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1

2

3 A B A B

4 LETS

5 1 [1][2] n n 4

6 5 2 ( )

7 2 2.1.,,,,,. [3] [4]..,.,.,,.,, [5]. 6

8 7,., [5].,,.,,, [5].,,.,.,, 0,., [5] ,....

9 ,.,,., [4]

10 9 [4] 3 [4]

11 10 Edy( ) Suica( ) 1 [6] 2.1: 2.2: IC 1 IC 1 IC

12 11 2 [4] 2.3: 2.4:

13 ( )

14 13 2.4,,,,,., ,,,.,,,,..,,.,,.,,,.,,,., [7] , ,

15 14,,,. ( ) 1.,,,.,.,,. 2.,,.,.,,,,. ( ) 1.,,.,,. 2.

16 15,,,.,,.,,,,,,.,, ,,,, [3]. 1.., ,.,,.,,.

17 16 2.,.,,,.,,.,,. 3..,,.,,,,,,.,.,.,.,,,,,. 4..

18 17 5. ( ). 6. 1

19 ( )

20 19

21 ,,, 3.,. [9] 0

22 21 [9],.,.,.,. [9] , 2,000, 100.,, LETS.LETS,1983,,, [10].

23 22 LETS LETS,LETS, 4,.,LETS,,, LETS,.,LETS. LETS, LETS.LETS,,.,.,.,,, [10]. LETS,,..,LETS,.,,,,

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

25 24 2.5: LETS 2.6 ( ),..,,., [11]. 2,1, 1.

26 ,.,.,,., ,.,,, 2.

27 26 2.7, ( ) ( ) ( ) [12] [13]

28 27 n : (N, v) N = {1,, n} v N v N S S v(s) v

29 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

30 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 [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)

31 30 v(n) [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

32 31 2.7: ( ) ( ) 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

33 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

34 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

35 [1][2] 2.8 ( ) 2 2.8:

36 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))

37 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

38 37 A B

39 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))

40 3 39

41 A B 3.1: A B a b b a

42 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

43 A B 3.3:

44 43 1. A B :

45 4 S S

46 45 4.1: A B A B

47 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)

48 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 )

49 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)

50 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

51 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)

52 5 n n 51

53 52

54 [1] K.Hirotsugu,T.Yoshiaki et.al, A Local Currency System Reflecting Variety of Values, Proc. IEEE/IPSJ SAINT2011, pp , 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 , July [3] : pp57-68 (2005) [4] (2007) [5] (1998) [6] [7] (2000) [8] (2000) 53

55 54 [9] SNS (2008) [10] LETS [11] [12] [ ] (2011) [13] (2012). [14] (2012) [15] (2012) [16] (2004) [17] (2008) [18] (1985)

56 55

24 200902728 1 4 1.1......................... 4 1.2......................... 4 1.3......................... 5 1.4......................... 5 1.5........................... 5 1.6...................... 6

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