Title of paper:
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On Some Representations and Modifications of Markov Chains
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Author(s):
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Aleksander Kacprzyk
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Prof. Asen Zlatarov University, Burgas, 1 Prof. Yakimov Blvd., Burgas 8010, Bulgaria
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Zhivko Tomov
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Prof. Asen Zlatarov University, Burgas, 1 Prof. Yakimov Blvd., Burgas 8010, Bulgaria
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zhivko57@yandex.ru
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Krassimir Atanassov
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Prof. Asen Zlatarov University, Burgas, 1 Prof. Yakimov Blvd., Burgas 8010, Bulgaria Department of Bioinformatics and Mathematical Modelling,Institute of Biophysics and Biomedical Engineering, Bulgarian Academy of Sciences, Acad. G. Bonchev Str., Block 105, 1113 Sofia
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krat@bas.bg
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Velin Andonov
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Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, Acad. G. Bonchev Str., Block 8, 1113 Sofia, Bulgaria
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velin_andonov@math.bas.bg
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Published in:
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"Issues in Intuitionistic Fuzzy Sets and Generalized Nets", Volume 14 (2018/19), pages 62-76
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Download:
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PDF (162 Kb, File info)
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Abstract:
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Two new representations of Markov chains are proposed. One of them uses the novel concept of Index Matrix (IM) which has greater modelling capabilities in comparison to the standard matrix. A new normalization operator over IMs is introduced. The other new representation proposed in the present paper uses Generalized Nets (GNs). Two GN models of Markov chain are described. It has been made an attempt to classify them with respect to the DM techniques (neural networks, genetic algorithms, etc.) and the tools used, as well as on the basis of the different areas of DM application (education, medicine, genetics, etc).
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Keywords:
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Markov Chains, Index Matrices, Generalized Nets.
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References:
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- Alexieva, J., E. Choy, E. Koycheva, Review and bibloigraphy on generalized nets theory and applications. In:A Survey of Generalized Nets (E. Choy, M. Krawczak, A. Shannon and E. Szmidt, Eds.), Raffles KvB Monograph No. 10, 2007, 207–301.
- Atanassov, K., Generalized index matrices. Comptes rendus de l’Academie Bulgare des Sciences, Vol.40, 1987, No 11, 15–18.
- Atanassov, K., Generalized Nets. World Scientific, Singapore, London, 1991.
- Atanassov, K., On Generalized Nets Theory. Prof. M. Drinov Academic Publ. House, Sofia, 2007.
- Atanassov, K., Index Matrices: Towards an Augmented Matrix Calculus. Springer, Cham, 2014.
- Markov, A. A., Extension of the law of large numbers to quantities, depending on each other (1906). Reprint. Journal Electronique d’Histoire des Probabilits et de la Statistique[electronic only] 2.lb (2006), Article 10, 12 p.
- Gallager, R. G., Stochastic processes: theory for applications. Cambridge University Press, 2013.
- Ibe, O., Markov processes for stochastic modeling. Newnes, 2013.
- Atanassov, K., Generalized Nets as a Tool for the Modelling of Data Mining Processes. Innovative Issues in Intelligent Systems (V. Sgurev, R. Yager, J. Kacprzyk, V. Jotov, Eds.), Cham, Springer, 2016, 161–215.
- Zoteva, D., M. Krawczak, Generalized Nets as a Tool for the Modelling of Data Mining Processes. A Survey. Issues in Intuitionistic Fuzzy Sets and Generalized Nets, 13, 2017, 1–60.
- Molloy, M. K., Performance Analysis Using Stochastic Petri Nets. IEEE Trans. Computers, 31, 1982, 913-917.
- Natkin, S., Les Reseaux de Petri Stochastiques et leur Application a 1’Evaluation des Systemes Informatiques. These de Docteur Ingegneur, CNAM, Paris, France, 1980.
- Shapiro, S., A Stochastic Petri Net with Applications to Modelling Occupancy Times for Concurrent Task Systems. Networks, Vol. 9, No. 4, 1979, 375–379.
- M. K. Molley, “Performance modeling using stochastic Petri nets”, IEEE Trans. Comput, vol. C-31, pp. 913-917, Sept. 1982.
- MacDonald, I. L., & Zucchini, W., Hidden Markov and other models for discrete-valued time series (Vol. 110). CRC Press, 1997.
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