Solutions to the functional equation I(x,y)=I(x,I(x,y)) for three types of fuzzy implications derived from uninorms

Authors:
Aifang Xie;Huawen Liu;Feng Qin;Zilin Zeng
Affiliations:
School of Mathematics, Shandong University, Jinan, Shandong 250100, PR China;School of Mathematics, Shandong University, Jinan, Shandong 250100, PR China;College of Mathematics and Information Science, Jiangxi Normal University, 330022 Nanchang, PR China;Nanchang Military Academy, 300103 Nanchang, PR China
Venue:
Information Sciences: an International Journal
Year:
2012

Citing 16
Cited 3

Uninorm aggregation operators

Fuzzy Sets and Systems
Structure of uninorms

International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems
The structure of continuous uni-norms

Fuzzy Sets and Systems
Automorphisms, negations and implication operators

Fuzzy Sets and Systems - Implication operators
On locally internal monotonic operations

Fuzzy Sets and Systems - Special issue: Preference modelling and applications
Construction of fuzzy indices from fuzzy DI-subsethood measures: Application to the global comparison of images

Information Sciences: an International Journal
On the characterizations of fuzzy implications satisfying I(x,y)=I(x,I(x,y))

Information Sciences: an International Journal
On the characterizations of (S,N)-implications

Fuzzy Sets and Systems
Two types of implications derived from uninorms

Fuzzy Sets and Systems
Fuzzy Implications

Fuzzy Implications
S- and R-implications from uninorms continuous in ]0,1[2 and their distributivity over uninorms

Fuzzy Sets and Systems
(U,N)-implications and their characterizations

Fuzzy Sets and Systems
Discovering a cover set of ARsi with hierarchy from quantitative databases

Information Sciences: an International Journal
Solutions to the functional equation I(x,y)=I(x,I(x,y)) for a continuous D-operation

Information Sciences: an International Journal
A characterization of residual implications derived from left-continuous uninorms

Information Sciences: an International Journal
Some remarks on the characterization of idempotent uninorms

IPMU'10 Proceedings of the Computational intelligence for knowledge-based systems design, and 13th international conference on Information processing and management of uncertainty

Fuzzy implications derived from additive generators of continuous Archimedean t-norms

International Journal of Intelligent Systems
A generalization of Yager's f-generated implications

International Journal of Approximate Reasoning
A new class of fuzzy implications derived from generalized h-generators

Fuzzy Sets and Systems

Quantified Score

Hi-index	0.07

Visualization

Abstract

This paper investigates an iterative Boolean-like law with fuzzy implications derived from uninorms. More precisely, we characterize the solutions to the functional equation I(x,y)=I(x,I(x,y)) that involve RU-, (U,N)- and QLU-implications generated by the most usual classes of uninorms.