. . , d s
, d , s. , , d, s.
:
, , d s, s. , , , :
P (d Ù s)= P (s) * P (d | s)
P (d Ù s)= P (d)* P (s | d).
:
P (d | s) d , s P (s | d). P (d) d, P (d | s) , , d , , s . , P (d | s) P (s | d).
, , P (d ∧ s). . X _Y
, , _Z. P ( _Z | _Y), , ,
_Z _Y. , , . , P ( _Z Ù _Y).
, , , . , , _Y _Z. , , _Z _Y.
|
|
, P ( _Y | _Z) .
, . , m * n + m + n , m
, n . , , .
, . :
(m * n) k + m + nk , k . , P (s1 Ù Ù sk) P (s1 | s2 Ù Ù sk) *
P (s2 | s3 Ù Ù sk)** P (sk). , , , si sj P (si Ù sj) = P (si) * P (sj). ,
, . - . , , , . , . , , ,
.
54. ? , . , ? . .
, . ∈ , , .
. , : . , f, , X
f (X) = , X Î A.
, , 150 :
CAR (X) MAX SPEED (X) > 150
GT150(X) = ,
, CAR (X) MAX_SPEED (X) :
|
|
{ X Î CAR | MAX_SPEED (X) > 150 }.
, CAR, 150 . , , , . , () . , . f (X) [0, 1]. , X f (X) = 1, , f (X) = 0, . f (X) . , . , fFAST (80) = 0 fFAST (180) = 1,
, [0, 1].
FAST_CAR , ,
:
fFAST_CAR (X) = f FAST (MAX_SPEED (X)).
, , (, ), :
FAST_CAR = {(Porshe 944, 0,9), (BMW 316, 0,6), (Chevy NIVA, 0,1)}.
. , , 0 1, . , , ., .
, , , : F(X) = 1 - F(X), F ( ).
:
f F ∧ G(X) = min(f F(X), f G(X)),
f F ∨ G(X) = max(f F(X), f G(X)).
, Porshe 944 FAST_CAR(Porshe-944) PRETENTIOUS_CAR(Porshe-944). FAST_CAR(Porshe-944) = 0,9, PRETENTIOUS_CAR(Porshe-944) 0,7. , :
FAST_CAR(Porshe-944) ∧ PRETENTIOUS_CAR(Porshe-944)=
=min(0,9, 0,7)=0,7.
:
FAST_CAR (Porshe-944) ∧ FAST_CAR (Porshe-944) = 0,1.
, , :
P (FAST_CAR (Porshe-944) | FAST_CAR (Porshe-944)) = 0.
min (0,9, 1 - 0,9) = 0,1. , . . FAST_CAR (Porshe-944) = 0,9 , 90% , , , , 1. 0,1 , Porshe-944 , - , - .
, . , X Y. X Y , .
|
|
. , 10 , , . , ?
, , , , . , P (RED) , [0, 1]. , , : fSEVERAL = {(2, 0.1), (3, 0.2), (4, 0.6), (5, 1.0), (6, 1.0), (7, 0.6), (8, 0.3), (9, 0.1)}.
, 3 10 , fSEVERAL (3) = 0.2. 5, 6 , 1 10 , . , . , .
, :
{(0.2,0.1), (0.3,0.2), (0.4,0.6), (0.5,1.0), (0.6,1.0), (0.7,0.6), (0.8,0.3), (0.9,0.1)}.
, , P (RED) = 0.3 20%. fP(RED) .
, . , . , fTRUE: [0, 1]→[0, 1]. , , , . ,
TRUE (FAST_CAR (Porsche-944)) = 1.
, , Porsche-944 , , .
55. , , -. -.
(DempsterShafer) ,
6 ,
. 0
(frame of discernment). ,
h1.....hn, 6,
A1..., Ak, .
U
:U -> 20,
U .
. ,
, u U
|
|
. ,
, .
,
.
(b
basic probability assignment), 20
[0,1], ,
m( ) = 0
S[((i) - 1];
Ai 20 .
Bel
. , Bel ,
2 [0,1], ,
Bel(A) = SB Î m(B).
1(0) 1, (O).
. 1(O) = 1 :
, 0
, . m(O) , , 0. Bel , .
,
, 1 - l(A)> A A.
A, ls(A),
ls(A)= S A^B m(B).
,
-A, :
ls (A) = 1 - el (-A).
,
-.
, Bel ,
[el(A), Pls(A)].
.
, . Bel1 l2
,
1 . 1+2,
l1+ l2, , .
1+2() 1() m2(Y), X
Y , .
, .
k ,
0, 1+2(0) , m1+m2
(1 - k).
,
m1+m2= SX^Y=A[m1(X)m2(Y)]/[1- S X^Y = {m1(X)m2(Y)}]
, 1 m2
. ,
.