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Abstrakty
The article introduces a new proposal of a def uzzification method, which can be implemented in fuzzy controllers. The first chapter refers to the origin of fuzzy sets. Next, a modern development based on this theory is presented in the form of ordered fuzzy numbers (OFN). The most important characteristics of ordered fuzzy numbers are also presented. In the following chapter, details about the defuzzification process are given as part of the fuzzy controller model. Then a new method of defuzzification is presented. The method is named center of circles intersection (CCI). The authors compare this method with a similar geometric solution: triangular expanding (TE) and geometric mean (GM). Also, the results are compared with other methods such as center of gravity (COG), first of maxima (FOM) and last of maxima (LOM). The analysis shows that the proposed solution works correctly and provides results for traditional fuzzy numbers as well as directed fuzzy numbers. The last chapter contains a summary, in which more detailed conclusions are provided and further directions of research are indicated.
Słowa kluczowe
Rocznik
Tom
Strony
185--190
Opis fizyczny
Bibliogr. 33 poz., rys., tab.
Twórcy
autor
- University of Information Technology and Management Copernicus, ul. Inowrocławska 56, 53-648 Wrocław, Poland
autor
- Institute of Technology, Department of Computer Science, Kazimierz Wielki University, ul. Chodkiewicza 30, 85-064 Bydgoszcz, Poland
autor
- Institute of Technology, Department of Computer Science, Kazimierz Wielki University, ul. Chodkiewicza 30, 85-064 Bydgoszcz, Poland
autor
- Technická univerzita v Košiciach, Letná 9, 042 00 Košice, Slovakia
Bibliografia
- [1] K.T. Atanassov, Intuitionistic Fuzzy Sets. Heidelberg: Physica-Verlag HD, 1999, pp. 1–137. https://doi.org/10.1007/978‒3‒7908‒1870‒31
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- [4] A. Milik, M. Chmiel, and E. Hrynkiewicz, “On the systematic method of conditional control program execution by a plc,” Bull. Pol. Ac.: Tech., 64(1), 161–170, 2016.
- [5] A. Mreła, O. Sokolov, and W. Urbaniak, “The method of learning outcomes assessment based on fuzzy relations,” Bull. Pol. Ac.: Tech., 67(3), 527–533 (2019).
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- [8] W. Kosiński, K. Piechór, P. Prokopowicz, and K. Tyburek, “On algorithmic approach to operations on fuzzy numbers,” AI-METH, 95–98 (2001).
- [9] W. Kosiński, P. Prokopowicz, and D. Ślęzak, “Fuzzy reals with algebraic operations: Algorithmic approach,” in ADV SOFT COMP 2002. Springer, 2002, pp. 311–320.
- [10] H.J. Greenberg and W.P. Pierskalla, “A review of quasi-convex functions,” Oper. Res., 19(7), 1553–1570 (1971).
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- [12] B. Martos, Nonlinear programming theory and methods. North-Holland, 1975.
- [13] H.-J. Zimmermann, Fuzzy set theory and its applications. Springer Science & Business Media, 2011.
- [14] J. Czerniak, H. Zarzycki, W. Dobrosielski, and J. Szczepański, “Application of of n notation in the f uzzy observation of wig20 index trend for the period 2008‒2016,” in Uncertainty and Imprecision in Decision Making and Decision Support: Cross Fertilization, New Models, and Applications. Selected Papers f rom BOS-2016 and IWIFSGN-2016, pp. 190–201 (eds. K.T. Atanassov et al.) Cham: Springer International Publishing, 2018.
- [15] H. Zarzycki, J. Czerniak, and W. Dobrosielski, “Detecting nasdaq composite index trends with ofns,” in Theory and Applications of Ordered Fuzzy Numbers. A Tribute to Professor Witold Kosiński, pp. 195–205 (eds. P. Prokopowicz et al.). Springer, Cham, 2017.
- [16] D. Wilczyńska-Sztyma and K. Wielki, “Direction of research into methods of defuzzification for ordered fuzzy numbers,” in XII International PhD Workshop OWD, 2010.
- [17] K. Simiński, “Analysis of new method of initialization of neurofuzzy systems with support vector machines,” TAAI, 24, 243–254 (2012).
