Raquel García Catalán

Universidad Pública de Navarra | UPNA · Department of Statistics Informatics and Mathematics

A fuzzy set on a finite universe can be interpreted as a vector in a unit cube. This gives rise to a huge variety of approaches in order to aggregate finite fuzzy sets or to modify a given one. We analyze several geometrical methods and discuss possible applications in a multidisciplinary setting.

The attitude of Elementary teachers facing their task as mathematics teachers has more to do with their previous experiences as students of the discipline than with the contents they have learned during the subjects of mathematics teaching in the Degrees of Education. This issue has an impact on the subsequent mathematical instruction of children,...

In this paper we analyze the notion of a finite mean from an axiomatic point of view. We discuss several axiomatic alternatives, with the aim of establishing a universal definition reconciling all of them and exploring theoretical links to some branches of Mathematics as well as to multidisciplinary applications.

We investigate the structure of acyclic binary relations from different points of view. On the one hand, given a nonempty set we study real-valued bivariate maps that satisfy suitable functional equations, in a way that their associated binary relation is acyclic. On the other hand, we consider acyclic directed graphs as well as their representatio...

We analyze the main properties of binary relations, defined on a nonempty set, that arise in a natural way when dealing with real-valued functions that satisfy certain classical functional equations on two variables. We also consider the converse setting, namely, given binary relations that accomplish some typical properties, we study whether or no...

We show that the definition of a fuzzy set is directly related to the existence of a weightable quasi-metric on a universe. This relationship is also explored in terms of functional equations coming either from the membership function of a fuzzy set or from the disymmetry function of a quasi-metric.

The original definition of a fuzzy set hides several additional structures related to functional equations. In the present paper, we analyze the separability functional equation and some of its variants, proving that the solutions of those equations can be described in terms of pairs of linked fuzzy sets on the same universe. In addition, we show t...

Relacionamos subconjuntos Fuzzy y las soluciones quasinormales de algunas ecuaciones funcionales. Revisamos los resultados conocidos para la ecuación de Sincov y analizamos en profundidad la ecuación de Sincov generalizada.

Throughout the paper it is shown that the classical definition of a fuzzy subset carries additional structures. The concept of a fuzzy subset is regarded from an alternative point of view: namely, the characteristic function of a fuzzy subset may be reinterpreted in terms of a Sincov’s functional equation in two variables. Since the solutions of a...

We introduce the concept of a fuzzy total preorder. Then we analyze its numerical representability through a real-valued order-preserving function defined for each α-cut.

We introduce a survey, including the historical back- ground, on different techniques that have recently been issued in the search for a characterization of the represen- tability of semiordered structures, in the sense of Scott and Suppes, by means of a real-valued function and a strictly positive threshold of discrimination.

In the present paper we show an striking relationship between the existence of solutions of a generalization of the Abel functional equation, and the ScottSuppes representability of semiordered structures. We analyze this relationship and, in addition, we study other functional equations related to the numerical representability of semiordered stru...

We analyze various models introduced in social choice to aggregate individual preferences. We show that on the basis of most of these models there is a system of functional equations such that, in many cases, the origin of impossibility results in a social choice model is the non-existence of a solution for the corresponding system. Among the funct...

In this work, the proofs concerning the continuity of the disequilibrium, Shannon information and statistical complexity in the space of distributions are presented. Also, some results on the existence of Shannon information for continuous systems are given. Comment: 4 pages, 0 figures

We discuss some aspects of the extension to continuous systems of a statistical measure of complexity introduced by López-Ruiz, Mancini, and Calbet [Phys. Lett. A 209, 321 (1995)]. In general, the extension of a magnitude from the discrete to the continuous case is not a trivial process and requires some kind of choice. In the present study, severa...

The problem of how an oversampling of translations affects the bounds of an affine frame has been proposed by Chui and Shi. In particular, they proved that tightness is preserved if the oversampling factor is coprime with the dilation factor. In this paper we study, in the dyadic dilation case, oversampling of translation by factors which do not sa...

The problem of how an oversampling of translations affects the bounds of an affine frame has been proposed by Chui and Shi. In particular, they proved that tightness is preserved if the oversampling factor is coprime with the dilation factor. In this paper we study, in the dyadic dilation case, oversampling of translation by factors which do not sa...

We see that we can apply a new sampling theorem based on the Shannon-Whittaker-Kotel’nikov theorem to some kinds of band-limited signals using less samples by a time-unity than the rate given by Nyquist frequency associated to the signal.

If ψ is a BLc wavelet, a Chui-Shi family of redundant tight frames {Ψ(k);k∈ℤ} can be built. Its redundancy is studied through the subspaces of coefficients in l 2 (ℤ 2 ). It is proved that these subspaces converge to zero when ψ is a uniformly continuous wavelet. Also, a Whittaker-Shannon-Kotel’nikov type sampling theorem is given for discrete vect...

Contenido: Introducción; Transformada de Laplace; Ecuaciones diferenciales lineales con coeficientes constantes; Ecuaciones diferenciales de primer orden; Sistemas de ecuaciones; Problemas.