. , , ,

,,,

—

- , .

- , , .

Knowledge system - .

- .

, .






- , , . . , .

. , , .

, .

, , .


.

.

: ; .

, .. , , . , , , . . . . .




















.

. , . . .

.

. . .

.

t t.

=  t t

:

(1999) = { -1-99, -1-98, , -1-94, -1-99,}

(1998) = { -1-98, -1-97, , -1-93, -1-98,}

 t t = { }

= { , , , , }







1






4 , , .

2





5

3

( : 1 1, 22, , nn)


. , ; .

. , , .

:

( :

)

.

:

(:

_,

_,

_,

_,

_,

_)

, .

:

:

(: 11,22, , nn) .

(: ii)

:

(, , _)

(, , _)

(, , )

(_, , _)

(_, , )

.

(: ii)

(: 11,22, , nn)

:

( )

( )

.

  1. (: 11,22, , nn)

i

i ,

:

(:

__,

_)

  1. (: ii)

:

(, __,

, _)

  1. (1,2, , n)

  2. (1,2, , n)

:

( (__, _),

(, ))

:

(: 11,22, , nn) ii

:

:

(: -

-

) -

:

(: ii)  , ii

:

:

(1, , ) - 1, 2

(1, , ) -

(2, , )

(2, , )

:

(1,2, , n)

( (, ) -

, , .

- (, , ).

(, , , ).

:

(1, , , 760)

0  100

0  1

-1  1

0 .

.

(

(1, , , 760)

(1, , , 740)




*


1, , , 740)


* (, , , 760, 740)

, , .

:

(_, , , _, ).

_, -, _ , .

.

.

, . . - . (). . .

1

2

 . . . . .

n

1

2

 . . . . .

n

.

(1,2, , n) . . .

, .

2

2

1

1

47

54

60

50

2

1

.


i sup j sup ; sup .

i j, t Ki t  Kj t

( t i j)

Npr .

.

sup


sup


sup


sup


sup






sup .

K

sup


sup


sup


sup


sup


sup


sup


sup


sup


sup


sup


sup


sup


sup


























































i part of Kj - Ki part Kj

Ki Kj, Ki Kj.

part


part


sup


sup







part


part


part


part
















part


part


part





sup


sup


sup


sup
















.

k

isa




isa K -

K
i ius K -

1 ius K

K2 ius K

. . . . . . .

Kn ius K

, 1, 2, , n, i.


4.

.

.

Ki sup Kj Kj sup Km

Ki sup Km

Ki part Kj Kj part Km

Ki part Km

,

.

K1 ins K2, K2 ins K3,,Kn-1 ins Kj

, Kn ins K1

K isa Ki sup Kj

K isa Kj

isa

sup

isa

K1




K2

K3



K5

K4

R6

R7




R3

R2

R1

R5

R4



.

Ki ins K

℧ Ki , ,

Ki sup K

℧ Ki = K


  =

 =  =  =∅

(, , , _, )

={, }

, = \

K (K1, K2, K3, K4, K5)

K\K5 5.

.

⋃=

⋃=∅

(_

,

_)

(K A1K1, A2K2)

K1/(K, K2)

, .

, .

:


K

<> < > < > < > < > <>.

.. -1-98 4 -301.

(:

_

_

_

_

)

.

(ER )

Entety Relation Diagramm







N 1

*




1 N . * .














, , ,









. .






.











(), .

.

, .

1- . 1- .

:

.

S

- .

f- ;

;

.

Z .


-

={0;1}


-


2-;

1-;


S={, , , _, _, }

1) : ;

f A1 B

2) :  ;

3) : 

4) : 

5) _:  _

6) _:  _

7) 0 : 

C B

1: 

.

.

.

t: 

8) _:_

_:  _

9) : _

: _

10) _:

_:

11) +: *

12): *

(. ) -

  2. . .

  3. - .

= {.1, .2, .3, .4}

= {.1, .2, 3}

={1,2, 3, 4, 5, 6, 7, 8}

_ = {_, _}

_ = {, }

= {1,2,,t}

- .

.

  1. .(.1)=1

.(.2)=1

.(.3)=2

..

2) .(.1)= .3

.(.2)= .1

.(.3)= .3

3) .(.1)=0

.(.2)=5

.(.3)=5

..

