Dual representable aggregation functions and their derived S-implications

  • Authors:

  • Isabel Aguiló;Marc Carbonell;Jaume Suñer;Joan Torrens

  • Affiliations:

  • Department of Mathematics and Computer Science, University of the Balearic Islands, Palma de Mallorca, Spain;Department of Mathematics and Computer Science, University of the Balearic Islands, Palma de Mallorca, Spain;Department of Mathematics and Computer Science, University of the Balearic Islands, Palma de Mallorca, Spain;Department of Mathematics and Computer Science, University of the Balearic Islands, Palma de Mallorca, Spain

  • Venue:
  • IPMU'10 Proceedings of the Computational intelligence for knowledge-based systems design, and 13th international conference on Information processing and management of uncertainty
  • Year:
  • 2010

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Abstract

In this paper dual representable aggregation functions (DRAF's) are introduced and studied. After giving a representation theorem for them, it is proved that they can be viewed as a nonassociative generalization of nilpotent t-conorms, some basic properties are proved and some examples are given. On the other hand, using DRAF's a new kind of strong implications are derived and some usual properties are studied for this new class of implications. In particular, it is shown that they have an easy structure always divided into three parts depending on the strong negation.