Residuated logics based on strict t-norms with an involutive negation


Cintula, Petr, Klement, Erich Peter, Mesiar, Radko, Navara, Mirko
Mathematical Logic Quarterly
Volume 52, Number 3, Pages 269-282
May, 2006

Abstract

In general, there is only one fuzzy logic in which the standard interpretation of the strong conjunction is a strict triangular norm, namely, the product logic. We study several equations which are satisfied by some strict t-norms and their dual t-conorms. Adding an involutive negation, these equations allow us to generate countably many logics based on strict t-norms which are different from the product logic.

Keywords

fuzzy set, fuzzy logic, involutive fuzzy negation, triangular norm, Hamacher product

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Bibtex entry

@Article{CintulaKlementMesiarNavara-MLQ_Ham,
  author =     {Cintula, Petr and Klement, Erich Peter and 
                Mesiar, Radko and Navara, Mirko},
  title =      {Residuated logics based on strict t-norms
                with an involutive negation},
  year =       {2006},
  month =      {May},
  pages =      {269--282},
  journal =    {Mathematical Logic Quarterly},
  publisher =  {Johann Ambrosius Barth},
  address =    {Heidelberg, Germany},
  issn =       {0942-5616},
  volume =     {52},
  number =     {3},
  annote = {In general, there is only one fuzzy logic in which the
    standard interpretation of the strong conjunction is a strict
    triangular norm, namely, the product logic. We study several
    equations which are satisfied by some strict t-norms and their
    dual t-conorms.  Adding an involutive negation, these equations
    allow us to generate countably many logics based on strict t-norms
    which are different from the product logic.  },
  keywords =   {fuzzy set, fuzzy logic, involutive fuzzy negation, 
                triangular norm, Hamacher product},
  psurl = {[PDF]},
}