Supports of quasi-copulas Fernández-Sánchez, Juan; Quesada-Molina, José Juan; Úbeda-Flores, Manuel
Fuzzy sets and systems,
09/2023, Letnik:
467
Journal Article
Recenzirano
Odprti dostop
It is known that for every s∈1,2 there is a copula whose support is a self-similar fractal set with Hausdorff —and box-counting— dimension s. In this paper we provide similar results for (proper) ...quasi-copulas, in both the bivariate and multivariate cases.
In this paper we complement and generalize some constructions of fuzzy implications based on two arbitrary copulas, obtaining new fuzzy implications. By means of (restricted) aggregation functions ...acting on 0,1S, where S is a fixed finite or infinite set, and related S-systems of fuzzy implications and transforming functions, we introduce and discuss a rather general method for constructing fuzzy implications. Several examples illustrating our results are also included.
In this paper, we introduce the concept of monotonicity according to a direction for a set of random variables. This concept extends well-known multivariate dependence notions, such as corner set ...monotonicity, and can be used to detect dependence in multivariate distributions not detected by other known concepts of dependence. Additionally, we establish relationships with other known multivariate dependence concepts, outline some of their salient properties, and provide several examples.
Extensions of Discrete Copulas to Sparse Copulas Fernandez-Sanchez, Juan; Quesada-Molina, Jose Juan; Ubeda-Flores, Manuel
IEEE transactions on fuzzy systems,
2021-Nov., 2021-11-00, Letnik:
29, Številka:
11
Journal Article
Recenzirano
Odprti dostop
In this article, we answer positively an open question posed in G. Mayor, J. Suñer, and J. Torrens, "Copula-like operations on finite settings," IEEE Trans. Fuzzy Syst. , vol. 13, no. 4, pp. 468-477, ...Aug. 2005 concerning the extensions of discrete copulas to shuffles of Min. Moreover, we also use the extension of discrete copulas to sparse copulas, associated with discrete copulas, of idempotent copulas, in particular, the copula <inline-formula><tex-math notation="LaTeX">M</tex-math></inline-formula>, in order to answer the open question in an alternative way.
In this comprehensive study, we delve deeply into the concept of multivariate total positivity, defining it in accordance with a direction. We rigorously explore numerous salient properties, shedding ...light on the nuances that characterize this notion. Furthermore, our research extends to establishing distinct forms of dependence among the order statistics of a sample from a distribution function. Our analysis aims to provide a nuanced understanding of the interrelationships within multivariate total positivity and its implications for statistical analysis and probability theory.
In this paper we prove that the set of all irreducible discrete quasi-copulas coincides with the set of all discrete quasi-copulas with minimal range. We also provide answers, throughout some ...counterexamples, to two questions posed in Aguiló et al. 2 regarding both discrete quasi-copulas with minimal range and irreducible discrete quasi-copulas. Some additional results concerning discrete (quasi-)copulas are also given.
We introduce the notion of diagonal plane section of a trivariate copula as an additional tool to describe its tail dependence behavior. This notion extends the concept of diagonal section of a ...bivariate copula. We provide existence results for trivariate copulas with a given diagonal plane function. Related results are discussed, especially about extensions to a higher dimensional setting.
We introduce a family of multivariate copulas – a special type of
n-ary aggregation operations – depending on a univariate function. This family is used in the construction of a special aggregation ...operation that satisfies a Lipschitz condition. Several examples are provided and some statistical properties are studied.
Quasi-copulas and signed measures Nelsen, Roger B.; Quesada-Molina, José Juan; Rodríguez-Lallena, José Antonio ...
Fuzzy sets and systems,
09/2010, Letnik:
161, Številka:
17
Journal Article
Recenzirano
Odprti dostop
We study the relationship between multivariate quasi-copulas and measures that they may or may not induce on
0
,
1
n
. We first study the mass distribution of the pointwise best possible lower ...bound for the set of
n-quasi-copulas for
n
≥
3
. As a consequence, we show that not every
n-quasi-copula induces a signed measure on
0
,
1
n
.
PDF
