Piecewise linear aggregation functions based on triangulation

Authors:
B. De Baets;H. De Meyer;R. Mesiar
Affiliations:
Department of Applied Mathematics, Biometrics and Process Control, Ghent University, Coupure links 653, B-9000 Gent, Belgium;Department of Applied Mathematics and Computer Science, Ghent University, Krijgslaan 281 S9, B-9000 Gent, Belgium;Department of Mathematics and Descriptive Geometry, Slovak University of Technology, Radlinského 11, 813 68 Bratislava, Slovakia and Institute for Research and Applications of Fuzzy Modelling ...
Venue:
Information Sciences: an International Journal
Year:
2011

Citing 10
Cited 6

Aggregation operators: properties, classes and construction methods

Aggregation operators
Monotone approximation of aggregation operators using least squares splines

International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems
Weighted aggregation operators based on minimization

Information Sciences: an International Journal
Construction of aggregation functions from data using linear programming

Fuzzy Sets and Systems
On some construction methods for 1-Lipschitz aggregation functions

Fuzzy Sets and Systems
Flipping and cyclic shifting of binary aggregation functions

Fuzzy Sets and Systems
Aggregation Functions: A Guide for Practitioners

Aggregation Functions: A Guide for Practitioners
Loss optimal monotone relabeling of noisy multi-criteria data sets

Information Sciences: an International Journal
An Introduction to Copulas

An Introduction to Copulas
Binary survival aggregation functions

Fuzzy Sets and Systems

Conic aggregation functions

Fuzzy Sets and Systems
Biconic aggregation functions

Information Sciences: an International Journal
Aggregation functions and contradictory information

Fuzzy Sets and Systems
Granular representation and granular computing with fuzzy sets

Fuzzy Sets and Systems
Directional dependence of random vectors

Information Sciences: an International Journal
On a certain class of aggregative operators

Information Sciences: an International Journal

Quantified Score

Hi-index	0.07

Visualization

Abstract

We introduce a method to construct piecewise linear binary aggregation functions on the unit interval, based on a triangulation of the unit square with one additional vertex. We derive conditions under which such piecewise linear aggregation functions possess additional interesting properties, such as idempotence, symmetry, Lipschitz continuity and 2-monotonicity. This construction method can also be used to approximate binary aggregation functions. In this way, copulas and quasi-copulas are approximated by singular copulas.