Workshop Applied Topological Structures WATS'17
URI permanente para esta colecciónhttps://riunet.upv.es/handle/10251/126958
General Topology has become one of the fundamental parts of mathematics. Nowadays, as a consequence of an intensive research activity, this mathematical branch has been shown to be very useful in modeling several problems which arise in some branches of applied sciences as Economics, Artificial Intelligence and Computer Science.Due to this increasing interaction between applied and topological problems,we have promoted the creation of an annual workshop to encourage the collaboration between different national and international research groups in the area of General Topology and its Applications.
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Publicación On the problem of relaxed indistinguishability operators aggregation(Editorial Universitat Politècnica de València, 2017-10-23) Calvo Sánchez, T.; Fuster Parra, Pilar; Valero, O.; Ministerio de Economía y Competitividad[EN] In this paper we focus our attention on exploring the aggregation of relaxed indistinguishability operators. Concretely we characterize, in terms of triangular triplets with respect to a t-norm, those functions that allow to merge a collection of relaxed indistinguishability operators into a single one.Publicación The distribution function of a probability measure on a space with a fractal structure(Editorial Universitat Politècnica de València, 2017-10-23) Gálvez-Rodríguez, José Fulgencio; Sánchez Granero, Miguel Ángel; Ministerio de Economía y Competitividad[EN] In this work we show how to define a probability measure with the help of a fractal structure. One of the keys of this approach is to use the completion of the fractal structure. Then we use the theory of a cumulative distribution function on a Polish ultrametric space and describe it in this context. Finally, with the help of fractal structures, we prove that a function satisfying the properties of a cumulative distribution function on a Polish ultrametric space is a cumulative distribution function with respect to some probability measure on the space.Publicación A proposal toward a possibilistic multi-robot task allocation(Editorial Universitat Politècnica de València, 2017-10-23) Guerrero, José; Ministerio de Economía y Competitividad[EN] One of the main problems to solve in a multi-robot systems is to select the best robot to execute each task (task allocation). Several ways to address this problem have been proposed in the literature. This paper focuses on one of them, the so-called response threshold methods. In a recent previous work, it was proved that the possibilistic Markov chains outperform the classical probabilistic approaches when they are used to implement response threshold methods. The aim of this paper is to summarize the advances given by or research group toward a new possibilistic swarm multi-robot task allocation framework.Publicación Fuzzy contractive sequences(Editorial Universitat Politècnica de València, 2017-10-23) Gregori Gregori, Valentín; Sapena Piera, Almanzor; Departamento de Matemática Aplicada; Escuela Politécnica Superior de Gandia; Instituto de Investigación para la Gestión Integrada de Zonas Costeras; Ministerio de Economía y Competitividad[EN] In this paper we survey some results on contractive sequences in fuzzy metric spaces in the sense of George and Veeramani.Publicación Probabilistic uniformities of uniform spaces(Editorial Universitat Politècnica de València, 2017-10-23) Rodríguez López, Jesús; Romaguera Bonilla, Salvador; Sanchis, Manuel; Departamento de Matemática Aplicada; Escuela Técnica Superior de Ingeniería Aeroespacial y Diseño Industrial; Instituto Universitario de Matemática Pura y Aplicada; Ministerio de Economía y Competitividad[EN] Usually, fuzzy metric spaces are endowed with crisp topologies or crisp uniformities. Nevertheless, some authors have shown how to construct in this context different kinds of fuzzy uniformities like a Hutton [0, 1]- quasi-uniformity or a probabilistic uniformity. In 2010, J. Guti´errez Garc´ıa, S. Romaguera and M. Sanchis [7] proved that the category of uniform spaces is isomorphic to a category whose objects are sets endowed with a fuzzy uniform structure, i. e. a family of fuzzy pseudometrics satisfying certain conditions. We will show here that, by means of this isomorphism, we can obtain several methods to endow a uniform space with a probabilistic uniformity. Furthermore, we obtain a factorization of some functors introduced in [6].Publicación Extension of $b_f$-continuous functions defined on a product of $b_f$-groups(Editorial Universitat Politècnica de València, 2017-10-23) Sanchis, Manuel; Ministerio de Economía y Competitividad[EN] Let X be a bf -space and let G be a bf -group. By means of the exponential mapping we characterize when a bf -continuous function on X × G with values in a topologically complete sapce Z has a bf -continuous extension to β(X) × G. As a consequence we show that the product of a pseudocompact space and a bf -group is a bf -group. This result generalizes the fact that the product of a pseudocompact space and a pseudocompact group is pseudocompact.Publicación Quasi-metrics, midpoints and applications(Editorial Universitat Politècnica de València, 2017-10-23) Valero, Oscar; Ministerio de Economía y Competitividad[EN] In this short note we want to explicitly state that there is a growing research activity in the field of information aggregation via midpoint theory and its applications to decision making.Publicación Some