On negations on [0,1].

• Autores: Francisco Esteva, Xavier Domingo Roura
• Localización: Stochastica: revista de matemática pura y aplicada, ISSN 0210-7821, Vol. 4, Nº. 2, 1980, págs. 141-166
• Idioma: español
• Títulos paralelos:
  • Sobre funciones de negación en [0,1].
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• Resumen

  • In [12] Trillas proved that (P(X),n,U,-n) is a quasi-Boolean algebra if and only if its negation has an additive generator. In this paper such result is generalized to PJ(X) and the symmetry of J is analized.

    From the results of Esteva ([11]) weak negations on [0,1] are studied; it is proved that such functions are monotonic, non-increasing, left-continuous and symmetrical with respect to y=x. Their classification relative to C([0,1]) is also given and a canonical element of each class is found. Finally strong and weak negations on a finite J are studied.