On some geometric transformation of t-norms

• Autores: Erich Peter Klement, Radko Mesiar, Endre Pap
• Localización: Mathware & soft computing: The Magazine of the European Society for Fuzzy Logic and Technology, ISSN-e 1134-5632, Vol. 5, Nº. 1, 1998, págs. 57-67
• Idioma: inglés
• Títulos paralelos:
  • Transformación geométrica de t-normas
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• Resumen

  • Given a triangular norm T, its t-reverse T*, introduced by C. Kimberling (Publ. Math. Debrecen 20, 21-39, 1973) under the name invert, is studied. The question under which conditions we have T** = T is completely solved. The t-reverses of ordinal sums of t-norms are investigated and a complete description of continuous, self-reverse t-norms is given, leading to a new characterization of the continuous t-norms T such that the function G(x,y) = x + y - T(x,y) is a t-conorm, a problem originally studied by M.J. Frank (Aequationes Math. 19, 194-226, 1979). Finally, some open problems are formulated.