681.327
.. , .. , .. *
, , , , - . . , . , , . . , . . .
; ; .
L.S. Bershtein, S.L. Beliakov, A.V. Bozhenyuk
MAGHOUT METHOD FOR DEFINITION OF FUZZY BASE SET OF FUZZY TEMPORAL GRAPH
In this paper the notion offuzzy base set of a fuzzy temporal graph is considered. The fuzzy temporal graph is a generalization of a fuzzy graph on the one hand, and a temporal graph on the other hand. The incidence of graph vertices is changed in the discrete time in the fuzzy temporal graph. The majority of isomorphic transformations temporal fuzzy graphs alter their appearance without changing their signatures. In this regard, relevant are the issues related to the consideration of invariants of temporal fuzzy graphs. The method of definition of a fuzzy base set is considered. This method is an extension of Maghout method for the fuzzy temporal graph. The example of definition offuzzy base set is considered too.
Fuzzy temporal graph; subgraph of fuzzy temporal graph; incidence degree; fuzzy base set.
. . , , , , ,
- , , . [1-5]. . [6] ї. , , ї . , ( ) , .. [7]. , , [8-10].
*
12-01-00032a, 13-07-1303. 70
, , . , , . , .
[11] , , , .
[7, 10] G=(X,{ },), X - c X! = ; t = {1,2,...,} - , ; { } - , X t .
G< = (X ,1)
G=(X,{*},), X - , = ( ((,.) | (, .) X2} - t : X2 ^ [0,1].
t * X, [] , ' * , .
= (Xfe ,Xfe ,...,X; } -
t, , ,..., . = { , ,..., } . ^^ , -
^ = (X, ) ,


, ,
"1. = 0,

1 = .
1 X = {< ^ /1 >, < - /2 >,..., < ^1 / >} t ^.
1. & = _^ = (< /1 >,< /2 >,...,< / >} -
*=1,
G = (,{ },).
, 1, 2,..., t .
2. ,^ = * = {< /1 >,< /2 >,...,< / >} -
*=1,

G=(X,{ },).
, 1, 2,., I .
) , X I. .., /?() = (.),
1 .
(';) - X / I. t , :
() = (< / > &(^=1,)( >ї, (1)
(VB' B)[R(B') = {< ' /Xj >| Xj X&(3j = 1,)( < )}]. (2)
(1) , , . (2) , ' (1) . .
([, X.) - X { t. :
(^, ^ )[(X, ; ) < ] . (3)
, ,

X t .
, t [] X,
:
1.
t , .. ^ )[3 | (X , ) > ] .
2. ,
t , .. (3).
. [1], , , , [12-17].
t . , X X :
) -X- ;
) X, , , (X ., ) > t.
, :
(VxI )[X, V (X, ^ (, 1 , X) > ))] . (4)
X. X . , 1 ; 0 . (, ) >
^- = .
(4) ], : = & (. V (, ^ ^(-& )))).
1 1 1
( ^ = V ),
= &(1V 1V v(Pj & )).
1 j J J
, = 1,
= &(v( &)). (5)
3
, . (5) :
= ^(1. & 2. & ... & & ). (6)
1=1,1 1 1 1
: (6) . - , , , t.
* = 1,. & = _ , =
*=1, *=1,
.
1. [18] = (,{ },),
X = {], 2, 4}, = {], 2, 3}, = 4, N = 3, -
{} :
](])={<0,2/2>}, 2(])={<0,5/2>}, 2(2)={<0,4/3>}, (2)={<0,6/>}, ](3)={<0,2/4>}, 2(3)={<0,3/4>}, ](4)={<0,2/]>}, 2(4)={<0,9/2>},
3(4)={<0,1/]>, <]/2>}.
(. 1), = {1, 2, 3}.
{<0,2/1>,<0,5/2>}
{<0,2/1>,<0,1/3>}
{<0,4/2>,<0,6/3>}
{<0,2/1>,<0,3/2>}
. 1.
, , . 2-4.
. 2. G t=1
. 3. G t=2
. 4. G3 t=3
:
' = {< 0,2/1 >, < 1/4 >},
2 X = {< 0,3/1 >, < 0,4/2 >, < 0,9/3 >, < 1/4 >}
2x = {< 0,1/1 >, < 0,6/2 >, < 1/3 >, < 1/4 >}.
:
= {< 0,2/1 >,<0,2/2 >,<0,2/3 >,<1/4 >}
Bv ={< 0,3/1 >, < 0,6/2 >, < 1/3 >, < 1/4 >} . ,
, . 1, , 0,2, , , 0,6.

1. . . - .: , 1975.
2. . . . - .: , 1978.
3. . . - .: , 1973.
4. .. : // . - 2002. - 1. - . 20-22.
5. .. // . - 2010. - 9. - . 7-13.
6. Kostakos V. Temporal graphs. In Proc. of Physica A: Statistical Mechanics and its Applications. - 2008. - Vol. 388, Issue 6. - P. 1007-1023.
7. .., .. // . . - 2010. - 4 (105). - . 198-203.
8. .., .., .. // . - 2011. - . 18. - . 3. - . 414-415.
9. .., .., .. // . - 2011. - 3 (43). - . 15-20.
10. .., .., .. // . . - 2012. - 1 (126). - . 121-127.
11. .. // SWorld. - , , 2012ї. - . 4. - . 3. - : , 2012. - . 20-24.
12. .., .. // . - 2002. - 1. - . 12-15.
13. .., .. // . . - 2002. - 3. - . 116-122.
14. .. // SWorld. - 2012ї. - . 1. - . 10. - : , 2012. - . 23-25.
15. .., .. // . - 2007. - . 14. - . 5. - . 857.
16. Bershtein L.S., Bozhenuk A.V. Maghout Method for Determination of Fuzzy Independent, Dominating Vertex Sets and Fuzzy Graph Kernels // International Journal of General Systems.
- 2001. . 30, 1. - . 45-52.
17. BozhenyukA., Rozenberg I. Allocation of Service Centers in the GIS with the Largest Vitality Degree // Advances in Computational Intelligence. / S. Greco et al. (Eds.): IPMU 2012, Part II, Series: Communications in Computer and Information Science, Springer-Verlag Berlin Heidelberg, 2012. - Vol. 298. - . 98-106.
18. .., .. // . . - 2012. - 5 (130). - . 75-80.
..., .. .
- ї; e-mail: lsb@tti.sfedu.ru; 347928, . , . , 44; .: 88634371695; - ; ...; ; . .
- e-mail: beliacov@yandex.ru; ; ...; .
- e-mail: avb002@yandex.ru; ; ...; .
Bershtein Leonid Samoilovich - Federal State-Owned Autonomy Educational Establishment of Higher Vocational Education Southern Federal University; e-mail: lsb@tti.sfedu.ru; 44, Nekrasovskiy, Taganrog, 347928, Russia; phone: +78634371695; the department of information-analytical systems of safety; dr. of eng. sc.; professor; chief of department.
Beliacov Stanislav Leonidovich - e-mail: beliacov@yandex.ru; the department of information-analytical systems of safety; dr. of eng. sc.; professor.
Bozhenyuk Alexandr Vitalievich - e-mail: avb002@yandex.ru; the department of information-analytical systems of safety; dr. of eng. sc.; professor.