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The Golden Ratio of Area Method Based on Fuzzy Number Area as a Defuzzyfier

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Uncertainty and Imprecision in Decision Making and Decision Support: New Advances, Challenges, and Perspectives (IWIFSGN 2020, BOS/SOR 2020)

Part of the book series: Lecture Notes in Networks and Systems ((LNNS,volume 338))

Abstract

This article presents a new method of focusing, which may be implemented in fuzzy controllers. The peculiarity of the proposed method is the use of an universal solution in the form of Golden Ratio and the widely applied method of the centre of gravity. The traditional methods of defuzzying, such as: MOM, FOM, LOM, COG, BADD and many others are used in many fields, however they are not universal solutions. This conclusion enables the author of this paper to present a new solution that we refer to as the Golden Ratio of Area, in abbreviation: GRoA. To verify the efficiency of the GRoA method, the results are compared to existing defuzzying methods. An example of use is the controller process solution of the combustion process, for which only the resulting membership function is presented. To determine the fitness of this method, the measure of dispersion was used as standard deviation. The analysis of methods leads to the conclusion that there are cases that significantly deviate from central values and should be eliminated in the control. Another conclusion is that the application of a pattern other than central value will enable a surer selection of defuzzying methods. The analysis shows that the GRoA method works properly and may be used in fuzzy controller. In the last section, the author presents further propositions of research, for example ordered fuzzy numbers (OFN).

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Author information

Authors and Affiliations

  1. Kazimierz Wielki University, J.K. Chodkiewicza 30 Street, 85-064, Bydgoszcz, Kujawsko-Pomorskie, Poland

    Wojciech T. Dobrosielski

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  1. Wojciech T. Dobrosielski
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Correspondence to Wojciech T. Dobrosielski .

Editor information

Editors and Affiliations

  1. Department of Bioinformatics and Mathematical Modelling, Bulgarian Academy of Sciences, Institute of Biophysics and Biomedical Engineering, Sofia, Bulgaria

    Krassimir T. Atanassov

  2. Institute of Biophysics and Biomedical, Bulgarian Academy of Sciences, Sofia, Bulgaria

    Vassia Atanassova

  3. Systems Research Institute, Polish Academy of Sciences, Warsaw, Poland

    Janusz Kacprzyk

  4. Systems Research Institute, Polish Academy of Sciences, Warsaw, Poland

    Andrzej Kałuszko

  5. WIT-Warsaw School of Information Technology, Warsaw, Poland

    Maciej Krawczak

  6. Systems Research Institute, Polish Academy of Sciences, Warsaw, Poland

    Jan W. Owsiński

  7. Faculty of Technical Sciences, “Prof. Assen Zlatarov” University, Burgas, Bulgaria

    Sotir S. Sotirov

  8. Faculty of Natural Sciences, “Prof. Assen Zlatarov” University, Bourgas, Bulgaria

    Evdokia Sotirova

  9. Systems Research Institute, Polish Academy of Sciences, Warsaw, Poland

    Eulalia Szmidt

  10. Systems Research Institute, Polish Academy of Sciences, Warsaw, Poland

    Sławomir Zadrożny

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Dobrosielski, W.T. (2022). The Golden Ratio of Area Method Based on Fuzzy Number Area as a Defuzzyfier. In: Atanassov, K.T., et al. Uncertainty and Imprecision in Decision Making and Decision Support: New Advances, Challenges, and Perspectives. IWIFSGN BOS/SOR 2020 2020. Lecture Notes in Networks and Systems, vol 338. Springer, Cham. https://doi.org/10.1007/978-3-030-95929-6_8

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