In this note we study the extremes of the mass distribution associated with a tetravariate quasi-copula and compare our results with the bi- and trivariate cases, showing the important differences ...between them.
In this paper we show that the cardinality of the set of fuzzy numbers coincides with that of the real numbers. We also show that the set of triangular fuzzy numbers is nowhere dense within the set ...of fuzzy numbers (with a suitable distance) and that the set of real numbers is also nowhere dense within the set of triangular fuzzy numbers. In addition, we introduce the concept of quasilineability and study the set of bounded fuzzy number sequences that do not have a lower limit and that of monotonic decreasing, bounded with respect a partial ordering and not convergent.
In this paper, we propose two new estimators of the multivariate rank correlation coefficient Spearman's footrule which are based on two general estimators for Average Orthant Dependence measures. We ...compare the new proposals with a previous estimator existing in the literature and show that the three estimators are asymptotically equivalent, but, in small samples, one of the proposed estimators outperforms the others. We also analyse Pitman efficiency of these indices to test for multivariate independence as compared to multivariate versions of Kendall's tau and Spearman's rho.
The probability mass distribution of a class of copulas that are invariant under univariate truncation is presented. In particular, it is shown how (differential) properties of the generator of the ...copula are able to identify the singular (respectively, absolutely continuous) component of the induced measure and its support.
Extreme semilinear copulas Durante, Fabrizio; Fernández-Sánchez, Juan; Úbeda-Flores, Manuel
Fuzzy sets and systems,
01/2022, Letnik:
428
Journal Article
Recenzirano
We study the extreme points (in the Krein-Milman sense) of the class of semilinear copulas and provide their characterization. Related results into the more general setting of conjunctive aggregation ...functions (i.e., semi–copulas and quasi–copulas) are also presented.
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 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.
In this paper we find pointwise best-possible bounds on the set of copulas with a given value of the Spearman's footrule coefficient. We show that the lower bound is always a copula but, unlike the ...bounds on sets of copulas with a given value of other measures, such as Kendall's tau, Spearman's rho and Blonqvist's beta, the upper bound can be a copula or a proper quasi-copula. We characterised both of these 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.
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.
