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In this paper, we consider the problem of aggregating a collection of transitive fuzzy binary relations in such a way that the aggregation process preserves transitivity. Specifically, we focus our efforts on the characterization of those functions that aggregate a collection of fuzzy binary relations which are transitive with respect to a collection of t-norms preserving the transitivity. We characterize them in terms of triangular triplets. Further, the relationship between triangular triplets, the monotonicity of the aggregation function and an appropriate dominance notion is explicitly stated. Special attention is paid to a few classes of transitive fuzzy binary relations that are relevant in the literature. Concretely, we describe, in terms of triangular triplets, those functions that aggregate a collection of fuzzy pre-orders, fuzzy partial orders, relaxed indistinguishability relations, indistinguishability relations and equalities. A surprising relationship between functions that aggregate transitive fuzzy relations into a T M -transitive fuzzy relation and those that aggregate relaxed indistinguishability relations is shown. A few consequences of the new results are also provided for those cases in which all the t-norms of the given collection are the same. Some celebrated results are retrieved as a particular case from the exposed theory.

In many fields of applied sciences, the aggregation of numerical values, in order to get a final one which allows to make a decision, plays a central role. Many times these numerical values represe...

We propose a new type of weighted averaging functions given implicitly as a solution to an algebraic equation. The main ingredient is incorporation of weights performed by using a function different to the product. Strict triangular norms are one example of such functions. We show that the weights should be normalized in this case differently to the usual sum to one condition. We establish the conditions under which the implicit averages are well defined, are idempotent, monotone and bounded by the minimum and maximum of their arguments. We present many examples of implicit averages, some of which recover the existing families of functions while others define new families. In particular we provide new generalizations of power means, density based averages and weighted OWA functions.

An emotion communication system based on linearly ordered fuzzy preferences is proposed, whose objective is to determine the appropriate actions on the environment in order to enhance user comfort. Once a subset of elementary preferences is obtained via basic human-machine interactions, the rest of preference relations are determined in such a way that the consistency of the system is guaranteed. For this purpose, the Łukasiewicz t-conorm is applied as a rule for aggregation.

In 1982, E. Trillas introduced the notion of indistinguishability operator with the main aim of fuzzifying the crisp notion of equivalence relation. In the study of such a class of operators, an outstanding property must be stressed. 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. 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. The aforesaid generalized metrics are known as relaxed metrics. The main purpose of the present paper is to explore the possibility of making explicit a 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., This is a preprint version of the paper available from https://link.springer.com/article/10.1007/s00500-018-03675-9. This work is also supported by project PGC2018-095709-B-C21 (MCIU/AEI/FEDER, UE), and PROCOE/4/2017 (Govern Balear, 50% P.O. FEDER 2014-2020 Illes Balears).

The problem of the consistency of qualitative judgements about the difference of attractiveness between alternatives is studied. Our proposal deals with smooth t-conorms to be used for aggregation of elementary judgements.

HighlightsAn epidemiologic system analysis of cardiovascular risk is presented through a Bayesian network model.The Bayesian network model can serve as a generic tool for application oriented activities: explanation, prediction, monitoring and prevention.Due to cardiovascular disease is multifactorial, the application of this kind of model is of special interest, both from theoretical and practical point of view.The induced Bayesian network was used to make inferences taking into account three reasoning patterns: causal reasoning, evidential reasoning, and intercausal reasoning. An extensive, in-depth study of cardiovascular risk factors (CVRF) seems to be of crucial importance in the research of cardiovascular disease (CVD) in order to prevent (or reduce) the chance of developing or dying from CVD. The main focus of data analysis is on the use of models able to discover and understand the relationships between different CVRF. In this paper a report on applying Bayesian network (BN) modeling to discover the relationships among thirteen relevant epidemiological features of heart age domain in order to analyze cardiovascular lost years (CVLY), cardiovascular risk score (CVRS), and metabolic syndrome (MetS) is presented. Furthermore, the induced BN was used to make inference taking into account three reasoning patterns: causal reasoning, evidential reasoning, and intercausal reasoning. Application of BN tools has led to discovery of several direct and indirect relationships between different CVRF. The BN analysis showed several interesting results, among them: CVLY was highly influenced by smoking being the group of men the one with highest risk in CVLY; MetS was highly influence by physical activity (PA) being again the group of men the one with highest risk in MetS, and smoking did not show any influence. BNs produce an intuitive, transparent, graphical representation of the relationships between different CVRF. The ability of BNs to predict new scenarios when hypothetical information is introduced makes BN modeling an Artificial Intelligence (AI) tool of special interest in epidemiological studies. As CVD is multifactorial the use of BNs seems to be an adequate modeling tool.

