Structure of left-continuous triangular norms with strong induced negations (I) Rotation construction

DOI10.1080/11663081.2000.10510989zbMath1033.03512OpenAlexW1991238910MaRDI QIDQ4443413

Sándor Jenei

Publication date: 13 January 2004

Published in: Journal of Applied Non-Classical Logics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/11663081.2000.10510989

Mathematics Subject Classification ID

Fuzzy logic; logic of vagueness (03B52) Theory of fuzzy sets, etc. (03E72)

Related Items

The construction of left-continuous t-norms: a geometric approach in two dimensions, Co-rotation constructions of residuated semigroups, Generalizations to the constructions of t-norms: rotation(-annihilation) construction, Triangular norms. Position paper II: General constructions and parameterized families, \((S,N)\)- and \(R\)-implications: A state-of-the-art survey, The triple rotation method for constructing t-norms, A new axiomatization for involutive monoidal t-norm-based logic, A conditionally cancellative left-continuous t-norm is not necessarily continuous, On the structure of left-continuous t-norms that have a continuous contour line, T-norms and t-conorms continuous around diagonals, A method to construct fuzzy implications -- rotation construction, Projectivity and unification in substructural logics of generalized rotations, A new construction for t-norms and their application to an open problem of Alsina, Frank and Schweizer, Ordinal sums: from triangular norms to bi- and multivariate copulas, Gluing residuated lattices, Co-rotation-annihilations of residuated semigroups, Unnamed Item, Rotation logics, Triangular norms. Position paper I: Basic analytical and algebraic properties., How to construct left-continuous triangular norms -- state of the art., Residual implications and left-continuous t-norms which are ordinal sums of semigroups., Real coextensions as a tool for constructing triangular norms, A generalization of additive generator of triangular norms, Associativity of triangular norms characterized by the geometry of their level sets, Structure of left-continuous triangular norms with strong induced negations. III: Construction and decomposition, Unified forms of Triple I method, The coextension of commutative pomonoids and its application to triangular norms, Generalized continuous and left-continuous t-norms arising from algebraic semantics for fuzzy logics, MTL-algebras arising from partially ordered groups, On triangular norms and uninorms definable in Ł\(\Pi \frac{1}{2}\), Archimedean components of triangular norms, Regular left-continuous t-norms, Structure of left-continuous triangular norms with strong induced negations (II) Rotation-annihilation construction, A general method for constructing left-continuous t-norms, A characterization theorem on the rotation construction for triangular norms, Rotation-invariant t-norms: where triple rotation and rotation-annihilation meet, Representation by triples of algebras with an MV-retract, Totally Ordered Monoids Based on Triangular Norms, A note on the ordinal sum theorem and its consequence for the construction of triangular norms, Rotation-invariant t-norm solutions of a system of functional equations, Generating pseudo-t-norms and implication operators

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• On the structure of semi-groups on a compact manifold with boundary
• A plea for the use of Łukasiewicz triplets in the definition of fuzzy preference structures. I: General argumentation
• A survey on different triangular norm-based fuzzy logics
• Contrapositive symmetry of fuzzy implications
• New family of triangular norms via contrapositive symmetrization of residuated implications
• Naturally Totally Ordered Commutative Semigroups