Conic aggregation functions

Authors:
T. Jwaid;B. De Baets;J. Kalická;R. Mesiar
Affiliations:
Department of Applied Mathematics, Biometrics and Process Control, Ghent University, Coupure links 653, B-9000 Gent, Belgium;Department of Applied Mathematics, Biometrics and Process Control, Ghent University, Coupure links 653, B-9000 Gent, Belgium;Department of Mathematics and Descriptive Geometry, Slovak University of Technology, Radlinského 11, 813 68 Bratislava, Slovakia;Department of Mathematics and Descriptive Geometry, Slovak University of Technology, Radlinského 11, 813 68 Bratislava, Slovakia
Venue:
Fuzzy Sets and Systems
Year:
2011

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Abstract

Inspired by the notion of conic t-norms, we introduce conic aggregation functions. Such aggregation functions are completely characterized by their zero-set. Special classes of binary conic aggregation functions such as conic quasi-copulas and conic copulas are considered. We provide the necessary and sufficient conditions on the boundary curve of the zero-set of a conic aggregation function to obtain a conic (quasi-) copula and conclude that the class of conic copulas is a proper subclass of the class of conic quasi-copulas. Moreover, we characterize the class of singular conic copulas. We investigate some aggregations of conic (quasi-) copulas. Some examples are also provided.