Structure of left-continuous triangular norms with strong induced negations: (III) construction and decomposition

Authors:
Sándor Jenei
Affiliations:
Institute of Mathematics and Informatics, University of Pécs Ifjúság, u. 6, H-7624 Pécs, Hungary and Department of Applied Mathematics, Biometric and Process Control, Ghent Uni ...
Venue:
Fuzzy Sets and Systems
Year:
2002

Citing 5
Cited 10

Linear logic

Theoretical Computer Science
Contrapositive symmetry of fuzzy implications

Fuzzy Sets and Systems
A plea for the use of Łukasiewicz triplets in the definition of fuzzy preference structures: I. general argumentation

Fuzzy Sets and Systems
A survey on different triangular norm-based fuzzy logics

Fuzzy Sets and Systems - Special issue on analytical and structural considerations in fuzzy modeling
New family of triangular norms via contrapositive symmetrization of residuated implications

Fuzzy Sets and Systems

On the structure of left-continuous t-norms that have a continuous contour line

Fuzzy Sets and Systems
The triple rotation method for constructing t-norms

Fuzzy Sets and Systems
Generalizations to the constructions of t-norms: Rotation(-annihilation) construction

Fuzzy Sets and Systems
On the resolution and optimization of a system of fuzzy relational equations with sup-T composition

Fuzzy Optimization and Decision Making
Rotation-invariant t-norms: Where triple rotation and rotation--annihilation meet

Fuzzy Sets and Systems
Unified forms of Triple I method

Computers & Mathematics with Applications
Rotation-invariant t-norm solutions of a system of functional equations

Fuzzy Sets and Systems
Generalized continuous and left-continuous t-norms arising from algebraic semantics for fuzzy logics

Information Sciences: an International Journal
T-ferrers relations versus T-biorders

IFSA'03 Proceedings of the 10th international fuzzy systems association World Congress conference on Fuzzy sets and systems
Conic aggregation functions

Fuzzy Sets and Systems

Quantified Score

Hi-index	0.20

Visualization

Abstract

This paper is the continuation of Jenei (J. Appl. Non-Classical Logics 10 (2000) 83-92; 11 (2001) 351-366) where the rotation construction and the rotation-annihilation construction have been presented, respectively. Both constructions produce left-continuous (but not continuous) triangular norms with strong induced negations. Here, we show that these two constructions allow us to define indecomposability and that each decomposable left-continuous triangular norm with strong induced negation can be derived as result of one of the above constructions. In this way two general decomposition theorems arise. In addition, the decomposition of left-continuous triangular norms with strong induced negations can be defined in a unique way, namely, when the decomposition is done by the minimal decomposition point.