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

DOI10.1016/j.ins.2011.09.037zbMath1251.39017OpenAlexW1992748735MaRDI QIDQ425534

Hua-Wen Liu, Aifang Xie, Feng Qin, Zilin Zeng

Publication date: 8 June 2012

Published in: Information Sciences (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.ins.2011.09.037

zbMATH Keywords

uninorms(U,N)-implicationsiterative Boolean-like lawsQLU-implicationsRU-implications

Mathematics Subject Classification ID

Functional equations for functions with more general domains and/or ranges (39B52)

Related Items (5)

Characterizations and new subclasses of \(\mathcal{I}\)-filters in residuated lattices ⋮ On the stability of two functional equations for \((S, N)\)-implications ⋮ A new class of fuzzy implications derived from generalized \(h\)-generators ⋮ On \((G, N)\)-implications derived from grouping functions ⋮ Homomorphisms on the monoid of fuzzy implications and the iterative functional equation \(I(x, I(x, y)) = I(x, y)\)

Cites Work

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• On locally internal monotonic operations
• Triangular norms
• Automorphisms, negations and implication operators
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• On the characterizations of \((S,N)\)-implications
• Two types of implications derived from uninorms
• Definition and construction of fuzzy DI-subsethood measures
• A characterization of residual implications derived from left-continuous uninorms
• Structure of Uninorms
• Some Remarks on the Solutions to the Functional Equation I(x,y) = I(x,I(x,y)) for D-Operations
• Uninorm Basics

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