Resumen de On negations on [0,1].

Francisco Esteva, Xavier Domingo Roura

• 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.