Search

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 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...

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.

In this paper we focus our attention on exploring the aggregation of partial T-indistinguishability operators (relations). Concretely we characterize, by means of (T-\(T_{\min }\))-tuples, those functions that allow to merge a collection of partial T-indistinguishability operators into a single one. Moreover, we show that monotony is a necessary condition to ensure that a function aggregates partial T-indistinguishability operators into a new one. We also provide that an inter-exchange composition function condition is a sufficient condition to guarantee that a function aggregates partial T-indistinguishability operators. Finally, examples of this type of functions are also given.

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.