On MPT-implication functions for fuzzy logic.

Trillas, Enric, Alsina, Claudi, and Pradera, Ana. "On MPT-implication functions for fuzzy logic.." RACSAM 98.1 (2004): 259-271. <http://eudml.org/doc/41637>.

@article{Trillas2004,
abstract = {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.},
author = {Trillas, Enric, Alsina, Claudi, Pradera, Ana},
journal = {RACSAM},
keywords = {fuzzy logic; fuzzy implication; fuzzy inference; modus tollens},
language = {eng},
number = {1},
pages = {259-271},
title = {On MPT-implication functions for fuzzy logic.},
url = {http://eudml.org/doc/41637},
volume = {98},
year = {2004},
}

TY - JOUR
AU - Trillas, Enric
AU - Alsina, Claudi
AU - Pradera, Ana
TI - On MPT-implication functions for fuzzy logic.
JO - RACSAM
PY - 2004
VL - 98
IS - 1
SP - 259
EP - 271
AB - 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.
LA - eng
KW - fuzzy logic; fuzzy implication; fuzzy inference; modus tollens
UR - http://eudml.org/doc/41637
ER -