DOI: https://doi.org/10.15587/1729-4061.2019.157085

Identification of the state of an object under conditions of fuzzy input data

Serhii Semenov, Oksana Sira, Svitlana Gavrylenko, Nina Kuchuk

Abstract


The modernization of the methods for identification of the state of objects under conditions of fuzzy input data, described by their membership functions, was performed. The selected direction of improvement of traditional methods is associated with the fundamental features of solving this problem under actual conditions of a small source data sample. Under these conditions, to solve the problem of state identification, it is advisable to transfer to the technology of description of source data, based on the mathematical apparatus of fuzzy mathematics and less demanding in terms of information. This transition required the development of new formal methods for solving specific tasks. In this case, the procedure for solution of the fuzzy system of linear algebraic equations was developed for multidimensional discriminant analysis. To solve the clustering problem, a special procedure of comparison of fuzzy distances between objects of clustering and centers of grouping was proposed. The selected direction of improvement of the traditional method for regression analysis was determined by impossibility of using the classical least squares method under conditions when all variables are described fuzzily. This fact led to the need to construct a special two-step procedure for solving the problem. In this case, the linear combination of the measure of distance of the sought-for solution from the modal one and the measures of compactness of membership function of the explained variable are minimized. The technology of fuzzy regressive analysis was implemented in the important practical case when the source fuzzy data are described by general membership functions of the (L-R) type. In addition, the analytic solution to the problem in the form of calculation formulas was obtained. The discussion showed that the modernization of the classical methods for solving the problem of the state identification, considering the fuzzy nature of representation of source data, made it possible to identify objects under actual conditions of a small sample of fuzzy source data

Keywords


fuzzy; multidimensional discriminate; cluster; regression analyses; technologies for reducing fuzzy problems to well-posed problems

References


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Seraya, O. V., Demin, D. A. (2012). Linear regression analysis of a small sample of fuzzy input data. Journal of Automation and Information Sciences, 44 (7), 34–48. doi: https://doi.org/10.1615/jautomatinfscien.v44.i7.40

Tymchuk, S. (2013). Definition of information uncertainty in power engineering. Technology audit and production reserves, 6 (5 (14)), 33–35. Available at: http://journals.uran.ua/tarp/article/view/19648/17296

Semenov, S., Sira, O., Kuchuk, N. (2018). Development of graphic­analytical models for the software security testing algorithm. Eastern-European Journal of Enterprise Technologies, 2 (4 (92)), 39–46. doi: https://doi.org/10.15587/1729-4061.2018.127210

Mozhaev, O., Kuchuk, H., Kuchuk, N., Mozhaev, M., Lohvynenko, M. (2017). Multiservice network security metric. 2017 2nd International Conference on Advanced Information and Communication Technologies (AICT). doi: https://doi.org/10.1109/aiact.2017.8020083

Raskin, L., Sira, O. (2016). Method of solving fuzzy problems of mathematical programming. Eastern-European Journal of Enterprise Technologies, 5 (4 (83)), 23–28. doi: https://doi.org/10.15587/1729-4061.2016.81292

Strizhov, V. V., Krymova, E. A. (2010). Metody vybora regressionnyh modeley. Moscow: VC RAN, 60.


GOST Style Citations


The time course of individual face recognition: A pattern analysis of ERP signals / Nemrodov D., Niemeier M., Mok J. N. Y., Nestor A. // NeuroImage. 2016. Vol. 132. P. 469–476. doi: https://doi.org/10.1016/j.neuroimage.2016.03.006 

Li D.-F. Multiattribute decision making models and methods using intuitionistic fuzzy sets // Journal of Computer and System Sciences. 2005. Vol. 70, Issue 1. P. 73–85. Doi: https://doi.org/10.1016/j.jcss.2004.06.002 

Duda R., Hart P., Stork D. Pattern Classification. Wiley-Intersience, 2000. 688 р.

Borovikov V. P. Iskusstvo analiza dannyh. Piter: Sankt-Peterburg, 2005. 432 p.

Goia A., Vieu P. An introduction to recent advances in high/infinite dimensional statistics // Journal of Multivariate Analysis. 2016. Vol. 146. P. 1–6. doi: https://doi.org/10.1016/j.jmva.2015.12.001 

Fisher discriminant analysis with kernels / Mika S., Ratsch G., Weston J., Scholkopf B., Mullers K. R. // Neural Networks for Signal Processing IX: Proceedings of the 1999 IEEE Signal Processing Society Workshop (Cat. No.98TH8468). 1999. doi: https://doi.org/10.1109/nnsp.1999.788121 

Bessokirnaya G. P. Diskriminantniy analiz dlya otbora informativnyh peremennyh // Sociologiya: metodologiya, metody, matematicheskoe modelirovanie (4M). 2003. Issue 16. P. 25–35.

Bityukov V. K. Formatirovanie klassov ob'ektov metodom diskriminantnogo mnogomernogo analiza // Vestnik Voronezhskogo gosudarstvennogo universiteta inzhenernyh tekhnologiy. 2001. Issue 6. P. 13–19.

