Biconic aggregation functions

Jwaid, T.; Baets, Bernard De; Meyer, H. De

doi:10.1016/j.ins.2011.10.012

Cited by 27 publications

(7 citation statements)

References 22 publications

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“…Convexity plays a key role in the characterization of some classes of semilinear copulas, such as conic copulas [24] and biconic copulas [21]. A more general type of convexity, called generalized convexity, has been introduced in the literature and has been used, for instance, to characterize the comparability of two quasi-arithmetic means [5,32].…”

Section: Convexity and Generalized Convexitymentioning

confidence: 99%

“…Some of these methods start from given sections. Such sections can be the diagonal section and/or the opposite diagonal section [7,9,13,[20][21][22][23]25], or a horizontal section and/or a vertical section [12,27,33]. All of the above methods use sections that are determined by straight lines in the unit square, such as the diagonal, the opposite diagonal, a horizontal line or a vertical line.…”

Section: Introductionmentioning

confidence: 99%

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The role of generalized convexity in conic copula constructions

Jwaid

Meyer

Mesiar

et al. 2015

Journal of Mathematical Analysis and Applications

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Inspired by the notion of a conic semi-copula, we introduce upper conic, lower conic and biconic semi-copulas with a given section. Such semi-copulas are constructed by linear interpolation on segments connecting the graph of a strict negation operator to the points (0, 0) and/or (1, 1). The important subclasses of upper conic, lower conic and biconic (quasi-)copulas with a given section are characterized. The notion of generalized convexity turns out to play a key role in this characterization. Some examples are also provided.

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Section: Convexity and Generalized Convexitymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

The role of generalized convexity in conic copula constructions

Jwaid

Meyer

Mesiar

et al. 2015

Journal of Mathematical Analysis and Applications

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“…Note also that for f (x) = 1 − x, the class of biconic functions with a given opposite diagonal section is retrieved [16].…”

Section: Biconic Functions With a Given Sectionmentioning

confidence: 99%

“…(ii) For f (x) = 1 − x, inequality (2) is equivalent to the concavity of g C (see Lemma 2) and hence, the class of biconic copulas with a given opposite diagonal section (when the opposite diagonal section is piecewise linear) is retrieved [16].…”

Section: Remarkmentioning

confidence: 99%

Biconic semi-copulas with a given section

Jwaid¹,

Baets²,

Meyer³

et al. 2013

Proceedings of the 8th Conference of the European Society for Fuzzy Logic and Technology

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Inspired by the notion of biconic semi-copulas, we introduce biconic semi-copulas with a given section. Such semi-copulas are constructed by linear interpolation on segments connecting the graph of a continuous and decreasing function to the points (0, 0) and (1, 1). Special classes of biconic semi-copulas with a given section such as biconic (quasi-)copulas with a given section are considered. Some examples are also provided.

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“…Thus copulas link joint distribution functions to their one-dimensional margins. For a complete survey on copulas, see [22], and for some recent properties [1,6,11,18,21].…”

Section: Orthant Directional Dependence Copulas and Measures Of Assomentioning

confidence: 99%