Characterization of Quadratic Aggregation Functions

Tasena, Santi

doi:10.1109/tfuzz.2019.2900850

Cited by 3 publications

(3 citation statements)

References 20 publications

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“…To see that P is nondecreasing with respect to the last variable, x < a < and < z < . For each c > , let p = pc (a, z) = ln The characterization of quadratic aggregation functions has been done in [10]. Thus, we immediately have the following result.…”

Section: Resultsmentioning

confidence: 96%

Quadratic transformation of multivariate aggregation functions

Boonmee

Tasena

2020

Dependence Modeling

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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.

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Section: Resultsmentioning

confidence: 96%

Quadratic transformation of multivariate aggregation functions

Boonmee

Tasena

2020

Dependence Modeling

Self Cite

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“…This includes, for example, the constructions based on partial information such as constraints [7,11], forms [20,15,16], properties [25,32], or values on subsets of domains such as diagonal sections and curved sections [2,8,17,19,21,29,34,43]. Another example is the transformations of aggregation functions such as flippings [14,24], polynomial transformations [3,6,10,33,40,42,41], compositions [18,31] and others [27,28,30]. Penalty-based constructions also gain interest in recent years [1,4,5,13,12,23,35,36,39,42,38].…”

Section: Introductionmentioning

confidence: 99%

“…40]. Since there are 6 of such π ij and ζ ij , the set of quadratic bivariate aggregation functions can be represent by a octahedron with π ij and ζ ij as its vertices.…”

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confidence: 99%

Aggregation Function Constructed from Copula

BOONYASRI¹,

Tasena²

2022

CJM

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"In this work, we show that a slight change in the Sklar's formula tremendously affects the class of aggregation functions it represents. While the original formula can only be used to construct $d$-increasing aggregation functions, this new formula can be used to construct any continuous aggregation function excepted possibly those belong to the boundary of this set. In particular, all continuous aggregation functions can be approximated by aggregation functions in this form. This shows that it is sufficient to only consider aggregation functions in this form for most cases. Construction examples via this method are also given."

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Polynomial bivariate copulas of degree five: characterization and some particular inequalities

Šeliga

Kauers

Saminger‐Platz

et al. 2021

Dependence Modeling

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Bivariate polynomial copulas of degree 5 (containing the family of Eyraud-Farlie-Gumbel-Morgenstern copulas) are in a one-to-one correspondence to certain real parameter triplets (a, b, c), i.e., to some set of polynomials in two variables of degree 1: p(x, y) = ax + by + c. The set of the parameters yielding a copula is characterized and visualized in detail. Polynomial copulas of degree 5 satisfying particular (in)equalities (symmetry, Schur concavity, positive and negative quadrant dependence, ultramodularity) are discussed and characterized. Then it is shown that for polynomial copulas of degree 5 the values of several dependence parameters (including Spearman’s rho, Kendall’s tau, Blomqvist’s beta, and Gini’s gamma) lie in exactly the same intervals as for the Eyraud-Farlie-Gumbel-Morgenstern copulas. Finally we prove that these dependence parameters attain all possible values in ]−1, 1[ if polynomial copulas of arbitrary degree are considered.

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Characterization of Quadratic Aggregation Functions

Cited by 3 publications

References 20 publications

Quadratic transformation of multivariate aggregation functions

Quadratic transformation of multivariate aggregation functions

Aggregation Function Constructed from Copula

Polynomial bivariate copulas of degree five: characterization and some particular inequalities

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