The arity gap of order-preserving functions and extensions of pseudo-Boolean functions

被引：8
|
作者：
Couceiro, Miguel [2 ]
Lehtonen, Erkko [1 ]
Waldhauser, Tamas [2 ,3 ]
机构：
[1] Univ Luxembourg, Comp Sci & Commun Res Unit, L-1359 Luxembourg, Luxembourg
[2] Univ Luxembourg, Math Res Unit, L-1359 Luxembourg, Luxembourg
[3] Univ Szeged, Bolyai Inst, H-6720 Szeged, Hungary
来源：
DISCRETE APPLIED MATHEMATICS | 2012年 / 160卷 / 4-5期
关键词：
Arity gap; Order-preserving function; Aggregation function; Owen extension; Lovasz extension; OPERATIONS;
D O I：
10.1016/j.dam.2011.07.024
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
The aim of this paper is to classify order-preserving functions according to their arity gap. Noteworthy examples of order-preserving functions are the so-called aggregation functions. We first explicitly classify the Lovasz extensions of pseudo-Boolean functions according to their arity gap. Then we consider the class of order-preserving functions between partially ordered sets, and establish a similar explicit classification for this function class. (c) 2011 Elsevier B.V. All rights reserved.
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页码：383 / 390
页数：8
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