ИНТЕЛЛЕКТУАЛЬНЫЕ ИНФОРМАЦИОННЫЕ СИСТЕМЫ
.PDF/ 0 / % 0& Q< ) ' ' ' " P m = > %' " Q< Ψm) " ' G, G
F 0 / % 0& Q< 0 "%; " ?
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' >
1%" / mr(D|U ) R % " <' D "0 U @ ' ' mi(D|U ) % " " " " D "0 U M
1 |
> mr(D|U ) > 0, |
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mi(D|U ) = 0) |
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> mi(D|U ) > 0, |
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mr(D|U ) = 0 |
1 |
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0 " " Q < " " %<;
CF (D|U ) = mr(D|U ) − mi(D|U ).
J ' CF 0 " = " H[wYXnbY\ vXHYcw>
F % " CF %" " <' <) "
CF R * < " / ' CF ' ) ' /" / %
<' " P ? " /" " " 0 ? " 0
%< % ) " " < " 0 ' 45 J ' 45 & % " / "
1 "0 " " ) " 0& * Q< * Q<
* 1 " / % * %' 0 < " 0 % " CF (Φ)) " 0 " 0 Φ "0 .& " ' % " "0 " %<;
Φ1 Φ2
CF (Φ1 AN D Φ2) = min CF (Φ1), CF (Φ2) , |
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CF (Φ1 |
CF (Φ1), CF (Φ2) . |
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OR Φ2) = max |
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. * % " %" "0 |
" ) ' CF = 1 |
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R " < ' p q) CF = −1 R |
' p q) CF = 0 R p <q |
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%' % " <' Q 0 % " "0 & CF ) %' 0 " ;/< 0& 0P ) 45 "
1 " " " " * " " 1%" /
: 5x=% / r > €8W = % r 0P >
‚ƒ`8 = r >.
@ ' % " 0 I7 =% / r > I8 = % r
0P >
1%" / % " CF = >r . 0 " ) " 45 I7! r 45 I8! r
) =p" * % " / " " q>) % " / * = >
1%" / / / / " " 0) " ? ) " %<;
* % " / " "
CF (L) = 0.7, CF (L) = 0.9.
F % " /< " % /) ' * …
I "' % / %<; % " = ' CF > 0 " " %<;
CF L €8W L = min ~x=L >) ~x=L > = min(0.7, 0.9) = 0.7,
CF = 0.7 · CF ( 1) = 0.7 · 0.8 = 0.56.
% " / / % " ) % % "
: 5x B ‚ƒ`8 W CF ( .
M % " / ; % % Q / " / ' CF ) "
% % % / % D… 1%" / 0
7 : 5x B ‚ƒ`8 W CF ( 7) ;
8 : 5x B ‚ƒ`8 W CF ( 8) .
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1 ) ' "0 U 1 U 2 < " " 0 M % / 0 % ) "
" ) " " & D) % " CF ? " " 0' "" " %<; %
CF = |
CF (7) + CF (8) − CF (7) · CF (8), |
" CF (7) > 0 CF (8) > 0, |
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CF (7) + CF (8) + CF (7) |
· |
CF (8), |
" CF (7) < 0 CF (8) < 0, |
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CF (7) + CF (8) |
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1 − min |CF (7)|, |CF (8)| |
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= ) ' % = > " ' CF [−1, 1]>
J ) ' = > "" " % * < 0 %
" " " - " / % ? ) Q / % / 0 < ' " ) " / % 0& % / D
" 0' " ) % 0 = >a= > < % 0 " " J 0&)
' CF ) 0' " ? % ) " % / % • J 0&)
' CF = > " % * ) ' " /
j" 0 % * " " "& % * ' " / "0 0& ) " /" "' % "
? * ' 1 <" % ? %& ) 0&
% " CF (7) = 0.8) R CF (8) = 0.9
7 : 5x A = a1 €8W B = b2 ‚ƒ`8 D := d1 [0.8];
8 : 5x C = c0 ‚ƒ`8 B := b2 [0.9].
