Monotonicity in the Construction of Ordinal Sums of Fuzzy Implications

  • Michał BaczyńskiEmail author
  • Paweł Drygaś
  • Radko Mesiar
Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 581)


In this contribution we discus the problem of monotonicity of intervals in the ordinal sums of fuzzy implication constructions. As a result, new ways of constructing of ordinal sums of fuzzy implications are obtained. These methods allow to adapt the value of fuzzy implication to specific requirements. For our new methods of construction, several sufficient properties for obtaining a fuzzy implication as a result are presented. Moreover, preservation of some properties of the ordinal sums are examined. Among others neutrality property, identity property, and ordering property are considered.



The work on this paper for Michał Baczyński was partially supported by the National Science Centre, Poland, under Grant No. 2015/19/B/ST6/03259. The work on this paper for Paweł Drygaś was partially supported by the Centre for Innovation and Transfer of Natural Sciences and Engineering Knowledge in Rzeszów, through Project Number RPPK.01.03.00-18-001/10. The work on this paper for Radko Mesiar was supported by the Grant APVV-14-0013.


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Copyright information

© Springer International Publishing AG 2018

Authors and Affiliations

  • Michał Baczyński
    • 1
    Email author
  • Paweł Drygaś
    • 2
  • Radko Mesiar
    • 3
  1. 1.Institute of MathematicsUniversity of Silesia in KatowiceKatowicePoland
  2. 2.Faculty of Mathematics and Natural SciencesUniversity of RzeszówRzeszówPoland
  3. 3.Faculty of Civil EngineeringSlovak University of TechnologyBratislavaSlovakia

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