...,, massel@isem.irk.ru, -,,. -. -., -.,, ( - ),,,.. /.. //. 2016.. 6, 2(20). -. 149-161. DO: 10.18287/2223-9537-2016-6-2-149-161. [1], [2]., -,,, -, - -,,. 1 90-,, [3-5]. -, 1975,, - [6]., -,. -,, ( ( ) ( ), ). - ( ) -, [7]. 2(20) 149
, -,,. ( ) ( ) -, -,. -,,. ; - -. [4],,,. -,,, - -. 2 (, -, [4-5].),. -,., «-», -, «-» [8]. - (), -,,.. -,,,,, ( - ), ( ) [9]. - ( ) ( ) - [1, 2]., - -. -,. -, -. - - ( ). -, -. - ( - ). - - -,,..,, ( ). 2(20)
- ( ). (),,, ; -. -.,,, - ( «- -»,, - - )., - -,,,,. -, [9]. : «,?»,,.,. 3, - - -, - [2]. ( ) L, - l i : L li, i 1, n. l i P j, : l P, j 1, m. i j -, - (S, F, G) L ( - ) l i, : 1) S ; 2) l i - ; 3) S S s, i 1, n, s S, s i i i s j, i, S i ; 4) F ( ) F F : s s, F f : l l, j j i i j j l m k k m s, s S, l s, l s, i j k i m j, ( l i l i s j ); 2(20)
5) G ( ( - ), ), G 0, Gi, g j, i 1, n, j 1, m, G o - S, G i - s i, g j - l j, G o (S), (G 1 (s 1 ) G 2 (s 2 ) G n (s n )), G i (S i ), (g 1 (l 1 ) g 2 (l 2 ) g m (l m )). 1 - ( S), ( -,, ), S i Fj i. 1-4 - -,, «-», - ( - ).,,,. -,,, ( ).,,,., -, - -.,,. L ( 2a), (, ). - 2(20)
2. ( 2 ). 3. L/3 L/3 2 L (a) ( ) ( ) 2 3 (. 3), - : (1) D = 2 / 3 H,,, -,.. H = H(L)., 3, 2 3. - : 2 H = H(L / 3). : H(L) ~ L 2 / 3. 2 / 3 D (1), H(L) ~ L D.. : = ( ) D. 5 - ( - ) : -,,,,.,. 2(20)
, -. - ( ). ( ), [2].,,, :, - ( ) - ( ). - :,, ; ( ) ;, -, ; ( ),., [10].... ( ) - -. - - -,, -,, -, (, ) -, [11]. - :, - ( - - ).,,. - - -, 4. - - - ( ), (S, F, G), S -, F -, G -. - S, -, ( ) 2(20)
( S ), ( S ) ( S T )., S ( S D, S M ); S - ( S P, SM ). : F : S S, FT : S ST, FT : S ST. - (G),., ; Web-. F T F F T 4 - -,, [12], -,. -, -,, -. - ( ):, ( ), ( - ) (). [13]. - E, {D} - {T}: E = {D} {T}. - : 2(20)
D = {D, D B, D V, D G, D R }, D, D B -, D V, D G -, D R ( 5). D R D G D V D B D 5 -, -, -. 8 : F B : D D B - ; F V : D D V - - ; F G : D D G - ; B F G : D B D G - - ; B F V : D B D V - ; V F G : D V D G - ; G F R : D G D R - ; V F R : D V D R -. : T = {T V, T T, T E },, T V (), T T -, T E - ( - ). 2(20)
, D : D = {D k } {Z k }, D k, Z k. -,. - ( -, -, -, -, ),,,,, [11]., - (, -, -,.), - (). -,., - -., - -,,,. -,, 90-,, -, ( - ). 6-8 MapTools, -.,, 6. - ( 7),. 8 - -,,,, - (, )., -,, [14-16], - [17].., 2(20)
, -. -, -, ; -.,,, [18-20]. 6 - - 7-2(20)
8 -, -,.,.. - -.,, - 16-07-00474 16-07-00569, 229 (2015-2017). [1] /.. //.. - -94.. 1 -, 1994. -. 46-49. [2] /.: -..,... - :,., 1995. -. 40-67. [3] /...:, 1991. 176. [4] / V..:, 1988. 682. [5]. /..,.. //. «(,, - )» /...,.. -:, 1995.. 84-129. [6]. /.-.,....:, 1993. 176. [7] Fractals: Non-integral Dimensions and Applications / Under the direction of G. herbit. - New York, John Wiley & Sons, 1991. - 249 p. [8] [9] /..,... -.:, 1991.- 228. /..,....:, 1992. 200. 2(20)
[10] - /..,.. // - = Open Semantic Technologies for ntelligent Systems (OSTS-2015): V -..-.. (19-21 2015., ) :, 2015.. 199-204. [11] - - /..,. //.. - 2006. - 3.. 86-93. [12] /..,.. //. 2004. 2(18). 98-103. [13] /..,..,... //. 2013. 10(81).. 16-21. [14] -. T. //. 2014. - 4(14).. 69-77. [15] /.. //. 2014. 4(14).. 78-89. [16] /..,..,..,..,.. // :. (8-10 2013.,, ).. 2. :, 2013. -. 29-38. [17] /... -.:, 2000.- 352. [18] = The Fractal Geometry of Nature /.. -.:, 2002. - 656. [19] A History of Fractal Geometry / J.J. O'onnor, E.F. Robertson // MacTutor History of Mathematics archive. School of Mathematics and Statistics.- University of St Andrews, Scotland, 2009. URL: http://www-history.mcs.st-andrews.ac.uk/histtopics/fractals.html. 22.04.2016 [20]. Fractals. A Very Short ntroduction / K. Falconer. - Oxford University Press, 2013. - 152 p. FRATAL APPROAH TO KNOWLEDGE STRUTURNG AND EXAMPLES OF TS APPLATON Melentiev Energy Systems nstitute SB RAS, rkutsk, Russia massel@isem.irk.ru Abstract The article describes proposed by author a fractal approach to knowledge structuring, which actively used for developing to the ontological space of knowledge, primarily in the energy field. We introduce the methodological concept of the fractal information space and the concept of fractal stratified (FS) model. t s given mathematical description of the FS-model and one method for determining of the fractal dimension. The examples of the application of fractal approach and FS-model in the work carried out under the guidance of author were considered. fractal approach, the fractal stratified model, stratum, mapping, invariant, ontological knowledge space Massel LV. Fractal approach to knowledge structuring and examples of its application. Ontology of designing. 