1%" / * " D) p " Q q =" > 0"
A = a1 " % " CF (A) = 0.7 1 0 * ' % / 0
% %< * / R ' B 1 "& & % 8)
0 " p" ; ' Cq 1 ) ' / / ' C = c0 " % " CF (C) = 0.9 1 8 " 0 ) ; p " % Q q B = b2 " % " CF (B) = CF (C) · CF (8) = 0.9 · 0.9 = 0.81
"& % 7 1 " / % %" " = & 0 0 0" 0 p " Q q>) " 0 D " " ' D = d1
P 0' " " % " ? " "
CF (A = a1 €8W B = b2) = min CF (A), CF (B) = min(0.7, 0.81) = 0.7 R % " / "
" "0 7(
CF (D) = 0.7 · CF (7) = 0.7 · 0.8 = 0.56 R " " / %' " " D = d1
T J & " %' & ' / "
' % " CF O ' " 0 "' " 0 / " %' ) " CF
0P CF I " " & ) ' % "
' " 0 /P ' ' , ) " % / 0
X %' ' x0 " % " CF (X) CF )
LX = x0 0" " p " % Q q) "' " ) ' ' X
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1 0 / ' ' " "" " " % "/ " )
% P " / * ' " & " F%; " %* 0 "" " ) %<; & ' " 0 & " Q =1 1
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& " %' 0 O / 0 ' & " =vlŠŠ\ Z[YZ> R ' =vlŠŠ\ ecgnH> 1 ? %' P " " ' .. =ZcvY Hc]|lYnbg> I "" " 0 ) ; " ? &
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* " " " % " / ? = Q >) |
<; & 0 ; " " < ? ? "" < " P/ |
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0 " " >) |
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/" " ' K " <; " * % % " " 0 ' = ' > 1 ' " R 0 * " 0 ' * J " ? " ) ' ? 0 " ) <; ; " " ) % / ? " " ' " ) " " ) / ? %
" % " ' " /< 1 & 0" 0 p? x
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? x % " %
@ ' ' U = {x} % " / " ? , ' "
A U 0 " " % " / {x, µA(x)}) x U ) % * µ : U → [0, 1] 0 "
% * " ' " A |
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L% * " " /< "0 |
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" J F@ .Œ = / " % ' > % * |
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0, |
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µ |
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(h) = |
h |
170 |
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h < 170; |
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−15 |
" 170 h 185; |
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1, |
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" h > 185, |
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1.0
m ( )
()
170 175 180 185
I " % . 0
' µA(x) % * " x 0 " " /< "
? ? ' % " % A
j" % " / " ' U = {x1 . . . , xi . . . , xn}) ' " A
"0 /
A = |
x1 |
, . . . , |
xi |
, . . . , |
xn |
, |
µ1 |
µi |
µn |
µi = µA(xi), i = 1, . . . , n
) ' % * " µA(x) " / "P & " ' " % * χA : U → {0, 1} 0' = ' > " A( χA(x) ' =?
" % A>) =? A>
J % * " 0 / " < / 0 F ' " " "/
0 0& " 0& % * & " =" " > F 0 % *
" 0 P < /P " ' @ ) " " P / " * ' " %< '%) 0 / & ;%< % % * " ) ?
/" %'P & % / 0 " " 0) ' " / % * "
I "
A " (
7+ & J0" ' " A 0 " & * % *
"
hgt(A) = sup µA(x).
x U
" % " / " U 0" ' " % " % "
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7+ * , ' " A 0 " / 0 ) " 0" *
, ' " ) <; " / 0 ) 0 < " "% / 0 , * R
"% / ' " A / A R "
µA (x) = µA(x) . hgt(A)
7+ , , " ' " A 0 " ' " supp(A)
% " / " U ) ? 0 < % 0 " "
supp(A) = {x U : µA(x) > 0} .
7+ % , ' " 0 " %" 0 ) " " / " %" 0
"
7+ ) ' " 0 " ' " % " /
" ) ? 0 < " " ) 0 *
core(A) = {x U : µA(x) = 1} .
"% / ' " %"
7+ 4 α" ' = " α% > ' " A 0 " '
" Aα % " / " U ) ? 0 < |
" |
" /P 0 α Aα = {x U : µA(x) α} ' α 0 < |
α% , " / |
= > "" / " ' ' " % = ' > % I "% <" % " ) ) α" ' α% ' "
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0.8 |
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0.6 |
0.4 |
0.2 |
x |
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I " 2 α3 |
7+ "
@ ' & " 0& * Q ) " '
% 0 / ; 0 0' " J ' 0' 0& " )
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/ ' [0, 1] 1 ? % ' " 0 *
% 0 / 0 % " ) ' 0 ' & * Q ) "
' ' " / % / 0)
" / 0' 0& " 0& * , 0 ' &
" 0& * ) 0& O
@ Q ' & " A B U 0 " ' " A B " % *
"
µA B(x) = max {µA(x), µB(x)}
1 " ' ' & " A B U 0 " ' " A ∩ B " % *
"
µA∩B(x) = min {µA(x), µB(x)}
¯
' " A U 0 " ' " A " % *
" µ ¯(x) = 1 − µA(x)
A
, " ' " " 0&
mAB (x)
1.0 |
1.0 |
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1.0 |
mA (x) |
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mA(x) |
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mB(x) |
mB(x) |
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mA(x) |
m |
(x) |
mA(x) |
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A B |
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I "
8 = ! ! ' &
max min ! )
, % /) ' " / & 0& * % * "
µA(x), µB(x) & " ' " % * χA(x) χB (x)) %' " " %< ; & * 0' 0& " J ? " 0" ' & " " ;
0' 0& = ' &> "
= ' " :+ " <
. % " & / ' " ? ) <; /
p ' q p / q " ? " 1 * % %'
? 0 " + = f[vlŠn•HXYncb>) ' " F%; " % " / " " 0 ? * % 0 I "" " " 0 &
, E F 1%" / ' " A ' " '
"U ) A = x1/µ1, . . . , xi/µi, . . . , xn/µn T " ' " A 0 "
? |
n |
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µi |
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i=1 |
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x = |
i=1 xi µi |
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n |
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0 " %' =U R ' " " > "% < "
x = U xµA(x) dx .U µA(x) dx
J ? & 0 & % p* " q ' " " % ' ' 0
, J ' " " ' "
A 0 " ? x " " 0 /P ' " " A
max µA(x) = µA(x ).
