Learning fuzzy measures for aggregation in fuzzy rule-based models

Comunicación presentada al 15th International Conference on Modeling Decisions for Artificial Intelligence, MDAI 2018 (15 - 18 october 2018).Fuzzy measures are used to express background knowledge of the information sources. In fuzzy rule-based models, the rule confidence gives an important information about the final classes and their relevance. This work proposes to use fuzzy measures and integrals to combine rules confidences when making a decision. A Sugeno $$\lambda $$ -measure and a distorted probability have been used in this process. A clinical decision support system (CDSS) has been built by applying this approach to a medical dataset. Then we use our system to estimate the risk of developing diabetic retinopathy. We show performance results comparing our system with others in the literature.This work is supported by the URV grant 2017PFR-URV-B2-60, and by the Spanish research projects no: PI12/01535 and PI15/01150 for (Instituto de Salud Carlos III and FEDER funds). Mr. Saleh has a Pre-doctoral grant (FI 2017) provided by the Catalan government and an Erasmus+ travel grant by URV. Prof. Bustince acknowledges the support of Spanish project TIN2016-77356-P

Pre-aggregation functions: construction and an application

In this work we introduce the notion of preaggregation function. Such a function satisfies the same boundary conditions as an aggregation function, but, instead of requiring monotonicity, only monotonicity along some fixed direction (directional monotonicity) is required. We present some examples of such functions. We propose three different methods to build pre-aggregation functions. We experimentally show that in fuzzy rule-based classification systems, when we use one of these methods, namely, the one based on the use of the Choquet integral replacing the product by other aggregation functions, if we consider the minimum or the Hamacher product t-norms for such construction, we improve the results obtained when applying the fuzzy reasoning methods obtained using two classical averaging operators like the maximum and the Choquet integral.This work was supported in part by the Spanish Ministry of Science and Technology under projects TIN2008-06681-C06-01, TIN2010- 15055, TIN2013-40765-P, TIN2011-29520

Construction of Capacities from Overlap Indexes

In many problems, it is crucial to find a relation between groups of data. Such relation can be expressed, for instance, in terms of an appropriate fuzzy measure or capacity([10, 21]) which reflects the way the different data are connected to each other [20]. In this chapter, taking into account this fact and following the developments in [8],we introduce a method to build capacities ([20, 21]) directly from the data (inputs) of a given problem. In order to do so, we make use of the notions of overlap function and overlap index ([5, 12, 13, 7, 4, 14, 16]) for constructing capacities which reflect how different data are related to each other. This paper is organized as follows: after providing some preliminaries, we analyse, in Section 3, some properties of overlap functions and indexes. In Sections 4 we discuss a method for constructing capacities from overlap functions and overlap indexes. Finally, we present some conclusions and references

A Fairness Relation Based on the Asymmetric Choquet Integral and Its Application in Network Resource Allocation Problems

The recent problem of network resource allocation is studied where pairs of users could be in a favourable situation, given that the allocation scheme is refined by some add-on technology. The general question here is whether the additional effort can be effective with regard to the user’s experience of fairness. The computational approach proposed in this paper to handle this question is based on the framework of relational optimization. For representing different weightings for different pairs of users, the use of a fuzzy measure appears to be reasonable. The generalized Choquet integrals are discussed from the viewpoint of representing fairness and it is concluded that the asymmetric Choquet integral is the most suitable approach. A binary relation using the asymmetric Choquet integral is proposed. In case of a supermodular fuzzy measure, this is a transitive and cycle-free relation. The price of fairness with regard to a wireless channel allocation problem taking channel interference into account is experimentally studied and it can be seen that the asymmetric on relation actually selects allocations that perform on average between maxmin fairness and proportional fairness, and being more close to maxmin fairness as long as channel interference is not high

Belief functions on MV-algebras of fuzzy sets: An overview

Belief functions are the measure theoretical objects Dempster-Shafer evidence theory is based on. They are in fact totally monotone capacities, and can be regarded as a special class of measures of uncertainty used to model an agent's degrees of belief in the occurrence of a set of events by taking into account different bodies of evidence that support those beliefs. In this chapter we present two main approaches to extending belief functions on Boolean algebras of events to MV-algebras of events, modelled as fuzzy sets, and we discuss several properties of these generalized measures. In particular we deal with the normalization and soft-normalization problems, and on a generalization of Dempster's rule of combination. © 2014 Springer International Publishing Switzerland.The authors also acknowledge partial support by the FP7-PEOPLE-2009-IRSES project MaToMUVI (PIRSES-GA-2009- 247584). Also, Flaminio acknowledges partial support of the Italian project FIRB 2010 (RBFR10DGUA-002), Kroupa has been supported by the grant GACR 13-20012S, and Godo acknowledges partial support of the Spanish projects EdeTRI (TIN2012-39348-C02-01) and Agreement Technologies (CONSOLIDER CSD2007-0022, INGENIO 2010).Peer Reviewe