Approximation of definable sets by compact families, and upper bounds on homotopy and homology

We prove new upper bounds on homotopy and homology groups of o-minimal sets in terms of their approximations by compact o-minimal sets. In particular, we improve the known upper bounds on Betti numbers of semialgebraic sets defined by quantifier-free formulae, and obtain for the first time a singly exponential bound on Betti numbers of sub-Pfaffian sets.Comment: 20 pages, 2 figure

Relations on FP-Soft Sets Applied to Decision Making Problems

In this work, we first define relations on the fuzzy parametrized soft sets and study their properties. We also give a decision making method based on these relations. In approximate reasoning, relations on the fuzzy parametrized soft sets have shown to be of a primordial importance. Finally, the method is successfully applied to a problems that contain uncertainties.Comment: soft application

The Open Method of Coordination and integration theory: are there lessons to be learned?

This paper seeks to contextualize the Open Method of Coordination (OMC) and enrich our understanding of it by submitting constructivist insights to its policy assessment with a focus on the Employment Strategy (EES). The most developed and longest-standing OMC policy area, employment provides fertile ground for the assessment of a rapidly expanding theoretical perspective in IR and European integration applied to a growing policy process. Normative considerations as to the essence of the EU and its future trajectory were highly influential in the process of launching the OMC. The paper provides a framework of integration theory and highlights the particular contribution that the ‘thin’ variant of constructivism has made in understanding different aspects of EU policy and politics. In the next section, the OMC is discussed and its core characteristics identified. I claim that most of the OMC’s core elements are directly linked to constructivist assumptions about policy change. The paper identifies three of those, namely policy discourse, learning and participation in policy-making. I subject those to an empirical and theoretical assessment by use of the relevant literature. Concluding that the record shows such mechanisms to be hardly present in the Employment Policy OMC, I argue that an institutionalist reading of OMC provides a credible alternative by focusing on power resources, preferences and strategies available to core OMC actors, namely member states and the Commission. The paper concludes with a twofold argument: firstly, constructivist hopes on OMC are, at least in the current context, ill-founded. Secondly, while the OMC retains a number of advantages, practical policy suggestions that will enhance its appeal to policy-makers and the public alike are due before it becomes a credible policy option

A comprehensive study of implicator-conjunctor based and noise-tolerant fuzzy rough sets: definitions, properties and robustness analysis

© 2014 Elsevier B.V. Both rough and fuzzy set theories offer interesting tools for dealing with imperfect data: while the former allows us to work with uncertain and incomplete information, the latter provides a formal setting for vague concepts. The two theories are highly compatible, and since the late 1980s many researchers have studied their hybridization. In this paper, we critically evaluate most relevant fuzzy rough set models proposed in the literature. To this end, we establish a formally correct and unified mathematical framework for them. Both implicator-conjunctor-based definitions and noise-tolerant models are studied. We evaluate these models on two different fronts: firstly, we discuss which properties of the original rough set model can be maintained and secondly, we examine how robust they are against both class and attribute noise. By highlighting the benefits and drawbacks of the different fuzzy rough set models, this study appears a necessary first step to propose and develop new models in future research.Lynn D’eer has been supported by the Ghent University Special Research Fund, Chris Cornelis was partially supported by the Spanish Ministry of Science and Technology under the project TIN2011-28488 and the Andalusian Research Plans P11-TIC-7765 and P10-TIC-6858, and by project PYR-2014-8 of the Genil Program of CEI BioTic GRANADA and Lluis Godo has been partially supported by the Spanish MINECO project EdeTRI TIN2012-39348-C02-01Peer Reviewe