- [18] W. Sitek and A. Irla, “The use of fuzzy systems for forecasting the hardenability of steel,” Arch. Metall. Mater., 61(2), 797–802 (2016).
- [19] L. Apiecionek, H. Zarzycki, J. Czerniak, W. Dobrosielski, and D. Ewald, “The cellular automata theory with fuzzy numbers in simulation of real fires in buildings,” in Uncertainty and Imprecision in Decision Making and Decision Support: Cross Fertilization, New Models, and Applications. Selected Papers from BOS-2016 and IWIFSGN-2016, pp. 169–182 (eds. K. T. Atanassov et.al.) Cham: Springer International Publishing, 2018.
- [20] W. Dobrosielski, J. Czerniak, H. Zarzycki, and J. Szczepański, “Fuzzy numbers applied to a heat furnace control,” in Theory and Applications of Ordered Fuzzy Numbers. A Tribute to Professor Witold Kosiński, pp. 271–290 (eds. P. Prokopowicz et al.) Springer, Cham, 2017.
- [21] G. Śmigielski, R. Dygdała, H. Zarzycki, and D. Lewandowski, “Real-time system of delivering water-capsule for firefighting,” in International Multi-Conference on Advanced Computer Systems. Springer, 2016, pp. 102–111.
- [22] H. Zarzycki, J. M. Czerniak, D. Lakomski, and P. Kardasz, “Performance comparison of crm systems dedicated to reporting failures to it department,” in Software Engineering: Challenges and Solutions, pp. 133–146, Springer, 2017.
- [23] H. Zarzycki, “Computer system for the evaluation of options contracts with monte carlo approach,” Stud. Proc. Pol. Assoc. Knowl. Manag, 22, 226–233 (2009).
- [24] H. Zarzycki, “Application of the finite difference cn method to value derivatives,” Stud. Proc. Pol. Assoc. Knowl. Manag, 42, 267–277 (2011).
- [25] J. Kacprzyk, Multistage Fuzzy Control: A Prescriptive Approach, 1st ed. New York, NY, USA: John Wiley & Sons, Inc., 1997.
- [26] L.A. Zadeh, “Towards a theory of fuzzy systems,” Fuzzy sets, fuzzy logic, and fuzzy systems: selected papers by Lotfi A. Zadeh, 83–104 (1996).
- [27] L.A. Zadeh, “Is there a need for fuzzy logic?” INFORM SCIENCES, 178 (13), 2751–2779 (2008).
- [28] J. Kacprzyk, A. Wilbik, and S. Zadrożny, “Linguistic summarization of time series using a fuzzy quantifier driven aggregation,” Fuzzy Sets Syst., 159(12), 1485–1499 (2008).
- [29] M. Ma, A. Kandel, and M. Friedman, “A new approach for defuzzification,” Fuzzy Sets Syst., 111 (3), 351‒356 (2000).
- [30] A. Piegat and K. Tomaszewska, “Optimal representation (ord) method of intuitionistic fuzzy defuzzification,” in IWIFSGN. Springer, 2016, pp. 71–82.
- [31] W. Dobrosielski, J. Czerniak, J. Szczepański, and H. Zarzycki, “Triangular expanding, a new defuzzification method on ordered fuzzy numbers,” in Advances in Fuzzy Logic and Technology 2017. Proceedings of: EUSFLAT-2017 – The 10th Conference of the European Society for Fuzzy Logic and Technology, IWIFSGN’2017, pp. 605–619 (eds. J. Kacprzyk et. al.) Cham: Springer International Publishing, 2017.
- [32] W.T. Dobrosielski, J.M. Czerniak, J. Szczepański, and H. Zarzycki, “Two new defuzzification methods useful for different fuzzy arithmetics,” in IWIFSGN. Springer, 2016, pp. 83–101.
- [33] W. Van Leekwijck and E.E. Kerre, “Defuzzification: criteria and classification,” Fuzzy Sets Syst., 108(2), 159–178 (1999).
Uwagi
PL
Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2020).
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Bibliografia
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bwmeta1.element.baztech-2d906fc7-17b7-45c1-8055-01a6f485bf4e