COMPARATOR IDENTIFICATION IN THE CONDITIONS OF BIFUZZY INITIAL DATA
Abstract
When solving a large number of problems in the study of complex systems, it becomes necessary to establish a relationship between a variable that sets the level of efficiency of the system's functioning and a set of other variables that determine the state of the system or the conditions of its operation. To solve this problem, the methods of regression analysis are traditionally used, the application of which in many real situations turns out to be impossible due to the lack of the possibility of direct measurement of the explained variable. However, if the totality of the results of the experiments performed can be ranked, for example, in descending order, thus forming a system of inequalities, the problem can be presented in such a way as to determine the coefficients of the regression equation in accordance with the following requirement. It is necessary that the results of calculating the explained variable using the resulting regression equation satisfy the formed system of inequalities. This task is called the comparator identification task.
The paper proposes a method for solving the problem of comparator identification in conditions of fuzzy initial data. A mathematical model is introduced to describe the membership functions of fuzzy parameters of the problem based on functions (L–R) – type. The problem is reduced to a system of linear algebraic equations with fuzzy variables.
The analytical relationships required for the formation of a quality criterion for solving the problem of comparator identification in conditions of fuzzy initial data are obtained. As a result, a criterion for the effectiveness of the solution is proposed, based on the calculation of membership functions of the results of experiments, and the transformation of the problem to a standard problem of linear programming is shown. The desired result is achieved by solving a quadratic mathematical programming problem with a linear constraint. The proposed method is generalized to the case when the fuzzy initial data are given bifuzzy
Downloads
References
Vuchkov, I., Bachdzhieva, L., Solakov, B. (1987). Prikladnoy lineyniy regressionnyy analiz. Moscow: Finansy i statistika, 239.
Rao, J. N. K., Subrahmaniam, K. (1971). Combining Independent Estimators and Estimation in Linear Regression with Unequal Variances. Biometrics, 27 (4), 971. doi: https://doi.org/10.2307/2528832
Petrov, K. E., Kryuchkovskiy, V. V. (2009). Komparatornaya strukturno-parametricheskaya identifikatsiya modeley skalyarnogo mnogofaktornogo otsenivaniya. Kherson: Oldi-plyus, 294.
Dotsenko, N. V., Kosenko, N. V. (2012). Comparator authentication of parameters of model of multifactor evaluation. Systemy upravlinnia, navihatsiyi ta zviazku, 2 (1 (21)), 140–143
Bondarenko, M. F., Shabanov-Kushnarenko, Yu. P., Sharonova, N. V. (2010). The ideas algebra interpretations. Bionics of Intelligence, 2 (73), 74–86.
Petrov, E., Petrov, K. (2014). Komparatornaya identifikatsiya modeley mnogofaktornogo otsenivaniya. Saarbrucken: Palmarium Academic Publishing, 224.
Suprun, T. S., Shabanov-Kushnarenko, S. Y. (2014). Isomorphism of predicate model comparator identification. Radio Electronic, Computer Science, Control, 14–24.
Raskin, L. G., Seraja, O. W. (2015). Information problems of canonical regression analysis. Systemy obrobky informatsiyi, 10, 230–234.
Gantmaher, F. R. (2004). Teoriya matrits. Moscow: Fizmatlit, 560.
Zadeh, L. A. (1965). Fuzzy sets. Information and Control, 8 (3), 338–353. doi: https://doi.org/10.1016/s0019-9958(65)90241-x
Raskin, L., Sira, O. (2020). Performing arithmetic operations over the (L–R)-type fuzzy numbers. Eastern-European Journal of Enterprise Technologies, 3 (4 (105)), 6–11. doi: https://doi.org/10.15587/1729-4061.2020.203590
Yeremenko, B., Ryabchun, Y., Ploska, G. (2018). The introduction of intellectual system for evaluating professional abilities of applicants into the activities of educational institutions. Technology audit and production reserves, 6 (2 (44)), 22–26. doi: https://doi.org/10.15587/2312-8372.2018.149680
Mulesa, O. (2015). Adaptation of fuzzy c-means method for determination the structure of social groups. Technology Audit and Production Reserves, 2 (2 (22)), 73–76. doi: https://doi.org/10.15587/2312-8372.2015.41014
Baranova, A., Samoilenko, N., Pitak, I. (2020). Forecasting of formation of pharmaceutical glass waste taking into account the COVID-19 database. ScienceRise, 4, 46–52. doi: https://doi.org/10.21303/2313-8416.2020.001392
Domin, D. (2013). Artificial orthogonalization in searching of optimal control of technological processes under uncertainty conditions. Eastern-European Journal of Enterprise Technologies, 5 (9 (65)), 45–53. doi: https://doi.org/10.15587/1729-4061.2013.18452
Popyk, N. (2014). Ontological approach and fuzzy modeling to describe objects of living environment. Technology Audit and Production Reserves, 6 (4 (20)), 7–9. doi: https://doi.org/10.15587/2312-8372.2014.32875
Kartavykh, S., Komandyrov, O., Kulikov, P., Ploskyi, V., Poltorachenko, N., Terenchuk, S. (2020). Adaptation of fuzzy inference system to solve assessment problems of technical condition of construction objects. Technology Audit and Production Reserves, 3 (2 (53)), 52–55. doi: https://doi.org/10.15587/2706-5448.2020.205364
Grigorovskiy, P., Terentyev, O., Mikautadze, R. (2017). Development of the technique of expert assessment in the diagnosis of the technical condition of buildings. Technology Audit and Production Reserves, 2 (2 (40)), 10–15. doi: https://doi.org/10.15587/2312-8372.2018.128548
Pasko, R., Terenchuk, S. (2020). The use of neuro-fuzzy models in expert support systems for forensic building-technical expertise. ScienceRise, 2, 10–18. doi: https://doi.org/10.21303/2313-8416.2020.001278
Pawlak, Z. (1982). Rough sets. International Journal of Computer & Information Sciences, 11 (5), 341–356. doi: https://doi.org/10.1007/bf01001956
Raskin, L., Sira, O. (2016). Fuzzy models of rough mathematics. Eastern-European Journal of Enterprise Technologies, 6 (4 (84)), 53–60. doi: https://doi.org/10.15587/1729-4061.2016.86739
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
Copyright (c) 2021 Lev Raskin, Oksana Sira, Tetiana Katkova
This work is licensed under a Creative Commons Attribution 4.0 International License.
Our journal abides by the CREATIVE COMMONS copyright rights and permissions for open access journals.
Authors, who are published in this journal, agree to the following conditions:
1. The authors reserve the right to authorship of the work and pass the first publication right of this work to the journal under the terms of a Creative Commons Attribution License, which allows others to freely distribute the published research with the obligatory reference to the authors of the original work and the first publication of the work in this journal.
2. The authors have the right to conclude separate supplement agreements that relate to non-exclusive work distribution in the form in which it has been published by the journal (for example, to upload the work to the online storage of the journal or publish it as part of a monograph), provided that the reference to the first publication of the work in this journal is included.