x U
j" " % " " * " ? ) ' " x 0' 0 " " ' ? ? "
" B '
1 P %< / & 1 P
; / ' " %' 1 ? % < " 0 0 " 0
" " M ) ) ? " Q " & 1
" " ? % & ; " 0&
/ ' " " ' <; &" " % * J & ' & P " 0
0 0 P ) ) "& " "& " ) "0 <; &
' " " % *
j" " /) ' 0' P " " = >
) " " " 0 ) ' & = ; > 0' P ' %
* ) ' & 0' " ' %
7+ , ' 0 P R " & X, Y 0 " '
" R X ×Y F / " µR(x, y) 0 " /
0 P % ? x, y M ) ' P
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R |
X |
× |
Y " " |
% * µ |
R |
: X |
× |
Y |
→ |
[0, 1]) ) ' " ) % " & |
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x, y, µR(x, y) |
) (x, y) X × Y M ) ' ? 0 x X y Y & " P |
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) "0 |
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x |
y |
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Y = X |
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" X |
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1 1%" / X = Y |
= {0, 1, 2, 3} ' P p / q =≈> |
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' P % " / * |
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0 |
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1 |
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3 |
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1 0.5 1.0 0.6 0.3 |
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0 1.0 0.5 0.2 0.1 |
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2 0.2 0.6 1.0 0.8 . |
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30.1 0.3 0.8 1.0
0 0& " X = 0, 3 Y = 0, 3 ' P ≈ / " %< ; % * " µ≈(x, y) = e−0.2(x−y)2
1 ' P p"& q " %<; & * / "
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Ž *0= >) K & =K>) + " *0 =+>) , *0 =,>• |
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0.4 1.0 0.4 0.3 |
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1.0 |
0.4 |
0.2 0.1 |
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+ |
0.2 |
0.4 |
1.0 0.8 |
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, 0.1 |
0.3 |
0.8 1.0 |
." / 0' ) ' P 0 / / % % * " "& R * " * P " ) '
% ' & * ) ' % *0 , ' P
" / %< * <
, ' P /" ? " 0& * , ) %" / " ' " Q X = {x1, x2, . . . , xn}) 0 " < " & " /
% % 1 ." / % " * "& " N ? " 1%" / 0 (xi , xj )
Nij " M ' " ' " * "& " Q xi xj % 1
/ ' % rij = Nij /N M ) " X " ' P p & q j / ' " X × X
@ ) ' ' " A X / ; %
" / " X j" µA(x) R % * " ) 0 <; ) " / " / x X % " " % A) ' " %" / P
% ? x ? " "
7+ α" ' ' P R X × Y 0 " 0' P Rα ) " 0 <; " 0 (x, y) X × Y ) 0& " / 0 ' P R
/P α
Rα = (x, y) : (x, y) X
J " %' ' 0& " X Y '
rij = µR(xi, yj ) M α" ' Rα P
%
Rα = rijα , rijα =
+ '
× Y, µR(x, y) α .
P % / * R = rij ) R " * % *
1, rij α,
0, rij < α.
G ; 0 @ * * '
" A) X) ' P R X × Y /
' " B Y @ * * 0 / 0 " " ,
' " ' 0& & " / % " =]X• ]nb> * ) O
1%" / A R ' " X) % * " µA(x)) R R '
P X × Y " % * " µR(x, y) I % / |
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=]X• ]nb> * R ? |
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' " B = A ◦ R) % * " " |
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def |
max min µ |
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, µ |
(x, y) . |
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µB(y) = µA◦R(y) = |
x X |
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A |
R |
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j" " X Y ' 0) X = |
{ |
x1, . . . , xm |
} |
) Y = |
{ |
y1, . . . , yn |
} |
) |
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=]X• ]nb> * |
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' 0' " < |
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*% |
µR(xi, yj ) , |
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µA(x1), . . . , µA(xn) |
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R = |
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