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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.

The study of consistency in decision-making models is of great importance. Our proposal deals with a special type of extended aggregation functions to guarantee consistency that is based on T-S consistency of linearly ordered fuzzy preference relations (fuzzy ranking for preferences). Necessary conditions to ensure consistency in the aggregation process are provided. Moreover, sufficient conditions to guarantee the existence of extended aggregation functions verifying T-S consistency are presented. Some examples of functions of this type are also given. The equivalence between T-S consistency and the additive consistency for fuzzy preference relations is established.

In this contribution we address our attention on the aggregation of partial T-indistinguishability operators (relations) and partial pseudo-metrics. A characterization of those functions that allow to merge a collection of partial T–indistinguishability operators into a new one was provided by Calvo et al. in [10] by means of ( T , T M ) -tuples, but here we present another characterization in terms of ( + , max ⁡ ) -tuples. Also, we analyze the aggregation of a collection ( E i ) i = 1 n of partial T i -indistinguishability operators. Moreover, we provide that a generalized inter–exchange composition functions condition is a sufficient condition to guarantee that a function merges partial T i -indistinguishability operators into a single one. In addition, we give different expressions of those aggregation functions that are object of our study, most of them are defined by means of the additive generators of the corresponding t-norms and another particular function. We see that the functions, that merge partial S-pseudo-metrics into a new one, are related to the functions that aggregate partial pseudo-metrics. Finally, we show the relation between the functions, that merge partial T-indistinguishability operators and the functions that preserve the partial T ⁎ -pseudo-metrics in the aggregation process.

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.

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 aim of this study is to rank some features that characterize the psychological dynamics of cooperative team work in order to determine priorities for interventions and formation: leading positive feedback, cooperative manager and collaborative manager features. From a dataset of 20 cooperative sport teams (403 soccer players), the characteristics of the prototypical sports teams are studied using an average Bayesian network (BN) and two special types of BNs, the Bayesian classifiers: naive Bayes (NB) and tree augmented naive Bayes (TAN). BNs are selected as they are able to produce probability estimates rather than predictions. BN results show that the antecessors (the top features ranked) are the team members' expectations and their attraction to the social aspects of the task. The main node is formed by the cooperative behaviors, the consequences ranked at the BN bottom (ratified by the TAN trees and the instantiations made), the roles assigned to the members and their survival inside the same team. These results should help managers to determine contents and priorities when they have to face team-building actions., This study was supported by a project of the Spanish Ministry of Economy and Competitiveness (TIN2013-42795-P).