i S } q i (x m+3,..., x m+n ) x m+1 s.t. i S x j i w j i, j = 1,..., m + n (4.6) i S (4.6)

49 v(s) = max (x i ) i S + i S { u i (x 1,..., x m ) i S p(x m+2 ) + i S q i (x m+3,..., x m+n ) } s.t. i S x j i w j i, j = 1,..., m + n (4.7) i S (4.2) (4.7) v(s) = max (x i ) i S + i S { u i (x 1,..., x m ) i S q i (x m+3,..., x m+n ) } s.t. i S x j i w j i, j = 1,..., m + n (4.8) i S (2.8) v(s) S S i u i

50 v(s) = max (x i ) i S s.t. i S { } u i (x 1,..., x m, x m+3,..., x m+n ) i S x j i w j i, j = 1,..., m + n (4.9) i S (4.9) (2.8)

5 n n 51

52

[1] K.Hirotsugu,T.Yoshiaki et.al, A Local Currency System Reflecting Variety of Values, Proc. IEEE/IPSJ SAINT2011, pp. 562-567, July2011 [2] K.Hirotsugu,T.Yoshiaki et.al, A local currency system reflecting variety of values with a swarm intelligence, Proc. IEEE/IPSJ SAINT 2012, pp.251-255, July. 2012 [3] : pp57-68 (2005) [4] (2007) [5] (1998) [6] http://www.digitalcashmap.com/ [7] (2000) [8] (2000) 53

54 [9] SNS (2008) [10] LETS http://e-public.nttdata.co.jp/f/repo/677_a1002/a1002.aspx [11] [12] [ ] (2011) [13] (2012). [14] (2012) [15] (2012) [16] (2004) [17] (2008) [18] (1985)

55