# On MPT-implication functions for fuzzy logic.

Enric Trillas; Claudi Alsina; Ana Pradera

RACSAM (2004)

- Volume: 98, Issue: 1, page 259-271
- ISSN: 1578-7303

## Access Full Article

top## Abstract

top## How to cite

topTrillas, 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 -

## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.