The psychological factors of sports injuries constitute a growing field of study, even from the point of view of the prediction of their occurrence. Most of them, however, do not take into account the likelihood of the injuries' occurrence and the weight and role of the psychological variables on it. We conducted a study building up a Bayesian Network on a big sample of athletes, trying to assess these probabilistic links among several relevant psychological variables and the injuries' occurrence. The sample was constituted by 297 athletes (239 males, 58 females) from a wide range of sports: track and field; judo; fencing; karate; boxing; swimming; kayaking; artistic rollerskating, and team sports as football, basketball, and handball (Mean age: 25.10 +/- -3.87; range: 21-38 years). Several psychological variables, such as anxiety, social support, and self-efficacy were studied. Also, we recorded the history of injuries as well the body mass index and personal epidemiological data. The overall picture of the generated graph and Bayesian Network and its analysis - including the use of hypothetical data by means of several instantiations - includes the nuclear role of the Self-Efficacy regarding the injuries' occurrence likelihood; the decreasing impact of the competitive anxiety previous to the injury; the probabilistic independence of the players' risk behaviors, and the relevance of the environmental clues such the use of coping strategies and social support in order to build up a good level of Self-Efficacy after the occurrence of an injury. All these data are relevant when designing both preventive and recovery interventions from the multidisciplinary as well as from the psychological point of view., This research was supported by the Spanish MINECO (Grant PSI2011-27000); and by Murcia Regional Football Association's Football Project (Grant FFRM-UMU-04 0092 321B 64502 14704).

The purpose of this paper was to discover the relationships among 22 relevant psychological features in semi-professional football players in order to study team’s performance and collective efficacy via a Bayesian network (BN). The paper includes optimization of team’s performance and collective efficacy using intercausal reasoning pattern which constitutes a very common pattern in human reasoning. The BN is used to make inferences regarding our problem, and therefore we obtain some conclusions; among them: maximizing the team’s performance causes a decrease in collective efficacy and when team’s performance achieves the minimum value it causes an increase in moderate/high values of collective efficacy. Similarly, we may reason optimizing team collective efficacy instead. It also allows us to determine the features that have the strongest influence on performance and which on collective efficacy. From the BN two different coaching styles were differentiated taking into account the local Markov property: training leadership and autocratic leadership.

This study analyzes the relationship between psychological and physical variables and sports injuries. A total of 297 athletes from 26 different sports participated in the study. Variables related to biomedical, psychological and sports injuries were collected. The analysis of data was performed through Bayesian networks. Our results suggest that a high probability of self-efficacy produce statistical dependence to high likelihood of sports injuries. This variable receives previous influences of biomedical variables (BMI) and psychological variables (stress). There are also consequential variables to the injury: coping strategies, and locus of control, Este estudio analiza la relación entre variables psicológicas y las lesiones deportivas. Participaron en el estudio un total de 297 deportistas, de 26 distintos deportes. Se recogieron variables biomédicas, deportivas, psicológicas y referentes a la lesión deportiva. El análisis de los datos se llevó a cabo por medio de redes Bayesianas. Nuestros resultados parecen indicar que una elevada probabilidad de autoeficacia produce dependencia estadística de más probabilidad de lesión deportiva. Esta variable recibe influencias antecedentes tanto de variables biomédicas (IMC) como de variables psicológicas (estrés). También existen variables consecuentes a la lesión: uso de estrategias de afrontamiento, y locus de control, Este estudo analisa a relação entre as variáveis psicológicas e as lesões esportivas. Participaram no estudo um total de 297 atletas de 26 deportos distintos. Foram recolhidas variáveis biomédicas, desportivas, psicológicos e referentes à lesão desportiva. A análise de dados foi realizada através de redes de Bayesianas. Os nossos resultados sugerem que uma alta probabilidade de auto-eficácia produz dependência de maior probabilidade de lesão desportiva. Esta variável recebe as influências antecedentes tanto de variáveis biomédicas (IMC) como de variáveis psicológicas (stress). Existem também variáveis consequentes à lesão: uso de estratégias de confronto e locus de controlo, Esta investigación ha podido ser realizada gracias a la ayuda del Ministerio de Ciencia e Innovación (actualmente Ministerio de Economía y Competitividad), referencia PSI2011-27000.

The purpose of this paper is the study of relationships between negative psychological features in young competitive team players via a Bayesian network (BN). The BN let us describe in graphical terms the dependencies and conditional independencies between variables in a multivariate context, and therefore it let us analyze the relationships between the type of motivational climate and orientation of team players (from two different frameworks: goal orientation theory, and self-determination motivation theory), and we took into account their willingness to accept the use of gamesmanship and cheating at the games, related with somatic and cognitive pre-competitive anxiety. The BN analysis includes three reasoning patterns: evidential reasoning, causal reasoning and intercausal reasoning. We built a BN from a data set composed of twelve psychological variables, which were identified as relevant to this study. The structure and parameters were learnt with TETRAD IV and the BN was implemented in Netica software.

