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Final solution to the problem of relating a true copula to an imprecise copulaOmladič, Matjaž ; Stopar, NikIn this paper we solve in the negative the problem proposed in this journal (I. Montes et al., Sklar's theorem in an imprecise setting, Fuzzy Sets and Systems, 278 (2015), 48-66) whether an order ... interval defined by an imprecise copula contains a copula. Namely, if ▫$\mathcal{C}$▫ is a nonempty set of copulas, then ▫$\underline{C} = \inf\{C\}_{C\in\mathcal{C}}$▫ and ▫$\overline{C}= \sup\{C\}_{C\in\mathcal{C}}$▫ are quasi-copulas and the pair ▫$(\underline{C},\overline{C})$▫ is an imprecise copula according to the definition introduced in the cited paper, following the ideas of ▫$p$▫-boxes. We show that there is an imprecise copula ▫$(A,B)$▫ in this sense such that there is no copula ▫$C$▫ whatsoever satisfying ▫$A \leqslant C\leqslant B$▫. So, is the proposed definition of the imprecise copula in accordance with the intentions of the initiators? Our methods may be of independent interest: We upgrade the ideas of Dibala et al. (Defects and transformations of quasi-copulas, Kybernetika, 52 (2016), 848-865) where possibly negative volumes of quasi-copulas as defects from being copulas were studied.Source: Fuzzy sets and systems : international journal of soft computing and intelligence. - ISSN 0165-0114 (Vol. 393, Aug. 2020, str. 96-112)Type of material - article, component part ; adult, seriousPublish date - 2020Language - englishCOBISS.SI-ID - 18685273
Author
Omladič, Matjaž |
Stopar, Nik
Topics
copula |
quasi-copula |
discrete copula |
imprecise copula |
defect
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source: Fuzzy sets and systems : international journal of soft computing and intelligence. - ISSN 0165-0114 (Vol. 393, Aug. 2020, str. 96-112)
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Omladič, Matjaž | 09573 |
Stopar, Nik | 32023 |
Source: Personal bibliographies
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