K-operators: An approach to the generation of interval-valued fuzzy implications from fuzzy implications and vice versa

  • Authors:

  • Renata Hax Sander Reiser;Benjamín Bedregal

  • Affiliations:

  • Center of Technology, Federal University of Pelotas, Pelotas, Brazil;Department of Informatics and Applied Mathematics, Federal University of Rio Grande do Norte, Natal, Brazil

  • Venue:
  • Information Sciences: an International Journal
  • Year:
  • 2014

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Abstract

This paper introduces the interval-valued fuzzy implications generated from fuzzy implications and from K-operators showing that this construction generalizes the canonical representation of fuzzy implications. Such generalization allows to recover the usual fuzzy implication properties when dealing with interval-valued fuzzy implications. In addition, the condition under which the converse construction, i.e. the generation of fuzzy implications by action of K-operators and interval-valued fuzzy implications, is discussed. Moreover, we analysed their conjugate construction obtained by action of interval automorphisms. Through commutative diagrams, the associativity related to compositions of conjugate, dual and K-operators performed over fuzzy implications is shown, also preserving their main properties.