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Novel Developments in Uncertainty Representation and Processing pp 75–84Cite as

A Proposal for a Method of Defuzzification Based on the Golden Ratio—GR

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Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 401))

Abstract

This article presents a proposal for a new method of defuzzification a fuzzy controller, which is based on the concept of the golden ratio, derived from the Fibonacci series [1]. The origin of the method was the observation of numerous instances of the golden ratio in such diverse fields as biology, architecture, medicine, and painting. A particular area of its occurrence is genetics, where we find the golden ratio in the very structure of the DNA molecule [2] (deoxyribonucleic acid molecules are 21 angstroms wide and 34 angstroms long for each full length of one double helix cycle). This fact makes the ratio in the Fibonacci series in some sense a universal design principle used by man and nature alike. In keeping with the requirements, the authors of the present study first explain the essential concepts of fuzzy logic, including in particular the notions of a fuzzy controller and a method of defuzzification. Then, they postulate the use of the golden ratio in the process of defuzzification and call the idea the Golden Ratio (GR) Method. In the subsequent part of the article, the proposed GR-based instrument is compared with the classical methods of defuzzification, including COG, FOM, and LOM. In the final part, the authors carry out numerous calculations and formulate conclusions which serve to classify the proposed method. At the end they present directions of further research.

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Authors and Affiliations

  1. Casimir the Great University in Bydgoszcz, Institute of Technology, ul. Chodkiewicza 30, 85-064, Bydgoszcz, Poland

    Wojciech T. Dobrosielski

  2. Institute of Fundamental Technological Research, Polish Academy of Sciences Warsaw, ul. Pawinskiego 5B, 02-106, Warsaw, Poland

    Janusz Szczepański

  3. Wroclaw School of Information Technology, ul. Wejherowska 28, 54-239, Wroclaw, Poland

    Hubert Zarzycki

Authors
  1. Wojciech T. Dobrosielski
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  2. Janusz Szczepański
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  3. Hubert Zarzycki
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Corresponding author

Correspondence to Wojciech T. Dobrosielski .

Editor information

Editors and Affiliations

  1. Inst. of Biophy. & Biomedical Eng., Bulgarian Academy of Sciences, Sofia, Bulgaria

    Krassimir T. Atanassov

  2. Division of Graduate Studies, Tijuana Institute of Technology, Tijuana, Baja California, Mexico

    Oscar Castillo

  3. Sys Res Intit of Polish Acad of Science, Intelligent Systems Laboratory, Warsaw, Poland

    Janusz Kacprzyk

  4. Warsaw School of Information Technology, Polish Academy of Sciences, Warsaw, Poland

    Maciej Krawczak

  5. Div of Gdu Stud,CalzTecn sn,Fra.TomAqu, Tijuana Institute of Technology, Tijuana, Baja California, Mexico

    Patricia Melin

  6. Intelligent Systems Laboratory, Asen Zlatarov University, Bourgas, Bulgaria

    Sotir Sotirov

  7. Intelligent Systems Laboratory, “Prof. Dr. Asen Zlatarov” University, Burgas, Bulgaria

    Evdokia Sotirova

  8. Systems Research Institute, Polish Academy of Sciences, Warszawa, Poland

    Eulalia Szmidt

  9. Dept. of Tele. & Info. Processing, Ghent University, Gent, Belgium

    Guy De Tré

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

    Sławomir Zadrożny

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Dobrosielski, W.T., Szczepański, J., Zarzycki, H. (2016). A Proposal for a Method of Defuzzification Based on the Golden Ratio—GR. In: Atanassov, K., et al. Novel Developments in Uncertainty Representation and Processing. Advances in Intelligent Systems and Computing, vol 401. Springer, Cham. https://doi.org/10.1007/978-3-319-26211-6_7

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  • DOI: https://doi.org/10.1007/978-3-319-26211-6_7

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-26210-9

  • Online ISBN: 978-3-319-26211-6

  • eBook Packages: Computer ScienceComputer Science (R0)

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