On a new class of fuzzy implications: h-Implications and generalizations

  • Authors:
  • Sebastia Massanet;Joan Torrens

  • Affiliations:
  • Department of Mathematics and Computer Science, University of the Balearic Islands, Ctra. de Valldemossa, Km.7.5, 07122 Palma de Mallorca, Spain;Department of Mathematics and Computer Science, University of the Balearic Islands, Ctra. de Valldemossa, Km.7.5, 07122 Palma de Mallorca, Spain

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

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Abstract

A new class of fuzzy implications called the h-implications is introduced. They are implications generated from an additive generator of a representable uninorm in a similar way of Yager's f- and g-implications which are generated from additive generators of continuous Archimedean t-norms and t-conorms. Basic properties of these implications are studied in detail. Modifications and generalizations of the initial definition are presented and their properties studied and compared between them. One of the modifications, called (h,e)-implications, is another example of a fuzzy implication satisfying the exchange principle but not the law of importation for any t-norm, in fact for any function F : [0,1]^2-[0,1].