The Novel Shape Normalization Operator for Fuzzy Numbers in OFN Notation

  • Jacek M. CzerniakEmail author
  • Iwona Filipowicz
  • Dawid Ewald
Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 641)


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.


Fuzzy numbers OFN Normalization operator 


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Copyright information

© Springer International Publishing AG 2018

Authors and Affiliations

  • Jacek M. Czerniak
    • 1
    Email author
  • Iwona Filipowicz
    • 1
  • Dawid Ewald
    • 1
  1. 1.AIRlab Artificial Intelligence and Robotics Laboratory, Institute of TechnologyCasimir the Great University in BydgoszczBydgoszczPoland

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