Muhamediev B. M. Ekonometrika i ekonometricheskoe prognozirovanie. Almaty, 2007. 198 p.

Egorenko M. V., Bohovko A. G. Cluster analysis as a tool for grouping researched variablese // Mezhdunarodniy nauchno-issledovatel'skiy zhurnal. 2016. Issue 7. P. 25–29. doi: http://doi.org/10.18454/IRJ.2016.49.096

Hong Y., Kwong S. To combine steady-state genetic algorithm and ensemble learning for data clustering // Pattern Recognition Letters. 2008. Vol. 29, Issue 9. P. 1416–1423. doi: https://doi.org/10.1016/j.patrec.2008.02.017 

Streke A., Ghosh J. Cluster Ensembles – A Knowledge Reuse Framework for Combining Multiple Partitions // Journal of Machine Learning Research. 2002. Issue 3. P. 583–617.

Krishna K., Narasimha Murty M. Genetic K-means algorithm // IEEE Transactions on Systems, Man and Cybernetics, Part B (Cybernetics). 1999. Vol. 29, Issue 3. P. 433–439. doi: https://doi.org/10.1109/3477.764879 

Chang Y.-H. O., Ayyub B. M. Fuzzy regression methods – a comparative assessment // Fuzzy Sets and Systems. 2001. Vol. 119, Issue 2. P. 187–203. doi: https://doi.org/10.1016/s0165-0114(99)00091-3 

Hong D. H., Lee S., Do H. Y. Fuzzy linear regression analysis for fuzzy input–output data using shape-preserving operations // Fuzzy Sets and Systems. 2001. Vol. 122, Issue 3. P. 513–526. doi: https://doi.org/10.1016/s0165-0114(00)00003-8 

Sira O. V., Al-Shqeerat K. H. A New Approach for Resolving Equations with Fuzzy Parameters // European Journal of Scientific Research. 2009. Vol. 38, Issue 4. P. 619–625.

Optimizing h value for fuzzy linear regression with asymmetric triangular fuzzy coefficients / Chen F., Chen Y., Zhou J., Liu Y. // Engineering Applications of Artificial Intelligence. 2016. Vol. 47. P. 16–24. doi: https://doi.org/10.1016/j.engappai.2015.02.011 

Yang M.-S., Lin T.-S. Fuzzy least-squares linear regression analysis for fuzzy input–output data // Fuzzy Sets and Systems. 2002. Vol. 126, Issue 3. P. 389–399. doi: https://doi.org/10.1016/s0165-0114(01)00066-5 

Zack Y. A. Fuzzy-regression models under conditions of the presence of non-numeric data in the statistical sample // System Research & Information Technologies. 2017. Issue 1. P. 88–96. doi: https://doi.org/10.20535/srit.2308-8893.2017.1.07 

Fuzzy pattern recognition-based approach to biometric score fusion problem / Fakhar K., El Aroussi M., Saidi M. N., Aboutajdine D. // Fuzzy Sets and Systems. 2016. Vol. 305. P. 149–159. doi: https://doi.org/10.1016/j.fss.2016.05.005 

Raskin L. G., Seraya O. V. Nechetkaya matematika. Osnovy teorii. Prilozheniya. Kharkiv: Parus, 2008. 352 p.

Semenov S. G., Gavrylenko S. Y., Chelak V. V. Developing parametrical criterion for registering abnormal behavior in computer and telecommunication systems on the basis of economic tests // Actual Problems of Economics. 2016. Issue 4. P. 451–459.

Seraya O. V., Demin D. A. Linear regression analysis of a small sample of fuzzy input data // Journal of Automation and Information Sciences. 2012. Vol. 44, Issue 7. Р. 34–48. doi: https://doi.org/10.1615/jautomatinfscien.v44.i7.40 

Tymchuk S. Definition of information uncertainty in power engineering // Technology audit and production reserves. 2013. Vol. 6, Issue 5 (14). P. 33–35. URL: http://journals.uran.ua/tarp/article/view/19648/17296

Semenov S., Sira O., Kuchuk N. Development of graphic­analytical models for the software security testing algorithm // Eastern-European Journal of Enterprise Technologies. 2018. Vol. 2, Issue 4 (92). P. 39–46. doi: https://doi.org/10.15587/1729-4061.2018.127210 

Multiservice network security metric / Mozhaev O., Kuchuk H., Kuchuk N., Mozhaev M., Lohvynenko M. // 2017 2nd International Conference on Advanced Information and Communication Technologies (AICT). doi: https://doi.org/10.1109/aiact.2017.8020083 

Raskin L., Sira O. Method of solving fuzzy problems of mathematical programming // Eastern-European Journal of Enterprise Technologies. 2016. Vol. 5, Issue 4 (83). P. 23–28. doi: https://doi.org/10.15587/1729-4061.2016.81292 

Strizhov V. V., Krymova E. A. Metody vybora regressionnyh modeley. Moscow: VC RAN, 2010. 60 p.







Copyright (c) 2019 Serhii Semenov, Oksana Sira, Svitlana Gavrylenko, Nina Kuchuk

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ISSN (print) 1729-3774, ISSN (on-line) 1729-4061