2016; v.6, 2(20): 149-161. - DO: 10.18287/2223-9537-2016-6-2-149-161. [1] [2] References Massel' LV. Fractal model of knowledge structuring [n Russian] / National conference with international participation "A-94": proceedings. Vol. 1. Rybinsk, 1994: 46-49. Massel' LV. Fractal approach to the construction of information technologies [n Russian]. nformation technology of energy development research. Novosibirsk: Nauka ; 1995: 40-67. 160 2(20)
[3] Feder E. Fractals [n Russian]. Moscow: Mir ; 1991. [4] Fractals in physics [n Russian]. V nternational Symposium on fractals in physics: proceedings. Moscow: Mir ; 1988. [5] Urickij VM, Muzalevskaja N. Fractal structures and processes in biology [n Russian]. Biomedical informatics and eniology (problems, results, perspectives). Eds.: Polonnikova R, Korotkova KG. Saint-Petersburg: Ol'ga ; 1995: 84-129. [6] Pajtgen H-O, Rihter PH. The beauty of fractals. mages of complex dynamical systems [n Russian]. Moscow: Mir ; 1993. [7] Fractals: Non-integral Dimensions and Applications. Under the direction of G. herbit. New York, John Wiley & Sons; 1991. [8] Novik B., Abdullaev ASh. ntroduction to the world of information [n Russian]. Moscow: Nauka ; 1991. [9] Gavrilova TA, hervinskaja KR. Extraction and structuring of knowledge for expert systems [n Russian]. Moscow: Radio i svjaz' ; 1992. [10] Massel LV, Massel' AG. Methods and tools for situational management in the energy sector based on semantic modeling [n Russian]. Proc. V nternational onference OSTS. Minsk: BGUR; 2015: 199-204. [11] Voropaj N, Massel' LV. T-infrastructure of energy system research and the provision of T-services[n Russian]. Proceedings of the Academy of Sciences Energetics, 2006; 3: 86-93. [12] Massel' LV, Vasil'ev V. The development of an information system for sociological research using stratified fractal model [n Russian]. Bulletin of rkutsk State Technical University, 2004; 2(18): 98-103. [13] Massel' LV, vanov RA, Massel' AG. Stages modeling of the decision making on the basis of network-centric approach [n Russian]. Bulletin of rkutsk State Technical University, 2013; 10(81): 16-21. [14] Vorozhcova TN. Ontology as a basis for the development of intelligent cyber security system [n Russian]. Ontology of designing, 2014; 4(14): 69-77. [15] Kopajgorodskij AN. The use of ontologies in the semantic information systems [n Russian]. Ontology of designing, 2014; 4(14): 78-89. [16] Massel' LV, Vorozhcova TN, Kopajgorodskij AN, Makagonova N.N, Skripkin SK. The use of ontologies in the research and decision making support in the energy sector [n Russian]. Proc. 4rd All-Russian onf. Knowledge Ontologies Theories (Novosibirsk, Russia, October 8-10, 2013). Vol. 2 Novosibirsk: Sobolev nstitute SB RAS; 2013: 29-38. [17] Kronover RM. Fractals and chaos in dynamic systems [n Russian]. Moscow: Postmarket 2000. [18] Mandel'brot B. The Fractal Geometry of Nature [n Russian]. Moscow: nstitute of omputer Science, 2002. [19] O'onnor JJ, Robertson FF. A History of Fractal Geometry. MacTutor History of Mathematics archive. School of Mathematics and Statistics, University of St Andrews, Scotland; 2009. Source: http://www-history.mcs.standrews.ac.uk/histtopics/fractals.html. [20] Falconer K. Fractals. A Very Short ntroduction. Oxford University Press, 2013., 1949.., «-» (1971). (1995). -,...., -. 200, -, -. (b. 1949) graduated from the Tomsk Polytechnic nstitute, Faculty of Automation and omputer Engineering in the specialty Applied Mathematics in 1971, Doctor of Technical Sciences (1995). hief Researcher, Head of nformation Technologies Laboratory in Melentiev Energy Systems nstitute SB RAS. Professor of Automated Systems Department of the ybernetic nstitute in the rkutsk National Research Technical University. The list of scientific works includes more than 200 articles in the field of semantic modeling, design of information systems and technologies, and the development of intelligent decision support systems in the field of energy solutions. 2(20) 161