Organización |
Dep. Intel. Artif. Fac. Inform. Univ. Politéc. Madrid, Boadilla del Monte (Madrid), España;Secc. Mat. Informàt. Dep. Estruct. Arquit. Univ. Politèc. Catalunya, Barcelona, España;Dep. Informát. Estad. Telemát. Esc. Sup. Cien. Exper. Tecnol. Univ. Rey Juan Carlos, Móstoles (Madrid), España |
Resumen inglés |
This paper deals with numerical functions J : [0,1] x [0,1] → [0,1] able to functionally express operators →: [0,1]X x [0,1]Y → [0,1]XxY defined as (μ → σ)(x,y) = J(μ(x),σ(y)), and verifying either Modus Ponens or Modus Tollens, or both. The concrete goal of the paper is to search for continuous t-norms T and strong-negation functions N for which it is either T(a, J(a,b)) ≤ b (Modus Ponens) or T(N(b), J(a,b)) ≤ N(a) (Modus Tollens), or both, for all a,b in [0,1] and a given J. Functions J are taken among those in the most usual families considered in Fuzzy Logic, namely, R-implications, S-implications, Q-implications and Mamdani-Larsen implications. En passant, the cases of conditional probability and material conditional's probability are analyzed. |