Miembros del Grupo
Líneas de Investigación
- Agregación de estructuras en lógica fuzzy
- Grupos topológicos.
- Lógica Fuzzy y Soft Computing.
- Topología Computacional.
- Aggegation operator
- Approximate reasoning
- Fuzzy operator
- Fuzzy relation
- Persistent homology
- Pontryagin duality
- Topological data analysis
- Topological group
- Weak topologies
Publicaciones Científicas desde 2018
Autores: Chasco Ugarte, María Jesús; Domínguez, X. (Autor de correspondencia); Tkachenko, M. G.Revista: JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONSISSN: 0022-247X Vol.508 N° 1 2022 págs. 125882ResumenWe study the properties of the free abelian topological group A(d)(X) on a metric space (X, d) endowed with the topology generated by the Graev extension d circumflex accent of a given metric d on X. We find that the group of Lipschitz functions Lip0(X, T) is the group of continuous characters of A(d)(X). From this fact we derive some interesting properties of the metric groups A(d)(X) and Lip(0)(X, T).
Autores: Aslam, J.; Ardanza-Trevijano Moras, Sergio; Xiong, J.; et al.Título: TAaCGH Suite for detecting cancer - specific copy number changes using topological signaturesRevista: ENTROPYISSN: 1099-4300 Vol.24 N° 7 2022 págs. 896ResumenCopy number changes play an important role in the development of cancer and are commonly associated with changes in gene expression. Persistence curves, such as Betti curves, have been used to detect copy number changes; however, it is known these curves are unstable with respect to small perturbations in the data. We address the stability of lifespan and Betti curves by providing bounds on the distance between persistence curves of Vietoris-Rips filtrations built on data and slightly perturbed data in terms of the bottleneck distance. Next, we perform simulations to compare the predictive ability of Betti curves, lifespan curves (conditionally stable) and stable persistent landscapes to detect copy number aberrations. We use these methods to identify significant chromosome regions associated with the four major molecular subtypes of breast cancer: Luminal A, Luminal B, Basal and HER2 positive. Identified segments are then used as predictor variables to build machine learning models which classify patients as one of the four subtypes. We find that no single persistence curve outperforms the others and instead suggest a complementary approach using a suite of persistence curves. In this study, we identified new cytobands associated with three of the subtypes: 1q21.1-q25.2, 2p23.2-p16.3, 23q26.2-q28 with the Basal subtype, 8p22-p11.1 with Luminal B and 2q12.1-q21.1 and 5p14.3-p12 with Luminal A.
Autores: Elorza Barbajero, Jorge (Autor de correspondencia); Recasens, J.Revista: FUZZY SETS AND SYSTEMSISSN: 0165-0114 Vol.450 2022 págs. 133 - 144ResumenFuzzy operators are an essential tool in many fields and the operation of composition is often needed. In general, composition is not a commutative operation. However, it is very useful to have operators for which the order of composition does not affect the result. In this paper, we analyze when permutability appears. That is, when the order of application of the operators does not change the outcome. We characterize permutability in the case of the composition of fuzzy consequence operators and the dual case of fuzzy interior operators. We prove that for these cases, permutability is completely connected to the preservation of the operator type. We also study the particular case of fuzzy operators induced by fuzzy relations through Zadeh's compositional rule and the inf--> composition. For this cases, we connect permutability of the fuzzy relations (using the sup-* composition) with permutability of the induced operators. Special attention is paid to the cases of operators induced by fuzzy preorders and similarities. Finally, we use these results to relate the operator induced by the transitive closure of the composition of two reflexive fuzzy relations with the closure of the operator this composition induces.
Autores: Bejines López, Carlos (Autor de correspondencia); Ardanza-Trevijano Moras, Sergio; Chasco Ugarte, María Jesús; et al.Revista: FUZZY SETS AND SYSTEMSISSN: 0165-0114 Vol.446 2022 págs. 53 - 67ResumenThe paper studies the aggregation of pairs of T-indistinguishability operators. More concretely we address the question whether A(E, El) is a T-indistinguishability operator if E, El are T-indistinguishability operators. The answer depends on the aggregation function, the t-norm T, and the chosen T-indistinguishability operators. It is well-known that an aggregation function preserves T-transitive relations if and only if it dominates the t-norm T. We show the important role of the minimum t-norm TM in this preservation problem. In particular we develop weaker forms of domination that are used to provide characterizations of TMindistinguishability preservation under aggregation. We also prove that the existence of a single strictly monotone aggregation that satisfies the indistinguishability operator preservation property guarantees all aggregations to have the same preservation property.
