Finding the set of k-additive dominating measures viewed as a flow problem

n this paper we deal with the problem of obtaining the set of k-additive measures dominating a fuzzy measure. This problem extends the problem of deriving the set of probabilities dominating a fuzzy measure, an important problem appearing in Decision Making and Game Theory. The solution proposed in the paper follows the line developed by Chateauneuf and Jaffray for dominating probabilities and continued by Miranda et al. for dominating k-additive belief functions. Here, we address the general case transforming the problem into a similar one such that the involved set functions have non-negative Möbius transform; this simplifies the problem and allows a result similar to the one developed for belief functions. Although the set obtained is very large, we show that the conditions cannot be sharpened. On the other hand, we also show that it is possible to define a more restrictive subset, providing a more natural extension of the result for probabilities, such that it is possible to derive any k-additive dominating measure from it

Regression games

The solution of a TU cooperative game can be a distribution of the value of the grand coalition, i.e. it can be a distribution of the payo (utility) all the players together achieve. In a regression model, the evaluation of the explanatory variables can be a distribution of the overall t, i.e. the t of the model every regressor variable is involved. Furthermore, we can take regression models as TU cooperative games where the explanatory (regressor) variables are the players. In this paper we introduce the class of regression games, characterize it and apply the Shapley value to evaluating the explanatory variables in regression models. In order to support our approach we consider Young (1985)'s axiomatization of the Shapley value, and conclude that the Shapley value is a reasonable tool to evaluate the explanatory variables of regression models

A constructive approach to multicriteria decision making

After a general introduction on multicriteria decision aid, we briefly present the two main approaches (outranking methods, multi-attribute utility). Then we focus on the multi-attribute utility framework, which we build in a new perspective, based on the MACBETH methodology and the notion of capacity. We show that the Choquet integral appears as a natural tool for aggregating criteria, and we study several types of capacities which are useful in practice (k-additive capacities, p-symmetric capacities). We end the paper by introducing bipolar models.Après une introduction générale à la problématique de la décision multicritère, nous présentons brièvement les deux approches principales (méthodes de surclassement, et approche de l'utilité multi-attributs). Nous nous focalisons ensuite sur l'approche de l'utilité multi-attributs, que nous essayons de construire dans une perspective nouvelle, basée sur la méthodologie MACBETH et la notion de capacité. Nous montrons qu'alors l'intégrale de Choquet apparaît comme un outil naturel pour l'agrégation des critères, et nous étudions différents types de capacités utiles en pratique (capacités k-additives, p-symétriques). Dans une dernière section, nous abordons les modèles bipolaires

Fuzzy integral for rule aggregation in fuzzy inference systems

The fuzzy inference system (FIS) has been tuned and re-vamped many times over and applied to numerous domains. New and improved techniques have been presented for fuzzification, implication, rule composition and defuzzification, leaving one key component relatively underrepresented, rule aggregation. Current FIS aggregation operators are relatively simple and have remained more-or-less unchanged over the years. For many problems, these simple aggregation operators produce intuitive, useful and meaningful results. However, there exists a wide class of problems for which quality aggregation requires non- additivity and exploitation of interactions between rules. Herein, we show how the fuzzy integral, a parametric non-linear aggregation operator, can be used to fill this gap. Specifically, recent advancements in extensions of the fuzzy integral to \unrestricted" fuzzy sets, i.e., subnormal and non- convex, makes this now possible. We explore the role of two extensions, the gFI and the NDFI, discuss when and where to apply these aggregations, and present efficient algorithms to approximate their solutions

Preassociative aggregation functions

The classical property of associativity is very often considered in aggregation function theory and fuzzy logic. In this paper we provide axiomatizations of various classes of preassociative functions, where preassociativity is a generalization of associativity recently introduced by the authors. These axiomatizations are based on existing characterizations of some noteworthy classes of associative operations, such as the class of Acz\'elian semigroups and the class of t-norms.Comment: arXiv admin note: text overlap with arXiv:1309.730

Computing the output distribution and selection probabilities of a stack filter from the DNF of its positive Boolean function

Many nonlinear filters used in practise are stack filters. An algorithm is presented which calculates the output distribution of an arbitrary stack filter S from the disjunctive normal form (DNF) of its underlying positive Boolean function. The so called selection probabilities can be computed along the way.Comment: This is the version published in Journal of Mathematical Imaging and Vision, online first, 1 august 201

Associative polynomial functions over bounded distributive lattices

The associativity property, usually defined for binary functions, can be generalized to functions of a given fixed arity n>=1 as well as to functions of multiple arities. In this paper, we investigate these two generalizations in the case of polynomial functions over bounded distributive lattices and present explicit descriptions of the corresponding associative functions. We also show that, in this case, both generalizations of associativity are essentially the same.Comment: Final versio

Order cones: A tool for deriving k-dimensional faces of cones of subfamilies of monotone games

In this paper we introduce the concept of order cone. This concept is inspired by the concept of order polytopes, a well-known object coming from Combinatorics. Similarly to order polytopes, order cones are a special type of polyhedral cones whose geometrical structure depends on the properties of a partially ordered set (brief poset). This allows to study these properties in terms of the subjacent poset, a problem that is usually simpler to solve. From the point of view of applicability, it can be seen that many cones appearing in the literature of monotone TU-games are order cones. Especially, it can be seen that the cones of monotone games with restricted cooperation are order cones, no matter the structure of the set of feasible coalitions

RflM mediates target specificity of the RcsCDB phosphorelay system for transcriptional repression of flagellar synthesis in Salmonella enterica: Repression of flhDC transcription by a RcsB-RflM complex

The bacterial flagellum enables directed movement of Salmonella enterica towards favorable conditions in liquid environments. Regulation of flagellar synthesis is tightly controlled by various environmental signals at transcriptional and post- transcriptional levels. The flagellar master regulator FlhD₄C₂ resides on top of the flagellar transcriptional hierarchy and is under autogenous control by FlhD₄C₂- dependent activation of the repressor rflM. The inhibitory activity of RflM depends on the presence of RcsB, the response regulator of the RcsCDB phosphorelay system. In this study, we elucidated the molecular mechanism of RflM- dependent repression of flhDC. We show that RcsB and RflM form a heterodimer that coordinately represses flhDC transcription independent of RcsB phosphorylation. RcsB-RflM complex binds to a RcsB box downstream the P1 transcriptional start site of the flhDC promoter with increased affinity compared to RcsB in the absence of RflM. We propose that RflM stabilizes binding of unphosphorylated RcsB to the flhDC promoter in absence of environmental cues. Thus, RflM is a novel auxiliary regulatory protein that mediates target specificity of RcsB for flhDC repression. The cooperative action of the RcsB-RflM repressor complex allows Salmonella to fine-tune initiation of flagellar gene expression and adds another level to the complex regulation of flagellar synthesis

Consensus-Based Agglomerative Hierarchical Clustering

Producción CientíficaIn this contribution, we consider that a set of agents assess a set of alternatives through numbers in the unit interval. In this setting, we introduce a measure that assigns a degree of consensus to each subset of agents with respect to every subset of alternatives. This consensus measure is defined as 1 minus the outcome generated by a symmetric aggregation function to the distances between the corresponding individual assessments. We establish some properties of the consensus measure, some of them depending on the used aggregation function. We also introduce an agglomerative hierarchical clustering procedure that is generated by similarity functions based on the previous consensus measuresMinisterio de Economía, Industria y Competitividad (ECO2012-32178)Junta de Castilla y León (programa de apoyo a proyectos de investigación – Ref. VA066U13