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The Novel Shape Normalization Operator for Fuzzy Numbers in OFN Notation

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Advances in Fuzzy Logic and Technology 2017 (EUSFLAT 2017, IWIFSGN 2017)

Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 641))

Abstract

In the article, the authors undertook to resolve a burdensome problem in the OFN calculus concerning so-called improper shapes. Although the calculations are possible for all shapes of the numbers in the OFN notation but the interpretation of the numbers of improper shapes has been rather poor and little intuitive. Moreover, indeed, an effective fast calculus in OFN arithmetic has lost some of its reliability due to those shapes, which was indicated by the critics. First the authors presented the definition for the adoption of an order by the created OFN number, which has a significant impact on the results of the calculations. Then they defined a new, unprecedented normalization operator - ShapeNO. For given four coordinates of an OFN number the authors presented all 256 variants of its theoretically possible shapes and normalized all of them, which resulted in only a dozen or so repetitions. This article is another element of the series of related basic studies on the artificial intelligence inspired by nature, where new methods in the OFN area allow creation and development of new meta-heuristic methods of swarm intelligence. Thanks to that operator, arithmetic operations have been simplified, fuzzy input and output data do not cause consternation during the interpretation and the time needed to perform the calculation itself has been shortened.

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Authors and Affiliations

  1. AIRlab Artificial Intelligence and Robotics Laboratory, Institute of Technology, Casimir the Great University in Bydgoszcz, ul. Chodkiewicza 30, 85-064, Bydgoszcz, Poland

    Jacek M. Czerniak, Iwona Filipowicz & Dawid Ewald

Authors
  1. Jacek M. Czerniak
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  2. Iwona Filipowicz
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  3. Dawid Ewald
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Corresponding author

Correspondence to Jacek M. Czerniak .

Editor information

Editors and Affiliations

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

    Janusz Kacprzyk

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

    Eulalia Szmidt

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

    Sławomir Zadrożny

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

    Krassimir T. Atanassov

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

    Maciej Krawczak

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Czerniak, J.M., Filipowicz, I., Ewald, D. (2018). The Novel Shape Normalization Operator for Fuzzy Numbers in OFN Notation. In: Kacprzyk, J., Szmidt, E., Zadrożny, S., Atanassov, K., Krawczak, M. (eds) Advances in Fuzzy Logic and Technology 2017. EUSFLAT IWIFSGN 2017 2017. Advances in Intelligent Systems and Computing, vol 641. Springer, Cham. https://doi.org/10.1007/978-3-319-66830-7_49

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  • DOI: https://doi.org/10.1007/978-3-319-66830-7_49

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