TY - JOUR
T1 - On the characterizations of fuzzy implications satisfying I(x,y) = I(x, I(x,y))
AU - Shi, Yun
AU - Ruan, Da
AU - Kerre, Etienne
A2 - Messaoudi, Nadia
N1 - Score = 10
PY - 2007/7
Y1 - 2007/7
N2 - Iterative boolean-like laws in fuzzy logic have been studied for functional equations with boolean background in which only fuzzy conjunctions, fuzzy disjunctions and fuzzy negations are contained. In this paper we study an iterative boolean-like law with fuzzy implications, more precisely we derive
characterizations of some classes of fuzzy implications satisfying I(x,y) = I(x,Ix,y)). Our discussion mainly focuses on the three important classes of implications: S-implications, R-implications and QL-implications. We
prove the sufficient and necessary conditions for an S-implication generated by any t-conorm and any fuzzy negation, an R-implication generated by a left-continuous t-norm, a QL-implication generated by a continuous t-conorm, a continuous t-norm and a strong fuzzy negation to satisfy I(x,y) = I(x,Ix,y), for all (x,y) in [0, 1].
AB - Iterative boolean-like laws in fuzzy logic have been studied for functional equations with boolean background in which only fuzzy conjunctions, fuzzy disjunctions and fuzzy negations are contained. In this paper we study an iterative boolean-like law with fuzzy implications, more precisely we derive
characterizations of some classes of fuzzy implications satisfying I(x,y) = I(x,Ix,y)). Our discussion mainly focuses on the three important classes of implications: S-implications, R-implications and QL-implications. We
prove the sufficient and necessary conditions for an S-implication generated by any t-conorm and any fuzzy negation, an R-implication generated by a left-continuous t-norm, a QL-implication generated by a continuous t-conorm, a continuous t-norm and a strong fuzzy negation to satisfy I(x,y) = I(x,Ix,y), for all (x,y) in [0, 1].
KW - Iterative boolean-like law
KW - Fuzzy implications
KW - S-implications
KW - R-implications
KW - QL-implications
UR - http://ecm.sckcen.be/OTCS/llisapi.dll/open/ezp_80892
UR - http://knowledgecentre.sckcen.be/so2/bibref/4267
U2 - 10.1016/j.ins.2007.01.026
DO - 10.1016/j.ins.2007.01.026
M3 - Article
VL - 177
SP - 2954
EP - 2970
JO - Information Sciences
JF - Information Sciences
SN - 0020-0255
IS - 14
ER -