On the characterizations of fuzzy implications satisfying I(x,y) = I(x, I(x,y))

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On the characterizations of fuzzy implications satisfying I(x,y) = I(x, I(x,y)). / Shi, Yun; Ruan, Da; Kerre, Etienne; Messaoudi, Nadia (Peer reviewer).

In: Information Sciences, Vol. 177, No. 14, 07.2007, p. 2954-2970.

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Shi, Yun ; Ruan, Da ; Kerre, Etienne ; Messaoudi, Nadia. / On the characterizations of fuzzy implications satisfying I(x,y) = I(x, I(x,y)). In: Information Sciences. 2007 ; Vol. 177, No. 14. pp. 2954-2970.

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@article{d6320a1e103640b2a8587b211add2f51,
title = "On the characterizations of fuzzy implications satisfying I(x,y) = I(x, I(x,y))",
abstract = "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].",
keywords = "Iterative boolean-like law, Fuzzy implications, S-implications, R-implications, QL-implications",
author = "Yun Shi and Da Ruan and Etienne Kerre and Nadia Messaoudi",
note = "Score = 10",
year = "2007",
month = jul,
doi = "10.1016/j.ins.2007.01.026",
language = "English",
volume = "177",
pages = "2954--2970",
journal = "Information Sciences",
issn = "0020-0255",
publisher = "Elsevier",
number = "14",

}

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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 -

ID: 221805