Two types of implications derived from uninorms

  • Authors:
  • M. Mas;M. Monserrat;J. Torrens

  • Affiliations:
  • Dpt. de Ciències Matemàtiques i Informàtica, Universitat de les Illes Balears, 07122 Palma de Mallorca, Spain;Dpt. de Ciències Matemàtiques i Informàtica, Universitat de les Illes Balears, 07122 Palma de Mallorca, Spain;Dpt. de Ciències Matemàtiques i Informàtica, Universitat de les Illes Balears, 07122 Palma de Mallorca, Spain

  • Venue:
  • Fuzzy Sets and Systems
  • Year:
  • 2007

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Abstract

This work deals with two kinds of operators derived from uninorms. On the one hand, QL-operators defined by I"Q(x,y)=U^'(N(x),U(x,y)) for all x,y@?[0,1], where N is a strong negation and U and U^' are a conjunctive and a disjunctive uninorm, respectively. On the other hand, the contraposition of QL-operators, called D-operators given by I"D(x,y)=U^'(U(N(x),N(y)),y). In both cases, a necessary condition on U^' is given in order for I"Q and I"D to be implication functions, and in a particular continuous case, necessary and sufficient conditions are given. Finally, several properties are studied and the non-continuous case is also discussed.