Miguel Couceiro
University of Lorraine
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Featured researches published by Miguel Couceiro.
Fuzzy Sets and Systems | 2010
Miguel Couceiro; Jean-Luc Marichal
We give several characterizations of discrete Sugeno integrals over bounded distributive lattices, as particular cases of lattice polynomial functions, that is, functions which can be represented in the language of bounded lattices using variables and constants. We also consider the subclass of term functions as well as the classes of symmetric polynomial functions and weighted minimum and maximum functions, and present their characterizations, accordingly. Moreover, we discuss normal form representations of these functions.
Theoretical Computer Science | 2008
Miguel Couceiro; Maurice Pouzet
It was proved few years ago that classes of Boolean functions definable by means of functional equations [O. Ekin, S. Foldes, P.L. Hammer, L. Hellerstein, Equational characterizations of boolean functions classes, Discrete Mathematics 211 (2000) 27-51], or equivalently, by means of relational constraints [N. Pippenger. Galois theory for minors of finite functions, Discrete Mathematics 254 (2002) 405-419], coincide with initial segments of the quasi-ordered set (@W,@?) made of the set @W of Boolean functions, suitably quasi-ordered. Furthermore, the classes defined by finitely many equations [O. Ekin, S. Foldes, P.L. Hammer, L. Hellerstein, Equational characterizations of boolean functions classes, Discrete Mathematics 211 (2000) 27-51] coincide with the initial segments of (@W,@?) which are definable by finitely many obstructions. The resulting ordered set (@W@?,@?) embeds into ([@w]^<^@w,@?), the set-ordered by inclusion-of finite subsets of the set @w of integers. We prove that (@W@?,@?) also embeds ([@w]^<^@w,@?). From this result, we deduce that the dual space of the distributive lattice made of finitely definable classes is uncountable. Looking at examples of finitely definable classes, we show that the classes of Boolean functions with a bounded number of essential variables are finitely definable. We provide a concrete equational characterization for each of these classes, and for the subclasses made of linear functions. We describe the classes of functions with bounded polynomial degree in terms of minimal obstructions.
Aequationes Mathematicae | 2010
Miguel Couceiro; Jean-Luc Marichal
In [6] the authors introduced the notion of quasi-polynomial function as being a mapping f : Xn → X defined and valued on a bounded chain X and which can be factorized as
Discrete Mathematics | 2009
Miguel Couceiro; Erkko Lehtonen
Algebra Universalis | 2005
Miguel Couceiro; Stephan Foldes
{f(x_1,\ldots,x_n)=p(\varphi(x_1),\ldots,\varphi(x_n))}
Order | 2011
Miguel Couceiro; Jean-Luc Marichal
International Journal of Foundations of Computer Science | 2007
Miguel Couceiro; Erkko Lehtonen
, where p is a polynomial function (i.e., a combination of variables and constants using the chain operations
Discrete Mathematics | 2012
Miguel Couceiro; Erkko Lehtonen; Tamás Waldhauser
Algebra Universalis | 2012
Miguel Couceiro; Erkko Lehtonen
{\wedge}
International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems | 2011
Miguel Couceiro; Tamás Waldhauser