Migrativity of aggregation functions

Authors:
H. Bustince;J. Montero;R. Mesiar
Affiliations:
Departamento de Automática y Computación, Universidad Pública de Navarra, Campus Arrosadia s/n, P.O. Box 31006, Pamplona, Spain;Facultad de Matemáticas, Universidad Complutense, 28040 Madrid, Spain;Department of Mathematics and Descriptive Geometry, Slovak University of Technology, SK-813 68 Bratislava, Slovakia and Institute of Information Theory and Automation, Czech Academy of Sciences, C ...
Venue:
Fuzzy Sets and Systems
Year:
2009

Citing 9
Cited 14

Fuzzy sets, uncertainty, and information

Fuzzy sets, uncertainty, and information
Open problems from the 2nd international conference on fuzzy sets theory and its applications

Fuzzy Sets and Systems
Uninorm aggregation operators

Fuzzy Sets and Systems
The functional equations of Frank and Alsina for uninorms and nullnorms

Fuzzy Sets and Systems
Aggregation operators: properties, classes and construction methods

Aggregation operators
Automorphisms, negations and implication operators

Fuzzy Sets and Systems - Implication operators
On continuous triangular norms that are migrative

Fuzzy Sets and Systems
A note on the convex combinations of triangular norms

Fuzzy Sets and Systems
Aggregation Functions: A Guide for Practitioners

Aggregation Functions: A Guide for Practitioners

Supermigrative semi-copulas and triangular norms

Information Sciences: an International Journal
Aggregation of asymmetric distances in Computer Science

Information Sciences: an International Journal
On the α-migrativity of semicopulas, quasi-copulas, and copulas

Information Sciences: an International Journal
An extension of the migrative property for triangular norms

Fuzzy Sets and Systems
An overview of migrative triangular norms

AIKED'11 Proceedings of the 10th WSEAS international conference on Artificial intelligence, knowledge engineering and data bases
On the α-migrativity of multivariate semi-copulas

Information Sciences: an International Journal
A generalization of the migrativity property of aggregation functions

Information Sciences: an International Journal
Cross-migrative triangular norms

International Journal of Intelligent Systems
On (α,β)-homogeneous copulas

Information Sciences: an International Journal
On the migrativity of triangular subnorms

Fuzzy Sets and Systems
An extension of the migrative property for uninorms

Information Sciences: an International Journal
Some properties of overlap and grouping functions and their application to image thresholding

Fuzzy Sets and Systems
Aggregating fuzzy implications

Information Sciences: an International Journal
Aggregation functions for typical hesitant fuzzy elements and the action of automorphisms

Information Sciences: an International Journal

Quantified Score

Hi-index	0.20

Visualization

Abstract

In this paper we introduce a slight modification of the definition of migrativity for aggregation functions that allows useful characterization of this property. Among other things, in this context we prove that there are no t-conorms, uninorms or nullnorms that satisfy migrativity (with the product being the only migrative t-norm, as already shown by other authors) and that the only migrative idempotent aggregation function is the geometric mean. The k-Lipschitz migrative aggregation functions are also characterized and the product is shown to be the only 1-Lipschitz migrative aggregation function. Similarly, it is the only associative migrative aggregation function possessing a neutral element. Finally, the associativity and bisymmetry of migrative aggregation functions are discussed.