MODIFIED METHOD OF INTRODUCING THRESHOLDING FUNCTIONS IN MODELS OF RELATIONAL FUZZY COGNITIVE MAPS
Grzegorz Słoń
g.slon@tu.kielce.plPolitechnika Świętokrzyska, Katedra Systemów Informatycznych (Poland)
Abstract
The article describes the method for introducing a threshold function into a model of the Relational Fuzzy Cognitive Map that uses fuzzy numbers arithmetic. Processing the fuzzy number by function causes deformations of the shape if this number and its support. It is proposed a geometrical approach to this problem, allowing to maintain constancy of the support and to keep the shape of the processed fuzzy number with an appropriate shift of the center of this number. The method was tested on fuzzy numbers with different membership functions.
Keywords:
computational intelligence, fuzzy systems, fuzzy cognitive maps, fuzzy numbersReferences
Bishop Ch. M.: Neural Networks for Pattern Recognition. Clarendon Press, Oxford 1996.
Google Scholar
Dickerson J. A., Kosko B.: Virtual worlds as fuzzy cognitive maps. Presence 3(2)/1994, 173–189, [DOI: 10.1162/pres.1994.3.2.173].
Google Scholar
Jastriebow A., Piotrowska K., Słoń G., Algorithm of Building the Intelligent Models Based on Relational Cognitive Maps. Computer Technologies in Science, Technology and Education, Institute for Sustainable Technologies - National Research Institute, Radom 2012, 138–151.
Google Scholar
Jastriebow A., Poczęta K.: Analysis of multi-step algorithms for cognitive maps learning. Bulletin of the Polish Academy of Sciences-Technical Sciences 62(4)/2014, 735–741, [DOI: 10.2478/bpasts-2014-0079].
Google Scholar
Kosko B.: Fuzzy cognitive maps. Int. Journal of Man-Machine Studies, 24/1986, 65–75, [10.1016/S0020-7373(86)80040-2].
Google Scholar
Kaufmann A., Gupta M. M.: Introduction to Fuzzy Arithmetic: Theory and Applications. Van Nostrand Reinhold, New York 1985, [DOI: 10.1016/0888-613X(87)90010-7].
Google Scholar
Papageorgiou E. I.: Learning Algorithms for Fuzzy Cognitive Maps – A Review Study. IEEE Transactions on Systems, Man and Cybernetics, Part C: Applications and Reviews 42(2)/2012, 150–163, [DOI: 10.1109/TSMCC.2011.2138694].
Google Scholar
Słoń G.: Analiza wybranych algorytmów adaptacji relacji w rozmytych mapach kognitywnych. Pomiary, Automatyka, Kontrola 56(12)/2010, 1445–1448.
Google Scholar
Słoń G.: Relacyjne rozmyte mapy kognitywne w modelowaniu złożonych systemów. Wydawnictwo Politechniki Świętokrzyskiej, Kielce 2013.
Google Scholar
Stylios C. D., Groumpos P. P.: Fuzzy cognitive maps in modeling supervisory control systems. Journal of Intelligent & Fuzzy Systems 8(2)/2000, 83–98.
Google Scholar
Zadeh L. A.: Outline of a New Approach to the Analysis of Complex Systems and Decision Processes. IEEE Transactions on Systems. Man and Cybernetics 1/1973, 28–44, [DOI: 10.1109/TSMC.1973.5408575].
Google Scholar
Authors
Grzegorz Słońg.slon@tu.kielce.pl
Politechnika Świętokrzyska, Katedra Systemów Informatycznych Poland
Statistics
Abstract views: 200PDF downloads: 93
License
This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.