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ИНТЕЛЛЕКТУАЛЬНЫЕ ИНФОРМАЦИОННЫЕ СИСТЕМЫ

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/ 0 / % 0& Q< ) ' ' ' " P m = > %' " Q< Ψm) " ' G, G

F 0 / % 0& Q< 0 "%; " ?

" / 0 <* ) % ' 0 0 / % 0&

" " / %' / ) " Ψk* ' = > " %& / % 0& Q< J ? " %' "

=mXHˆ YwXHˆnbg> ; " % / & %

0 " " / / % %< % Q< j" % 0 ? % )

"& Q ; % / 0P ) & " / % 0& Q< ) " ' " ' " " %" < M & /" /

%" 0 <* " / %< " ' 0 " ) <

; " / p / 0&q / Q< ) )

) "% / <' " " %<;

. " Q< % " /) " <' 0 Q< 0

Q< 0 0 M % ; < " / " " / " ' " 0&

Q< j" " ) % ; 0 0 / ) ' 0 % ; " Q<

0 0 0 / ) 0 "& "

O< Q< ) " ; * ) " " < ' /) 0 " ) " ; <) " " 0 0 "

%

Q< " <' /) " " % / 0 ) & ; " *

Q< " / ) <* ) " / %<; Q<

< 00 Q< ) %" % Q< % , ) "

Q<

p(X) p(b) q(Y ), p(c) p(Y ), p(b) p(X)

 

0 Q< " <' /)

"

% / 0 q(Y )

 

F % " Q< " ) " ' <; %" )

/" U9V " " " & " " 0

0 ' " 1I@O@E

# + ! !

1 " / % ' " %< 0& 0& " & " 0 < " " <' /

' ' " 0 ) " < " ? " ) " " /< /

" /) ' 0 ) / / % / " " 0 0 /

" /< % ) ' 0) 0 " ; % / " " ) " < 0 1 ""% & " ? " ' " & ' ? " / 0

0 * " " <' O< * < "& 0 0 <' ) %'

& " ) " ;/< & ) p "/ q) p q)p ' q

p q

." / ? & " ; / " @ "

< " ? " ) 0 0 0 ""% " J 0 &

%' % ? " ' " 0 " % / % " )

" % F ? " % " " ? " " " 0 h‰~58 U V . " 0

1 0 %; " 0 =p q p q>

1%" / % * pj" U ) Dq) U R "0 ) D R <

' ) % / 0 * % 0 = " " " %' ? "

' >

1%" / mr(D|U ) R % " <' D "0 U @ ' ' mi(D|U ) % " " " " D "0 U M

1

> mr(D|U ) > 0,

"

mi(D|U ) = 0)

 

> mi(D|U ) > 0,

 

mr(D|U ) = 0

1

"

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) ,

= >

CF (Φ1

CF (Φ1), CF (Φ2) .

= >

OR Φ2) = max

 

 

 

 

 

 

. * % " %" "0

" ) ' CF = 1

R " < ' p q) CF = 1 R

' p q) CF = 0 R p <q

 

%' % " <' 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) .

 

 

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,

 

CF (7) + CF (8) + CF (7)

·

CF (8),

" CF (7) < 0 CF (8) < 0,

= >

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

CF (7) + CF (8)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

1 min |CF (7)|, |CF (8)|

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

= ) ' % = > " ' 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

 

9

# +

1 0 / ' ' " "" " " % "/ " )

% P " / * ' " & " F%; " %* 0 "" " ) %<; & ' " 0 & " Q =1 1

+1 + > & " 0' 0 0 % 0 / '

0) " %< * < = ) p@ 0&

" % q) pj" % " * ) / + ,

* q>

) ' &) P 0& % / 0 " " ) ' " & " / /"

' 0 ) 0 % 0 / 0 " /< " 0

0 F%; " %< ) " " / 0& 0 " % ' ' )

)

) %P " " 0 " ' " ) " / 0 / …

"%; " / ' " 0 ' & &… P & *

& " %' 0 O / 0 ' & " =vlŠŠ\ Z[YZ> R ' =vlŠŠ\ ecgnH> 1 ? %' P " " ' .. =ZcvY Hc]|lYnbg> I "" " 0 ) ; " ? &

 

 

J

* " " " % " / ? = Q >)

