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

  • Wojciech T. DobrosielskiEmail author
  • Janusz Szczepański
  • Hubert Zarzycki
Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 401)


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.


Fuzzy logic Fuzy sets Fuzzy control system Deffuzification Fibonacci series 


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Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  • Wojciech T. Dobrosielski
    • 1
    Email author
  • Janusz Szczepański
    • 2
  • Hubert Zarzycki
    • 3
  1. 1.Casimir the Great University in BydgoszczInstitute of TechnologyBydgoszczPoland
  2. 2.Institute of Fundamental Technological ResearchPolish Academy of Sciences WarsawWarsawPoland
  3. 3.Wroclaw School of Information TechnologyWroclawPoland

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