On a new construction of 1-Lipschitz aggregation functions, quasi-copulas and copulas

Authors:
Anna KolesáRová;Radko Mesiar;Jana Kalická
Affiliations:
Institute of Information Engineering, Automation and Mathematics, Faculty of Chemical and Food Technology, Slovak University of Technology, Radlinského 9, 812 37 Bratislava, Slovakia;Department of Mathematics and Descriptive Geometry, Faculty of Civil Engineering, Slovak University of Technology, Radlinského 11, 813 68 Bratislava, Slovakia and Centre of Excellence IT4Inno ...;Department of Mathematics and Descriptive Geometry, Faculty of Civil Engineering, Slovak University of Technology, Radlinského 11, 813 68 Bratislava, Slovakia
Venue:
Fuzzy Sets and Systems
Year:
2013

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Abstract

A new method of constructing 1-Lipschitz aggregation functions is proposed and studied. As a by product, a new method of constructing (quasi-)copulas from a given (quasi-)copula C is obtained. Newly constructed copulas are negative quadrant dependent for any original copula C. The only invariant copula under this construction is the Frechet-Hoffding lower bound W. The method preserves several important properties of copulas, such as modularity, absolute continuity or symmetry, and commutes with some other constructions, e.g., the construction of survival copulas.