Quadratic transformation of multivariate aggregation functions

Boonmee Prakassawat () and Tasena Santi ()
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Boonmee Prakassawat: Graduate Degree Program in Mathematics, Faculty of Science, Chiang Mai University, Chiang Mai, 50200, Thailand
Tasena Santi: Data Science Research Center, Department of Mathematics, Faculty of Science, Chiang Mai University, Chiang Mai50200, Thailand

Dependence Modeling, 2020, vol. 8, issue 1, 254-261

Abstract: In this work, we prove that quadratic transformations of aggregation functions must come from quadratic aggregation functions. We also show that this is different from quadratic transformations of (multivariate) semi-copulas and quasi-copulas. In the latter case, those two classes are actually the same and consists of convex combinations of the identity map and another fixed quadratic transformation. In other words, it is a convex set with two extreme points. This result is different from the bivariate case in which the two classes are different and both are convex with four extreme points.

Keywords: quadratic transformation; quadratic construction; semi-copula; quasi-copula; aggregation function (search for similar items in EconPapers)
Date: 2020
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Persistent link: https://EconPapers.repec.org/RePEc:vrs:demode:v:8:y:2020:i:1:p:254-261:n:5

DOI: 10.1515/demo-2020-0015

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