On interval fuzzy negations

  • Authors:

  • Benjamín Callejas Bedregal

  • Affiliations:

  • Group of Logic, Language, Information, Theory and Applications -- LoLITA, Department of Informatics and Applied Mathematics -- DIMAp, Federal University of Rio Grande do Norte -- UFRN, 59.072-970 ...

  • Venue:
  • Fuzzy Sets and Systems
  • Year:
  • 2010

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Abstract

There exist infinitely many ways to extend the classical propositional connectives to the set [0,1], preserving their behaviors in the extremes 0 and 1 exactly as in the classical logic. However, it is a consensus that this issue is not sufficient, and, therefore, these extensions must also preserve some minimal logical properties of the classical connectives. The notions of t-norms, t-conorms, fuzzy negations and fuzzy implications taking these considerations into account. In previous works, the author, joint with other colleagues, generalizes these notions to the set U={[a,b]|0@?a@?b@?1}, providing canonical constructions to obtain, for example, interval t-norms that are the best interval representations of t-norms. In this paper, we consider the notion of interval fuzzy negation and generalize, in a natural way, several notions related with fuzzy negations, such as the ones of equilibrium point and negation-preserving automorphism. We show that the main properties of these notions are preserved in those generalizations.