observations on a fuzzy metric space(Editorial Universitat Politècnica de València, 2017-10-23) Gregori Gregori, Valentín; Miñana, J.J.; Miravet, David; Ministerio de Economía y Competitividad[EN] Let (X, d) be a metric space. In this paper we provide some observations about the fuzzy metric space in the sense of Kramosil and Michalek (Y, N, ∧), where Y is the set of non-negative real numbers [0, ∞[ and N(x, y, t) = 1 if d(x, y) ≤ t and N(x, y, t) = 0 if d(x, y) ≥ t.Publicación Relaxed metrics and indistinguishability operators: the relationship(Editorial Universitat Politècnica de València, 2017-10-23) Fuster-Parra, P.; Martín, Javier; Miñana, J.J.; Valero, O.; Ministerio de Economía y Competitividad[EN] In 1982, the notion of indistinguishability operator was introduced by E. Trillas in order to fuzzify the crisp notion of equivalence relation (\cite{Trillas}). In the study of such a class of operators, an outstanding property must be pointed out. Concretely, there exists a duality relationship between indistinguishability operators and metrics. The aforesaid relationship was deeply studied by several authors that introduced a few techniques to generate metrics from indistinguishability operators and vice-versa (see, for instance, \cite{BaetsMesiar,BaetsMesiar2}). In the last years a new generalization of the metric notion has been introduced in the literature with the purpose of developing mathematical tools for quantitative models in Computer Science and Artificial Intelligence (\cite{BKMatthews,Ma}). The aforementioned generalized metrics are known as relaxed metrics. The main target of this talk is to present a study of the duality relationship between indistinguishability operators and relaxed metrics in such a way that the aforementioned classical techniques to generate both concepts, one from the other, can be extended to the new framework.Publicación The distribution function of a probability measure on a Polish ultrametric space(Editorial Universitat Politècnica de València, 2017-10-23) Gálvez-Rodríguez, José; Sánchez-Granero, Miguel Ángel; Ministerio de Economía y Competitividad[EN] In this work we elaborate a theory of a cumulative distribution function on a Polish ultrametric space from a probability measure defined in this space. With that purpose, the idea is to define an order in the space from the collection of balls and show that the function defined plays a similar role to that played by a cumulative distribution function in the classical casePublicación A version of Stone-Weierstrass theorem in Fuzzy Analysis(Editorial Universitat Politècnica de València, 2017-10-23) Font, Juan J.; Sanchis, Delia; Sanchis, Manuel; Ministerio de Economía y Competitividad; Universitat Jaume I; Generalitat Valenciana[EN] Let C(K, E1) be the space of continuous functions defined between a compact Hausdorff space K and the space of fuzzy numbers E1 endowed with the supremum metric. We provide a sufficient set of conditions on a subspace of C(K, E1) in order that it be dense. We also obtain a similar result for interpolating families of C(K, E1).Publicación Two fixed point theorems on quasi-metric spaces via mw- distances(Editorial Universitat Politècnica de València, 2017-10-23) Alegre Gil, Maria Carmen; Departamento de Matemática Aplicada; Instituto Universitario de Matemática Pura y Aplicada; Escuela Técnica Superior de Ingeniería Informática; Ministerio de Economía y Competitividad[EN] In this paper we prove a Banach-type fixed point theorem and a Kannan-type theorem in the setting of quasi-metric spaces using the notion of mw-distance. These theorems generalize some results that have recently appeared in the literature.Publicación A characterizations of quasi-metric completeness(Editorial Universitat Politècnica de València, 2017-10-23) Dag, Hacer; Romaguera, Salvador; Tirado, Pedro; Ministerio de Economía y Competitividad[EN] Hu proved in [4] that a metric space (X, d) is complete if and only if for any closed subspace C of (X, d), every Banach contraction on C has fixed point. Since then several authors have investigated the problem of characterizing the metric completeness by means of fixed point theorems. Recently this problem has been studied in the more general context of quasi-metric spaces for different notions of completeness. Here we present a characterization of a kind of completeness for quasi-metric spaces by means of a quasi-metric versions of Hu’s theorem.Publicación An overview on transformations on generalized metrics(Editorial Universitat Politècnica de València, 2017-10-23) Miñana, Juan José[EN] We will present an overview on the results appeared in the literature about the study of those functions that preserve or transform a generalized metric.Publicación Irreducible fractal structures for Moran's theorems(Editorial Universitat Politècnica de València, 2017-10-23) Fernández-Martínez, Manuel; Sánchez-Granero, Miguel Ángel; Fundación Séneca-Agencia de Ciencia y Tecnología de la Región de Murcia; Ministerio de Economía y Competitividad[EN] In this paper, we deal with a classical problem in Fractal Geometry consisting of the calculation of the similarity dimension of IFS-attractors. The open set condition allows to easily calculate their similarity dimension though it depends on an external open set. We contribute a necessary condition to reach the equality among some fractal dimensions for the natural fractal structure for IFS-attractors and the similarity dimension. That condition, weaker than the SOSC, becomes more representative of the attractor’s self-similar structure.