Recently knowledge has been obtained about the Cooperative meta-dynamics in performance teams, and also on the fit between the manager’s and team member’s beliefs about teamwork and performance. To obtain this, a specific instrument has been created and validated, the Questionnaire on Cooperation in Performance Teams (CWQ). The need for such this kind of tool is double fold: first, to combine the most relevant conceptual theories in a short and friendly usable instrument, and to obtain easily applicable knowledge addressed to managers and coaches working with performance teams. In order to accomplish fully with this aim, a confirmatory analysis of the new instrument is required too. Consequently, the CWQ was administered to 218 players of performance sports teams (Mean age = 21.12; SD = 6.72; mean years of experience = 11.42; SD = 6.33). The data analysis consisted on the study of the main components (forcing and without forcing the number of factors), with a Varimax rotation. The results confirm the validation of the CWQ both for the “A” and “B” versions of the questionnaire and the existence of four meta-factors: 1. Global cooperation with the team; 2. Cooperation for personal growth in the team; 3. Emotional cooperation, and 4. Conditional cooperation. The four factors shown factorial weights similar to those obtained in the previous exploratory study. These data confirms its transcultural and transituational invariance of the CWQ, as along with its conceptual validity and the solid theoretical conception of the abovementioned factors, and also its applicability in various performance environments. In addition, a mathematical analysis has been introduced to evaluate the symmetry between cooperative work beliefs from both coach and player views, embedded in the conceptual framework of the Cognitive Dissonance Theory.

This paper addresses one of the main problems to solve in a multi-robot system, allocating tasks to a set of robots (multi-robot task allocation-MRTA). Among all the approaches proposed in the literature to face up MRTA problem, this paper is focused on swarm-like methods called response threshold algorithms. The task allocation algorithms inspired on response threshold are based on probabilistic Markov chains. In the MRTA problem literature, possibilistic Markov chains have proved to outperform the probabilistic Markov chains when a Max-Min algebra is considered for matrix composition. In this paper we analyze the system behavior when a more general algebra than the Max-Min one is taken for matrix composition. Concretely, we consider the algebra \(([0,1], S_{M},T)\), where \(S_{M}\) denotes the maximum t-conorm and T stands for any t-norm. The performed experiments show how only some well-known t-norms are suitable to allocate tasks and how the possibility transition function parameters are related to the used t-norm.

In this study, we try to discover the natural psychological dynamics in a cooperative work team. We have selected a group of individuals that can help us to explore the psychological processes when working in a team. A new tool is used which has been developed from the most relevant conceptual frameworks existing at the moment, the Cooperative Workteams Questionnaire, (CWQ). In this paper, we present the psychometric characteristics and impact encountered by the conceptual framework. We also present an analysis of the results obtained from applying this framework.

In 1981, J. Borsik and J. Dobos studied the problem of how to merge, by means of a function, a family of distances into a single one. To this end, they introduced the notion of distance aggregation function and gave a characterization of such functions. Later on, in 2010, the notion of distance aggregation function was extended to the framework of asymmetric distances by G. Mayor and O. Valero. Thus, asymmetric distance aggregation functions were introduced and a characterization of this new type of functions was also given. Concretely, the aforesaid characterization states that the functions which allow to merge a family of asymmetric distances into a single one are exactly those that are amenable, monotone and subadditive. In the present chapter we consider the problem of aggregating a family of bounded asymmetric distances. To this end, the notion of bounded asymmetric distance aggregation function is introduced and a full description of such functions is provided. The obtained results are illustrated by means of examples. Furthermore, the relationship between asymmetric aggregation functions and the bounded ones is discussed.

In this work, a new lattice L determined by the class of weighting triangles as a base of L-fuzzy subsets is proposed. Furthermore, extended orders and operators which are obtained by means of fuzzy binary relations \(F_{\triangle }\) associated to a weighting triangle are included. Moreover, some new expressions have been defined for Extended Ordered Weighted Averaging operators, and Extended Aggregation functions.

Background Because the accurate measure of body fat (BF) is difficult, several prediction equations have been proposed. The aim of this study was to compare different multiple regression models to predict BF, including the recently reported CUN-BAE equation. Methods Multi regression models using body mass index (BMI) and body adiposity index (BAI) as predictors of BF will be compared. These models will be also compared with the CUN-BAE equation. For all the analysis a sample including all the participants and another one including only the overweight and obese subjects will be considered. The BF reference measure was made using Bioelectrical Impedance Analysis. Results The simplest models including only BMI or BAI as independent variables showed that BAI is a better predictor of BF. However, adding the variable sex to both models made BMI a better predictor than the BAI. For both the whole group of participants and the group of overweight and obese participants, using simple models (BMI, age and sex as variables) allowed obtaining similar correlations with BF as when the more complex CUN-BAE was used (rho = 0:87 vs rho= 0:86 for the whole sample and rho= 0:88 vs rho= 0:89 for overweight and obese subjects, being the second value the one for CUN-BAE). Conclusions There are simpler models than CUN-BAE equation that fits BF as well as CUN-BAE does. Therefore, it could be considered that CUN-BAE overfits. Using a simple linear regression model, the BAI, as the only variable, predicts BF better than BMI. However, when the sex variable is introduced, BMI becomes the indicator of choice to predict BF., This work was supported by the Spanish Ministry of Science and Innovation (PI 13/01477). The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.