Revistas

Revista:
FUZZY SETS AND SYSTEMS

ISSN 0165-0114
Vol. 446
Año 2022
Págs.53 - 67

The 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.

Revista:
FUZZY SETS AND SYSTEMS

ISSN 0165-0114
Vol. 450
Año 2022
Págs.133 - 144

Fuzzy 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.

Revista:
FUZZY SETS AND SYSTEMS

ISSN 0165-0114
Vol. 418
Año 2021
Págs.170 - 184

Given 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.

Revista:
CHAOS (EEUU)

ISSN 1054-1500
Vol. 31
N° 7
Año 2021
Págs.073144

In this paper, we study the propagation of the cardiac action potential in a one-dimensional fiber, where cells are electrically coupled through gap junctions (GJs). We consider gap junctional gate dynamics that depend on the intercellular potential. We find that different GJs in the tissue can end up in two different states: a low conducting state and a high conducting state. We first present evidence of the dynamical multistability that occurs by setting specific parameters of the GJ dynamics. Subsequently, we explain how the multistability is a direct consequence of the GJ stability problem by reducing the dynamical system's dimensions. The conductance dispersion usually occurs on a large time scale, i.e., thousands of heartbeats. The full cardiac model simulations are computationally demanding, and we derive a simplified model that allows for a reduction in the computational cost of four orders of magnitude. This simplified model reproduces nearly quantitatively the results provided by the original full model. We explain the discrepancies between the two models due to the simplified model's lack of spatial correlations. This simplified model provides a valuable tool to explore cardiac dynamics over very long time scales. That is highly relevant in studying diseases that develop on a large time scale compared to the basic heartbeat. As in the brain, plasticity and tissue remodeling are crucial parameters in determining the action potential wave propagation's stability. (C) 2021 Author(s). All article content, except where otherwise noted, is licensed under a Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

Revista:
RETOS. NUEVAS TENDENCIAS EN EDUCACION FISICA, DEPORTE Y RECREACION

ISSN 1579-1726
N° 39
Año 2021
Págs.794 - 804

FlippedREF is a training project that was developed within the Navarre Committee of Soccer Referees (Spain) during the 2018-2019 season. The main objective of this plan is to carry out an educational experience from the Flipped Learning pedagogical approach, in the area of technical training for soccer referees and assistants. Thus, this article makes an approach to the scenario resulting from its development, which is characterized by a modular structure and by the two spaces and differentiated training times. In the first, participants establish a first contact with the didactic material prepared by the teaching team for each module, and work on it before the corresponding training session. In the second, trainers accompany, streamline, and guide the activities proposed in each of the face-to-face sessions for teamwork, organize the debates and moderate the discussions. In this way, a horizontal communicative and educational approach is sought, and contrary to the unidirectional and transmissive model that has characterized the training of this group for the work on the content of the rules of the game. The results of the evaluation of the experience are very positive in relation to the degree of the objectives proposed in the project, the educational resources used, and the methodological strategies addressed to promote participation, interaction, and collaboration among participants. However, greater differences are found when evaluating seine of the tools used in the work sessions. This proposal, and its pedagogical approach, aims to be transferable to other contexts in the field of physical activity and sport.

Revista:
AXIOMS: MATHEMATICAL LOGIC AND MATHEMATICAL PHYSICS

ISSN 2075-1680
Vol. 10
N° 3
Año 2021
Págs.201

Preservation 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.

Revista:
FUZZY SETS AND SYSTEMS

ISSN 0165-0114
Vol. 408
Año 2021
Págs.26 - 43

We 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.

Revista:
INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS

ISSN 0218-1274
Vol. 29
N° 8
Año 2019
Págs.1930021

Connexins are specialized ionic channels that control the action potential propagation between cardiac myocytes. In this paper, we study the connexin dynamics in a one-dimensional model of cardiac tissue. We show that the connexin dynamics may lead to a spatial organization of the gap junction conductance. In the numerical simulations presented in this paper we have found two different regimes for the spatial organization of the conductances: (a) a spatially uniform conductance; (b) a spatially complex pattern of local values of high and low conductances. in addition, we have observed that, locally, the two final states are limit cycles with a period equal to the period associated with the external excitation of the tissue strand. The conductance dispersion usually takes place on a very large time scale, i.e. thousands of heart beats, and on a very short spatial scale. Due to its simplicity, the one-dimensional setting allows a detailed study of the emerging structure and in particular very long simulations. We have studied the transition between the two aforementioned states as a function of the gap junction conductance characteristics. Furthermore, we have studied the effect of initially added noises on the outcome of the system. Finally, using spatial autocorrelation functions we have characterized the spatial dispersion in conductance values.

Revista:
FUZZY SETS AND SYSTEMS

ISSN 0165-0114
Vol. 373
Año 2019
Págs.164 - 179

In 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.

Revista:
FUZZY SETS AND SYSTEMS

ISSN 0165-0114
Vol. 369
Año 2019
Págs.122 - 131

We 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.

Revista:
LECTURE NOTES IN COMPUTER SCIENCE

ISSN 1611-3349
Vol. 11160
Año 2018
Págs.143 - 153

We 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.

Revista:
PHYSICAL REVIEW E

ISSN 2470-0045
Vol. 92
N° 6
Año 2015
Págs.2919

Defibrillation is the standard clinical treatment used to stop ventricular fibrillation. An electrical device delivers a controlled amount of electrical energy via a pair of electrodes in order to reestablish a normal heart rate. We propose a technique that is a combination of biphasic shocks applied with a four-electrode system rather than the standard two-electrode system. We use a numerical model of a one-dimensional ring of cardiac tissue in order to test and evaluate the benefit of this technique. We compare three different shock protocols, namely a monophasic and two types of biphasic shocks. The results obtained by using a four-electrode system are compared quantitatively with those obtained with the standard two-electrode system. We find that a huge reduction in defibrillation threshold is achieved with the four-electrode system. For the most efficient protocol (asymmetric biphasic), we obtain a reduction in excess of 80% in the energy required for a defibrillation success rate of 90%. The mechanisms of successful defibrillation are also analyzed. This reveals that the advantage of asymmetric biphasic shocks with four electrodes lies in the duration of the cathodal and anodal phase of the shock.

Revista:
INFORMATION SCIENCES

ISSN 0020-0255
Vol. 310
Año 2015
Págs.36 - 51

Fuzzy 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.

Revista:
FUZZY SETS AND SYSTEMS

ISSN 0165-0114
Vol. 218
Año 2013
Págs.73 - 89

In a previous paper, Elorza and Burillo explored the coherence property in fuzzy consequence operators. In this paper we show that fuzzy closing operators of mathematical morphology are always coherent operators. We also show that the coherence property is the key to link the four following families: fuzzy closing morphological operators, fuzzy consequence operators, fuzzy preorders and fuzzy closure and co-closure systems. This will allow to translate important well-known properties from the field of approximate reasoning to the field of image processing.

Revista:
LECTURE NOTES IN COMPUTER SCIENCE

ISSN 1611-3349
Vol. 8109
Año 2013
Págs.62 - 69

In this paper we study the permutability of the composition of fuzzy consequence operators (fuzzy closings) and fuzzy interior operators (fuzzy openings). We establish several characterizations and we show the relation of permutability with the fuzzy closure and fuzzy interior of a fuzzy operator. We also study the connection between permutability and the preservation of the operator type through the composition. More precisely, when the composition of two openings is an opening and the composition of two closings is a closing.

Revista:
LECTURE NOTES IN COMPUTER SCIENCE

ISSN 1611-3349
Vol. 8234
Año 2013
Págs.237 - 247

In this paper we study the permutability of the composition of fuzzy consequence operators when they are induced by fuzzy relations using the usual Zadeh's compositional rule. In particular, we study the case of fuzzy indistinguishability operators and fuzzy preorders. We study the connection between the permutability of the fuzzy relations and the permutability of their induced fuzzy operators

Revista:
CHAOS (EEUU)

ISSN 1054-1500
Vol. 23
Año 2013
Págs.043119

In this article, we compare quantitatively the efficiency of three different protocols commonly used in commercial defibrillators. These are based on monophasic and both symmetric and asymmetric biphasic shocks. A numerical one¿dimensional model of cardiac tissue using the bidomain formulation is used in order to test the different protocols. In particular, we performed a total of 4.8 × 106 simulations by varying shock waveform, shock energy, initial conditions, and heterogeneity in internal electrical conductivity. Whenever the shock successfully removed the reentrant dynamics in the tissue, we classified the mechanism. The analysis of the numerical data shows that biphasic shocks are significantly more efficient (by about 25%) than the corresponding monophasic ones. We determine that the increase in efficiency of the biphasic shocks can be explained by the higher proportion of newly excited tissue through the mechanism of direct activation.

Capítulos de libros

Libro:
Advances in Intelligent Systems and Computing

Editorial: Ed. Springer
Año 2018
Págs.159 - 167

Two 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.

Libro:
Aggregation functions in theory and in practice

Editorial: Ed. Springer
Año 2018
Págs.253 - 262

The 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.

Libro:
Computing in Cardiology 2015

Editorial: IEEE
Año 2015
Págs.437 - 440

Constant conductances are often assumed when model-
ing cardiac tissue. However experimental evidences have
shown that gap junctions (GJ) actually connect adjacent
cardiac myocytes. These GJ are complex proteins of the
connexin family (Cx40; Cx43; Cx45 are the most common
in human). These GJ modify the conductances between
cardiac cell through a dynamical process. The aim of this
study is to develop a bidomain model of the cardiac tis-
sue where the dynamics of the connexins is also included.
In particular we will compare the differences associated
with the use of a monodomain versus bidomain formula-
tion in inducing intra-cellular conductance variations. We
have found that the monodomain formulation gives con-
ductance variations a factor four to five larger with respect
to the bidomain formulation.

Libro:
Proceedings of the 2015 Conference of the International Fuzzy Systems Association and the European Society for Fuzzy Logic and Technology

Lugar de Edición: París
Editorial: Atlantis Press
Año 2015
Págs.59 - 65

Three ways to find lower approximations of a given fuzzy operator are given. A Representation Theorem for fuzzy consequence operators is obtained.

Libro:
Computing in Cardiology 2014

Editorial: IEEE
Año 2014
Págs.505 - 508

In the absence of a better solution, ventricular fibrillation is treated by applying one or several large electrical shocks to the patient. The question of how to lower the energy required for a successful shock is still a current issue in both fundamental research and clinical practice. In the study presented here we will compare defibrillation applied through a four electrode device with the standard procedure using two electrodes. The method is tested through intensive numerical simulations. Here we have used a one dimensional geometry. At the level of the cardiac tissue, the bidomain and the modified Beeler-Reuter models were used. Three different shock waveforms are tested: monophasic and two types of biphasic shocks. The results are compared with those obtained with standard two electrode device. A significant reduction in defibrillation thresholds is achieved for all the three tested waveforms when we use a four electrode device.

Libro:
ESTYLF : XVII Congreso Español sobre TECNOLOGÍAS Y LÓGICA FUZZY

Editorial: Universidad de Zaragoza
Año 2014
Págs.45 - 49

Composition of fuzzy operators often appears
and it is natural to ask when the order of compo-
sition does not change the result. In previous pa-
pers, we characterized permutability in the case
of fuzzy consequence operators and fuzzy inte-
rior operators. We also showed the connection
between the permutability of the fuzzy relations
and the permutability of their induced fuzzy op-
erators. In this work we present some examples
of permutability and non permutability of fuzzy
operators and fuzzy relations in order to illustrate
these results.

Libro:
Computing in Cardiology Conference 2013

Editorial: IEEE
Año 2013
Págs.1031 - 1034

The aim of this work was to find evidence of aging of ECG indicators in a population of young adults (52 subjects of age 19 ± 0.6 in 2002). For this purpose, an application which analyzes ECG signals was designed and implemented. The data consist in four different series for each subject of the studied population. Two ECG signals of 5 minute duration (one at rest and one after a mild effort) were taken in 2002 and the exact same procedure was repeated for each subject five years later in 2007. All these electrocardiographic signals were examined by computational techniques in order to extract the RR and QT intervals and the energy content of the T-wave. Next, we have compared all the data using first return maps and measured the data dispersion by evaluating the covariance ellipses. Relations between each of the four data series were studied. The analysis also included the gender and the categorical aspect ¿practicing sport¿.

Libro:
Aggregation functions in theory and in practise

Lugar de Edición: Berlín
Editorial: Springer
Año 2013
Págs.295 - 306

In this paper we generate fuzzy relations and fuzzy operators using different kind of generators and we study the relationship between them. Firstly, we introduce a new fuzzy preorder induced by a fuzzy operator. We generalize this preorder to a fuzzy relation generated by two fuzzy operators and we analyze its properties. Secondly, we introduce and explore two ways of inducing a fuzzy operator, one from a fuzzy operator and a fuzzy relation and the other one from two fuzzy operators. The first one is an extension of the well-known fuzzy operator induced by a fuzzy relation through Zadeh¿s compositional rule. Finally, we aggregate these operators using the quasi-arithmetic mean associated to a continuous Archimedean t-norm. The aim is to compare the operator induced by the quasi-arithmetic mean of the generators with the quasi-arithmetic mean of the generated operators.

Libro:
Computing in Cardiology Conference 2013

Editorial: IEEE
Año 2013
Págs.851 - 854

We develop and validate a three-dimensional model of ventricular fibrillation for use in studying defibrillation. Specifically, we use a rabbit ventricular geometry as a realistic model system for evaluating the efficacy of defibrillatory shocks. Data obtained from the simulations are analyzed in terms of a dose-response curve. In agreement with clinically relevant values, we find that an electric field strength of about 6.6 V/cm indicates a 50% probability of successful defibrillation for a 12-ms monophasic shock in our model. Our validated model will be useful for optimizing defibrillation protocols and for performing detailed studies of defibrillation mechanisms.

Libro:
Actas del XVI Congreso Español sobre Tecnologías y Lógica Fuzzy

Lugar de Edición: Valladolid
Editorial: Universidad de Valladolid
Año 2012
Págs.54-59

Paer we show a comprehensive summary on
the relationship between fuzzy morphological
operators, fuzzy consequence operators and
fuzzy preorders and we motivate the study
of morphological operators by using binary
relations as structuring elements in a more
general context, i.e., the context of fuzzy re-
lational systems for obtaining relevant infor-
mation.

Libro:
Actas del XV Congreso Español sobre Tecnologías y Lógica Fuzzy

Lugar de Edición: HUELVA
Editorial: Universidad de Huelva
Año 2010
Págs.133 - 138

In a previous paper [10] we explored the no-
tion of coherent fuzzy consequence operator.
It is well-known that the operator induced
by a fuzzy preorder through Zadeh's compo-
sitional rule is always a coherent fuzzy con-
sequence operator. It is also known that
the relation induced by a fuzzy consequence
operator is a fuzzy preorder if such opera-
tor is coherent [7]. Fuzzy closing operators
of mathematical morphology can be consid-
ered as fuzzy consequence operators. In [12]
we showed that they are coherent operators.
The aim of this paper is to analyze the rela-
tions between both classes of operators and
the class of all fuzzy preorders in order to
translate well know properties from Approxi-
mate Reasoning to the one of Image Process-
ing.