DeMorgan systems with an infinitely many negations in the strict monotone operator case

  • Authors:

  • József Dombi

  • Affiliations:

  • Department of Informatics, University of Szeged, 6720 Szeged, Árpád tér 2., Hungary

  • Venue:
  • Information Sciences: an International Journal
  • Year:
  • 2011

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Abstract

We give a new representation theorem of negation based on the generator function of the strict operator. We study a certain class of strict monotone operators which build the DeMorgan class with infinitely many negations. We show that the necessary and sufficient condition for this operator class is f"c(x)f"d(x)=1, where f"c(x) and f"d(x) are the generator functions of the strict t-norm and strict t-conorm.