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Journal Articles Discrete Applied Mathematics Year : 2012

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

Miguel Couceiro
Erkko Lehtonen

Abstract

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 Lovász 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.

Dates and versions

hal-01090604 , version 1 (03-12-2014)

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Miguel Couceiro, Erkko Lehtonen, Tamas Waldhauser. The arity gap of order-preserving functions and extensions of pseudo-Boolean functions. Discrete Applied Mathematics, 2012, 160 (4-5), pp.383-390. ⟨10.1016/j.dam.2011.07.024⟩. ