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Characterizations of discrete Sugeno integrals as polynomial functions over distributive lattices

Marichal, Jean-Luc; Couceiro, Miguel (2010), Characterizations of discrete Sugeno integrals as polynomial functions over distributive lattices, Fuzzy Sets and Systems, 161, 5, p. 694-707. http://dx.doi.org/10.1016/j.fss.2009.10.008

Type
Article accepté pour publication ou publié
External document link
http://arxiv.org/abs/0808.2619
Date
2010
Journal name
Fuzzy Sets and Systems
Volume
161
Number
5
Publisher
Elsevier
Pages
694-707
Publication identifier
http://dx.doi.org/10.1016/j.fss.2009.10.008
Metadata
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Author(s)
Marichal, Jean-Luc
Couceiro, Miguel
Abstract (EN)
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 infimum and supremum functions, and present their characterizations, accordingly. Moreover, we discuss normal form representations of these functions.
Subjects / Keywords
Discrete Sugeno integral; Distributive lattice; Lattice polynomial function; Normal form; Median decomposition; Homogeneity; Functional equation

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