Contrapositive symmetry of distributive fuzzy implications revisited

Authors:
Yang Li;Qin Feng
Affiliations:
College of Mathematics and Information Science, Jiangxi Normal University, Nanchang, P.R.China;College of Mathematics and Information Science, Jiangxi Normal University, Nanchang, P.R.China
Venue:
FUZZ-IEEE'09 Proceedings of the 18th international conference on Fuzzy Systems
Year:
2009

Citing 3
Cited 0

A new class of fuzzy implications, axioms of fuzzy implication revisited

Fuzzy Sets and Systems
Contrapositive symmetry of distributive fuzzy implications

International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems
Automorphisms, negations and implication operators

Fuzzy Sets and Systems - Implication operators

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Abstract

In this paper, we explore the solution of functional equations I(x, T(y, z)) = T(I(x, y), I(x, z)) and I(x, y) = I(N(y),N(x)) satisfied simultaneously, where T is a strict t-norm, I a fuzzy implication and N a strong negation. Under the assumptions of I continuous except the points (0, 0) and (1, 1), we get the full characterizations of the solutions for this functional equations.