4) (.1)=5

(.2)=12

(.3)=0

5) _(.1)=_

_(.2)=_

_(.3)=_

_(.4)=_

.

6) _. (.1)=

_. (.2)=

_. (.3)=

.

10) _(1)

_ (2)

_(3)

_ _
1 .1 .3 0 5 1 0
2 .1 .1 5 12 0 1
3 .2 .3 5 10 1 0
4 .2 .2 10 17 0 1
5 .3 .3 10 16 1 0
6 .3 .1 16 26 0 1
7 .4 .3 16 22 1 0
8 .4 .2 22 32 0 1

_
.1 _
.2 _
.3 _
.4 _

_
.1 .
.2 .
.3 .

3) :

:

) ,

) ,

) -

,

-

) -

,

, - .

) - , ,

) (), , .

) , :

, “x”

( )

) , ,

:

  1. b=> 2

_((2))=n

  1. 2 .1 .1 5 12

)

3)


8 12.11.99.


.

.

:

-

ii .

2- ,

- , .

, .

, .

m,n const

.

{n/y}:

(1) (2) => a(x)c(x,n) (5)

(3) (5) , {m/n}=> c(m,n) (6)

(4) (6) => 0


, .. , .

=>


, .

: ? a

a: - b,c,d.

b: - e,f.

c.

e.

f.

?-a

a(1)

a(2)

a(3)

1

2

3

4

5

6

?- a.

?-b,c,d

?-e,f,c,d

?-f,c,d

?-c,d

?-d

a:-b,c,d.

b:-e,f

e

f

c

d

-b,c,d.

-e,f,c,d

-f,c,d

-c,d

-d

0

a: - b;c

b: - d,e

c: - g,f.

e: - i,h

g: - h,j

d.

f.

h.

?-a

, -

; -

.

.

-


.

,

  • >:=< >

E <> < > [=< >]


:

5

=

=

=65 __

_=

0-100


27

=

=

=0 =10

.

, , .. - , ,

<>::<>[<>ȅ<>]

<>::=<>=<>

, , , -

<>::=<>=<>

<>:=<>=<>=< >

.

, .

, , , , .. = 100






, .

?


  1. 25

  2. 25 55

  3. 55

=min()


- ,

= =50

= =70

=0

( )





9 ()

1


2


3

4


5


, , , .


( )



6 7

2 3



1 2 3 4 5



4 5 6 7 8


F1 F2 F3 F4 F5


1

2

3

4

5

6

7

8

1

2

3

4

5

6

7

8

6,7

1,2


3

6

1


3

2,3

1,5,3


6,7,8

F1

F2


F3

F4

F5

.

,

. , ,


=60




7


. , , .

, .. .


.

, , .

, , .

. , .

. .


.

(i); Q; P; A; =B; N

(i) :

Q ;

P ( )

A=>B , - , - ;

N , , .

.

A111

P11

Q1

A112


Q2

P12

P21

P22

P23

..

..


(: 11, A2K2, .,AnKn)

(: A1k1, A2k2,.,An kn)

( :

1 ( 1)

2 ( 2)

..

n ( n))

.

- - .

. :

, , .


: , , .

:

  • ;

  • ;

  • ..


(FMS).

:

U unique

S same- -

R range ;

0 override


U .

S

U

=60

=30




=32



.

R

=2-200

=2-50




=32



, , .

=60

=30




=32



11 3.12.99


OPS-5

<->::=(<> {|<> <>}+)

{}+ -

< >::=({ })

<>::=< -> | < ->

(

)

( : , )

:

<>::=(< > <> <>)

<>::={<>}+

<>::=<> | - <>

<>::= < > | < > | < >

< >::=({>}+) |


# ( <> )


(<> [{<> <>}+] )

# ( )

, ..

(

<> )

..

< >::= (<> {<> <<{< >}+>>}+)

, . .

# (

<>

<< >> )

< >::= (< > {< >{{< >}+}}+)

# ( {<> 100 <> 200} )

( 160)

<>:={<>}+

<>::=(make < > | remove <> | (modif <> {<>< >} +)


# ( _

(

)

,

( ) >

(make

)

(modif1 ))


,


  2. ,

, .


  • , ,

.

:

  • ;

,

, , .

  • , .. , , , .

,

.

, , , .

- .

, .

  • .

