Characterizations of discrete Sugeno integrals as polynomial functions over distributive lattices

Marichal, Jean-Luc; Couceiro, Miguel

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

Publisher

Elsevier

Pages

694-707

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