<; & 0 ; " " < ? ? "" < " P/

" ? % " % =

0 " " >)

% " % = 0 " " >

 

@ 0 & ' " " " " 0 0' 0& "

/" " ' K " <; " * % % " " 0 ' = ' > 1 ' " R 0 * " 0 ' * J " ? " ) ' ? 0 " ) <; ; " " ) % / ? " " ' " ) " " ) / ? %

" % " ' " /< 1 & 0" 0 p? x

" % Aq < " 0" ) " / % & % /) " / p" / q " " /<

? x % " %

@ ' ' U = {x} % " / " ? , ' "

A U 0 " " % " / {x, µA(x)}) x U ) % * µ : U → [0, 1] 0 "

% * " ' " A

 

 

L% * " " /< "0

 

' " , ) '

" J F@ .Π= / " % ' > % *

 

 

 

 

0,

 

 

"

 

µ

 

(h) =

h

170

,

 

h < 170;

 

 

 

15

" 170 h 185;

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

1,

 

 

" h > 185,

"

 

 

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" ' " % " % "

" ?

 

 

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% ' "

 

1.0

0.8

α−

0.6

0.4

0.2

x

α−

I " 2 α3

7+ "

@ ' & " 0& * Q ) " '

% 0 / ; 0 0' " J ' 0' 0& " )

 

 

' & " " / " ' P/ ' )

/ ' [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 A(x), µB(x)}

1 " ' ' & " A B U 0 " ' " A ∩ B " % *

"

µA∩B(x) = min A(x), µB(x)}

¯

' " A U 0 " ' " A " % *

" µ ¯(x) = 1 − µA(x)

A

, " ' " " 0&

mAB (x)

1.0

1.0

 

1.0

mA (x)

 

 

 

mA(x)

mB(x)

mB(x)

 

 

 

mA(x)

m

(x)

mA(x)

 

 

A B

 

 

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 = x11, . . . , xii, . . . , xnn T " ' " A 0 "

?

n

 

 

 

µi

 

 

i=1

 

x =

i=1 xi µi

.

n

 

 

 

 

 

 

 

0 " %' =U R ' " " > "% < "

x = U A(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

 

R

X

×

Y " "

% * µ

R

: X

×

Y

[0, 1]) ) ' " ) % " &

 

 

 

 

 

 

 

 

 

 

 

 

 

x, y, µR(x, y)

) (x, y) X × Y M ) ' ? 0 x X y Y & " P

) "0

 

 

x

y

 

Y = X

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

R

 

 

 

"

R

 

J " %' )

 

 

 

) ' P 0 " P

" X

 

 

 

 

 

 

 

 

 

 

 

 

 

1 1%" / X = Y

= {0, 1, 2, 3} ' P p / q =>

' P % " / *

 

 

 

 

 

 

 

 

 

0

 

1

 

2

 

3

 

 

 

 

 

 

 

 

 

 

1 0.5 1.0 0.6 0.3

 

 

 

 

 

 

 

 

 

0 1.0 0.5 0.2 0.1

 

 

 

 

 

 

 

 

 

2 0.2 0.6 1.0 0.8 .

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

30.1 0.3 0.8 1.0

0 0& " X = 0, 3 Y = 0, 3 ' P / " %< ; % * " µ(x, y) = e0.2(x−y)2

1 ' P p"& q " %<; & * / "

9

 

Ž *0= >) K & =K>) + " *0 =+>) , *0 =,>•

 

 

K

 

K

+ ,

 

 

0.4 1.0 0.4 0.3

 

1.0

0.4

0.2 0.1

.

 

+

0.2

0.4

1.0 0.8

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

, 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 % /

 

=]X• ]nb> * R ?

' " B = A ◦ R) % * " "

 

 

 

 

def

max min µ

 

, µ

(x, y) .

 

= >

µB(y) = µA◦R(y) =

x X

 

A

R

 

 

 

 

 

 

j" " X Y ' 0) X =

{

x1, . . . , xm

}

) Y =

{

y1, . . . , yn

}

)

 

=]X• ]nb> *

' 0' " <

 

 

 

 

 

 

 

 

*%

µR(xi, yj ) ,

 

 

 

 

µA(x1), . . . , µA(xn)

 

R =

 

"