Continuous R-implications generated from representable aggregation functions

  • Authors:
  • M. Carbonell;J. Torrens

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

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

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Abstract

This paper deals with a new kind of residual fuzzy implications derived from non-associative aggregation functions. Some properties of such implications, including their expression through a continuous increasing unary function, are studied in detail. This allows for new families of continuous fuzzy implications satisfying the modus ponens for a given nilpotent t-norm.