## Person: Miranda Menéndez, Pedro Pedro
Miranda Menéndez
##### Faculty / Institute
Ciencias Matemáticas

## Search Results

Now showing 1 - 10 of 38
• Publication
Order cones: A tool for deriving k-dimensional faces of cones of subfamilies of monotone games
In this paper we introduce the concept of order cone. This concept is inspired by the concept of order polytopes, a well-known object coming from Combinatorics. Similarly to order polytopes, order cones are a special type of polyhedral cones whose geometrical structure depends on the properties of a partially ordered set (brief poset). This allows to study these properties in terms of the subjacent poset, a problem that is usually simpler to solve. From the point of view of applicability, it can be seen that many cones appearing in the literature of monotone TU-games are order cones. Especially, it can be seen that the cones of monotone games with restricted cooperation are order cones, no matter the structure of the set of feasible coalitions.
• Publication
Tutorial interactivo de ejemplos básicos y ejercicios de inferencia estadística no-paramétrica mediante software libre: implementación mediante R, R-studio y Swirl
(2019-07-04) Martín Apaolaza, Nirian; Castilla González, Elena María; Miranda Menéndez, Pedro; Pardo Llorente, Leandro
• Publication
Bottom-Up: a New Algorithm to Generate Random Linear Extensions of a Poset
(Springer Netherlands, 2018-10-09) García-Segador, P.; Miranda Menéndez, Pedro
In this paper we present a new method for deriving a random linear extension of a poset. This new strategy combines Probability with Combinatorics and obtains a procedure where each minimal element of a sequence of subposets is selected via a probability distribution. The method consists in obtaining a weight vector on the elements of P, so that an element is selected with a probability proportional to its weight. From some properties on the graph of adjacent linear extensions, it is shown that the probability distribution can be obtained by solving a linear system. The number of equations involved in this system relies on the number of what we have called positioned antichains, that allows a reduced number of equations. Finally, we give some examples of the applicability of the algorithm. This procedure cannot be applied to every poset, but it is exact when it can be used. Moreover, the method is quick and easy to implement. Besides, it allows a simple way to derive the number of linear extensions of a given poset.
• Publication
On vertices of the k-additive monotone core
(International Fuzzy Systems Association (IFSA); European Society for Fuzzy Logic and Technology (EUSFLAT), 2009) Miranda Menéndez, Pedro; Grabisch, Michel; Carvalho, J.P.; Dubois, D.; Kaymak, U.; Sousa, J.M.C.
Given a capacity, the set of dominating k-additive capacities is a convex polytope; thus, it is defined by its vertices. In this paper we deal with the problem of deriving a procedure to obtain such vertices in the line of the results of Shapley and Ichiishi for the additive case. We propose an algorithm to determine the vertices of the k-additive monotone core. Then, we characterize the vertices of the n-additive core and finally, we explore the possible translations for the k-additive case
• Publication
Restricted distance-type Gaussian estimators based on density power divergence and their aplications in hypothesis testing
(MDPI, 2023-03-17) Felipe Ortega, Ángel; Jaenada Malagón, María; Miranda Menéndez, Pedro; Pardo Llorente, Leandro
In this paper, we introduce the restricted minimum density power divergence Gaussian estimator (MDPDGE) and study its main asymptotic properties. In addition, we examine it robustness through its influence function analysis. Restricted estimators are required in many practical situations, such as testing composite null hypotheses, and we provide in this case constrained estimators to inherent restrictions of the underlying distribution. Furthermore, we derive robust Rao-type test statistics based on the MDPDGE for testing a simple null hypothesis, and we deduce explicit expressions for some main important distributions. Finally, we empirically evaluate the efficiency and robustness of the method through a simulation study
• Publication
Minimum ϕ-Divergence Estimation in Constrained Latent Class Models for Binary Data
(Springer, 2015) Felipe Ortega, Ángel; Miranda Menéndez, Pedro; Pardo Llorente, Leandro
The main purpose of this paper is to introduce and study the behavior of minimum (Formula presented.)-divergence estimators as an alternative to the maximum-likelihood estimator in latent class models for binary items. As it will become clear below, minimum (Formula presented.)-divergence estimators are a natural extension of the maximum-likelihood estimator. The asymptotic properties of minimum (Formula presented.)-divergence estimators for latent class models for binary data are developed. Finally, to compare the efficiency and robustness of these new estimators with that obtained through maximum likelihood when the sample size is not big enough to apply the asymptotic results, we have carried out a simulation study.
• Publication
On the vertices of the k-additive core
(Elsevier Science, 2008) Grabisch, Michel; Miranda Menéndez, Pedro
The core of a game upsilon on N, which is the set of additive games phi dominating upsilon such that phi(N) = upsilon(N), is a central notion in cooperative game theory, decision making and in combinatorics, where it is related to submodular functions, matroids and the greedy algorithm. In many cases however, the core is empty, and alternative solutions have to be found. We define the k-additive core by replacing additive games by k-additive games in the definition of the core, where k-additive games are those games whose Mobius transform vanishes for subsets of more than k elements. For a sufficiently high value of k, the k-additive core is nonempty, and is a convex closed polyhedron. Our aim is to establish results similar to the classical results of Shapley and Ichiishi on the core of convex games (corresponds to Edmonds' theorem for the greedy algorithm). which characterize the vertices of the core.
• Publication
On the structure of the k-additive fuzzy measures
(Elsevier Science Bv, 2010) Miranda Menéndez, Pedro; Combarro, Elías F.
In this paper we present some results concerning the vertices of the set of fuzzy measures being at most k-additive. We provide an algorithm to compute them. We give some examples of the results obtained with this algorithm and give lower bounds on the number of vertices for the (n - 1)-additive case, proving that it grows much faster than the number of vertices of the general fuzzy measures. The results in the paper suggest that the structure of k-additive measures might be more complex than expected from their definition and, in particular, that they are more complex than general fuzzy measures.
• Publication
On the structure of the k-additive fuzzy measures
(International Fuzzy Systems Association (IFSA); European Society for Fuzzy Logic and Technology (EUSFLAT, 2009) Combarro, Elías F.; Miranda Menéndez, Pedro; Carvalho, J.P.; Dubois, D.; Kaymak, U.; Sousa, J.M.C.
The family of k-additive measures has been introduced as a midterm between probabilities and general fuzzy measures and finds a wide number of applications in practice. However, its structure is different from other families of fuzzy measures and is certainly more complex (for instance, its vertices are not always {0, 1}-valued), so it has not been yet fully studied. In this paper we present some results concerning the extreme points of the k-additive fuzzy measures. We give a characterization of these vertices as well as an algorithm to compute them. We show some examples of the results of this algorithm and provide lower bounds on the number of vertices of the n - 1-additive measures, proving that it grows much faster than the number of vertices of the general fuzzy measures. This suggests that k-additive measures might not be a good choice in modeling certain decision problems when the value of k is high but not equal to n.
• Publication
On the structure of some families of fuzzy measures
(Institute of Electrical and Electronics Engineers, 2007-12) Miranda Menéndez, Pedro; Combarro, Elías F.
The generation of fuzzy measures is an important question arising in the practical use of these operators. In this paper, we deal with the problem of developing a random generator of fuzzy measures. More concretely, we study some of the properties that any random generator should satisfy. These properties lead to some theoretical problems concerning the group of isometries that we tackle in this paper for some subfamilies of fuzzy measures.