Pseudo-polynomial functions over finite distributive lattices
Waldhauser, Tamás; Couceiro, Miguel (2014), Pseudo-polynomial functions over finite distributive lattices, Fuzzy Sets and Systems, 239, p. 21-34. http://dx.doi.org/10.1016/j.fss.2012.09.007
TypeArticle accepté pour publication ou publié
External document linkhttp://arxiv.org/abs/1110.1811
Journal nameFuzzy Sets and Systems
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Abstract (EN)In this paper we consider an aggregation model f: X1 x ... x Xn --> Y for arbitrary sets X1, ..., Xn and a finite distributive lattice Y, factorizable as f(x1, ..., xn) = p(u1(x1), ..., un(xn)), where p is an n-variable lattice polynomial function over Y, and each uk is a map from Xk to Y. The resulting functions are referred to as pseudo-polynomial functions. We present an axiomatization for this class of pseudo-polynomial functions which differs from the previous ones both in flavour and nature, and develop general tools which are then used to obtain all possible such factorizations of a given pseudo-polynomial function.
Subjects / KeywordsSugeno integral; distributive lattice; lattice polynomial function; pseudo-polynomial function; axiomatization; factorization; multicriteria decision making
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Interpolation by polynomial functions of distributive lattices: a generalization of a theorem of R. L. Goodstein Waldhauser, Tamás; Couceiro, Miguel (2013) Article accepté pour publication ou publié