Solutions to the functional equation \(I(x,y)=I(x,I(x,y))\) for a continuous D-operation

DOI10.1016/J.INS.2010.01.023zbMath1204.03034OpenAlexW1523443251MaRDI QIDQ985075

Aifang Xie, Feng Qin

Publication date: 20 July 2010

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

Full work available at URL: https://doi.org/10.1016/j.ins.2010.01.023

zbMATH Keywords

D-operations, D-implications, iterative Boolean-like laws

Mathematics Subject Classification ID

Fuzzy logic; logic of vagueness (03B52) Functional equations and inequalities (39B99)

Related Items (12)

ON A NEW CLASS OF IMPLICATIONS: (g,min)-IMPLICATIONS AND SEVERAL CLASSICAL TAUTOLOGIES ⋮ Characterizations and new subclasses of \(\mathcal{I}\)-filters in residuated lattices ⋮ Some Remarks on the Solutions to the Functional Equation I(x,y) = I(x,I(x,y)) for D-Operations ⋮ On the stability of two functional equations for \((S, N)\)-implications ⋮ A characterization of residual implications derived from left-continuous uninorms ⋮ The \(\circledast\)-composition of fuzzy implications: closures with respect to properties, powers and families ⋮ Solutions to the functional equation \(I(x, y) = I(x, I(x, y))\) for three types of fuzzy implications derived from uninorms ⋮ Systemic approach to fuzzy logic formalization for approximate reasoning ⋮ A new class of fuzzy implications derived from generalized \(h\)-generators ⋮ Homomorphisms on the monoid of fuzzy implications and the iterative functional equation \(I(x, I(x, y)) = I(x, y)\) ⋮ Threshold generation method of construction of a new implication from two given ones ⋮ On a new class of fuzzy implications: \(h\)-implications and generalizations

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• On the first place antitonicity in QL-implications
• Fuzzy implications
• Fuzzy implication operators and generalized fuzzy method of cases
• Triangular norms
• Automorphisms, negations and implication operators
• Residual implications revisited. Notes on the Smets-Magrez theorem.
• On the characterizations of fuzzy implications satisfying \(I(x,y)=I(x,I(x,y))\)
• On contra-symmetry and MPT conditionality in fuzzy logic
• WhenQM-operators are implication functions and conditional fuzzy relations

This page was built for publication: Solutions to the functional equation \(I(x,y)=I(x,I(x,y))\) for a continuous D-operation