Autores: Bejines López, Carlos (Autor de correspondencia); Brutenicova, M.; Chasco Ugarte, María Jesús; et al.Revista: FUZZY SETS AND SYSTEMSISSN: 0165-0114 Vol.408 2021 págs. 26 - 43ResumenWe estimate the number of triangular norms on some classes of finite lattices. One of them is obtained from two chains by identifying their zero elements, unit elements and an atom. Another one is the set of the dual lattices of the previous one. The obtained formulas involve the number of triangular norms on the corresponding chains. We derive several properties of a triangular norm for this kind of lattices, that enable us to obtain better estimates. Moreover, we obtain the number of t-norms in another class of lattices, which includes the so-called Chinese lantern. Finally, we estimate the number of Archimedean t-norms and divisible t-norms on these lattices.
Autores: Bejines López, Carlos (Autor de correspondencia); Chasco Ugarte, María Jesús; Elorza Barbajero, JorgeTítulo: Aggregation of fuzzy subgroupsRevista: FUZZY SETS AND SYSTEMSISSN: 0165-0114 Vol.418 2021 págs. 170 - 184ResumenGiven an aggregation function, and two fuzzy subgroups of a group, this study investigates whether the aggregation of them is also a fuzzy subgroup. It is proven that if the cardinal of the group is a prime power, then it is always a fuzzy subgroup. For a general group, it is proven that the existence of a binary relation between the fuzzy subgroups determines if their aggregation is a fuzzy subgroup. Moreover, given two fuzzy subgroups, if the aggregation of them is a fuzzy subgroup for some strictly monotone aggregation function, then it is a fuzzy subgroup for any aggregation function. The present study also examines conditions on the aggregation function that characterise the case where the aggregation of two arbitrary fuzzy subgroups is also a fuzzy subgroup. (c) 2020 Elsevier B.V. All rights reserved.
Autores: Bejines López, Carlos; Ardanza-Trevijano Moras, Sergio; Elorza Barbajero, JorgeRevista: AXIOMS: MATHEMATICAL LOGIC AND MATHEMATICAL PHYSICSISSN: 2075-1680 Vol.10 N° 3 2021 págs. 201ResumenPreservation of structures under aggregation functions is an active area of research with applications in many fields. Among such structures, min-subgroups play an important role, for instance, in mathematical morphology, where they can be used to model translation invariance. Aggregation of min-subgroups has only been studied for binary aggregation functions. However, results concerning preservation of the min-subgroup structure under binary aggregations do not generalize to aggregation functions with arbitrary input size since they are not associative. In this article, we prove that arbitrary self-aggregation functions preserve the min-subgroup structure. Moreover, we show that whenever the aggregation function is strictly increasing on its diagonal, a min-subgroup and its self-aggregation have the same level sets.
Autores: Bejines López, Carlos (Autor de correspondencia); Chasco Ugarte, María Jesús; Elorza Barbajero, Jorge; et al.Revista: FUZZY SETS AND SYSTEMSISSN: 0165-0114 Vol.373 2019 págs. 164 - 179ResumenIn this paper we study the class of all fuzzy subgroups defined with respect to a given t-norm on a fixed group. We find necessary and sufficient conditions over two t-norms to guarantee that the class of all fuzzy subgroups induced by the first t-norm is contained in the class of all fuzzy subgroups with respect to by the second one. We characterize the functions that transform fuzzy subgroups into fuzzy subgroups. The close relationship between indistinguishability operators and fuzzy subgroups allows us to obtain similar results for some classes of indistinguishability operators.
Autores: Borsich, T.; Chasco Ugarte, María Jesús; Domínguez, X.; et al.Revista: JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONSISSN: 0022-247X Vol.473 N° 2 2019 págs. 1203 - 1214ResumenThe g-barrelled groups constitute a vast class of abelian topological groups. It might be considered as a natural extension of the class of barrelled topological vector spaces. In this paper we prove that g-barrelledness is a multiplicative property, thus we obtain new examples of g-barrelled groups. We also prove that direct sums and inductive limits of g-barrelled locally quasi-convex groups are g-barrelled, too. Other permanence properties are considered as well.