.. ,

  1. - , .

  2. .


.

  1. ,

  2. 3 2- 3-. =>

.


2

1.1. ׸ ,

    2. , ,

  2. .

, 2- .


12 10.12. 99.

[10,40]

[10;20]

[20;30]

[30;40]


1


0.7


0.1

10 15 40

-

-

-

- .

-




0.6


-

-

-

: - .

-

&



0,6 x


=> .


:


10 40

.

1 . .

.

.

.

.

.

| | | | | | | | x x

10 11 12 13 14 15 16 17 18 18




x x



A


x




AB


x







12 13 .





  1. .

A1,A2,.,An

x1,x2,,xn

x1 X1 x2 X2 xnXn

A1 xA2 x xAn = {<x (x1,x2,,xn )/( x1,x2,,xn )>}

x (x1,x2,,xn ) = min{A1 (x1), A2 (x2)An (xn) }


A = {<1/10>, <0.8/15>, <0.2/20>}

B = {<0.7/2>, <0.5/4>}

A xB = {<0.7/(10,2)>, <0.7/(15,2)>, <0.2/(20,2)>, <0.5/(10,4)>, <0.5/(15,4)>, <0.2/(20,4)>}

  1. .

An = {<An(x)/x>}

A2 = con(A) -

A

1


x




A

1 A2

A0.5


0

x2 < x x0.5 > x








A0.5 = dil(A)





.

2. 0 5.

x 0 1 2 3 4 5

n1

 - - - 10 8 4

n2

 10 10 10 - 2 6

A = n1 / (n1 + n2)

A (0) = 0

A (1) = 0

A (2) = 0

A (3) = 1

A (4) = 0.8

A (5) = 0.4

.


u

p

u

p

u

0 X















































L


x









x


u 1


.

<, x, A>

 -

 ,

.

<, T, , G, M>

 -

{, , },

[0; 1]

G

, {, , }, {, , ..}


 -

= {, , }

X = [0;1]

.

* =  G (T)


- .

(12) = 1 2

(1 , 1 , 1)

(2 , 2 , 2)

(12) = 1 2

(^) = ^1

( ) = con (A )

( ) = dil (A )


.

, , . , .

(kcus :

1( 1);

2( 2);

n( n))

(kcus

)

, , . . .

(kcus :

(S: )

(: )

11, 12 (cus: R1, )

1 (f: )

(: )

(sys: cus*1))

R1


(kcus :

(S: )

(: )

121, 22 (cus: R1, )

2 (f: )

(: )

(sys: cus*2))


(kcus :

(S: )

(: )

31, 32 (cus: R1, )

3 (f: )

(: )

(sys: cus*3))


.

<>R:<>

:

= cus: 11 R1 cus: 12 R1 K1 =

21R122R1K2 31R132R1K3

= 21R122R1K2 R1 31R132R1K3 R1 K1

, , . . .


.

1

2

3

4

5

:

TS = PR4dt&P1R3 10,P2&P2R1P3&P4R3 2,P5

t = 15 20

PR4dt , P1R3 10,P2  P2R4 dt + 10

P1R3 10,P2  P1R1P2

P4R3 2,P5  P4R1P5

TS* = P1R1P2& P1R1P3& P2R1P3& P4R1P5


.

, , , . . . , , .

i

+ = {01+, 02+0nj+} .

- = {01-, 02-0j-}

, , Kj.

. - .

Z = {z1, z2, , zr}

Zi = {zi1, zi2, , zini}

Qi = {z1j1, z2j2, , zrjr}.

- , - . : .


.

hij =

1, i- j-

0,





hij 

:

Z = {z1, z2} {, }

Z1 = {z11, z12} {, }

Z2 = {z21, z22, z23} {, , }

j+ = {01+, 02+} j- = {01-, 02-, 03-}

01+ = (z11, z21) 02+ = (z11, z22)

01- = (z11, z23) 02- = (z12, z21) 03- = (z12, z22)

&i hij -

0 = max(xij 1/i), 0 , xij , i .

:

0 = 3/5 1/2 = 0.1

j+ = {01+, 02+} j- = {01-}

+


-


-1+ = 0 -1- = {02-, 03-}



j+


j-


-1+


-1-




- , . - , , . Knowledge system -

 

 

 

! , , , .
. , :