Autores: Bello, H. J.; Chasco Ugarte, María Jesús; Domínguez, X. (Autor de correspondencia); et al.Revista: REVISTA DE LA REAL ACADEMIA DE CIENCIAS EXACTAS FISICAS Y NATURALES SERIE A-MATEMATICASISSN: 1578-7303 Vol.113 N° 3 2019 págs. 2145 - 2154ResumenWe introduce the notion of local pseudo-homomorphism between two topological abelian groups. We prove that it is closely related with the widely studied notions of local cross sections and splitting extensions in the category of topological abelian groups. In the final section we present an example of a non-splitting extension of (R,) by R, where is a metrizable group topology on R weaker than the usual one. This extension admits a local cross section.
Autores: Ardanza-Trevijano Moras, Sergio; Chasco Ugarte, María Jesús; Elorza Barbajero, Jorge (Autor de correspondencia)Revista: FUZZY SETS AND SYSTEMSISSN: 0165-0114 Vol.369 2019 págs. 122 - 131ResumenWe implement the notion of annihilator into fuzzy subgroups of an abelian group. There are different uses for the term annihilator in algebraic contexts that have been used fuzzy systems. In this paper we refer to another type of annihilator which is essential in classical duality theory and extends the widely applied notion of orthogonal complement in Euclidean spaces. We find that in the natural algebraic duality of a group, a fuzzy subgroup can be recovered after taking the inverse annihilator of its annihilator. We also study the behavior of annihilators with respect to unions and intersections. Some illustrative examples of annihilators of fuzzy subgroups are shown, both with finite and infinite rank.
Autores: Bejines López, Carlos (Autor de correspondencia); Chasco Ugarte, María Jesús; Elorza Barbajero, Jorge; et al.Revista: LECTURE NOTES IN COMPUTER SCIENCEISSN: 1611-3349 Vol.11160 2018 págs. 143 - 153ResumenWe compare four equivalence relations defined in fuzzy subgroups: Isomorphism, fuzzy isomorphism and two equivalence relations defined using level subset notion. We study if the image of two equivalent fuzzy subgroups through aggregation functions is a fuzzy subgroup, when it belongs to the same class of equivalence and if the supreme property is preserved in the class of equivalence and through aggregation functions.
Autores: Bejines López, Carlos; Chasco Ugarte, María Jesús; Elorza Barbajero, Jorge; et al.Libro: Advances in Intelligent Systems and ComputingISSN: 978-3-319-66829-1 Vol.641 2018 págs. 159 - 167ResumenTwo fuzzy subgroups mu,eta of a group G are said to be equivalent if they have the same family of level set subgroups. Although it is well known that given two fuzzy subgroups mu,eta of a group G their maximum is not always a fuzzy subgroup, it is clear that the maximum of two equivalent fuzzy subgroups is a fuzzy subgroup. We prove that the composition of two equivalent fuzzy subgroups by means of an aggregation function is again a fuzzy subgroup. Moreover, we prove that if two equivalent subgroups have the sup property their corresponding compositions by any aggregation function also have the sup property. Finally, we characterize the aggregation functions such that when applied to two equivalent fuzzy subgroups, the obtained fuzzy subgroup is equivalent to both of them. These results extend the particular results given by Jain for the maximum and the minimum of two fuzzy subgroups.
Autores: Bejines López, Carlos; Chasco Ugarte, María Jesús; Elorza Barbajero, Jorge; et al.Libro: Aggregation functions in theory and in practiceISSN: 978-3-319-59305-0 2018 págs. 253 - 262ResumenThe purpose of this paper is to study fuzzy operators induced by fuzzy relations and fuzzy relations induced by fuzzy operators. Many results are obtained about the relationship between *-preorders and fuzzy consequences operators for a fixed t-norm *. We analyse these properties by considering a semi-copula (generalization of t-norm concept) instead of a t-norm. Moreover, we show that the conditions imposed cannot be relaxed. We have been able to prove some important results about the relationships between fuzzy relations and fuzzy operators in this more general context.
Proyectos desde 2018
Título: Grupos topológicos: Dualidad, Grupos de Lie, AplicacioneCódigo de expediente: MTM2016-79422-PInvestigador principal: MARIA JESUS CHASCO UGARTE, SERGIO ARDANZA-TREVIJANO MORAS.Financiador: MINISTERIO DE CIENCIA E INNOVACIÓNConvocatoria: 2016 MINECO EXCELENCIA. PROYECTOS I+DFecha de inicio: 30-12-2016Fecha fin: 30-09-2021Importe concedido: 53.603,00€Otros fondos: Fondos FEDER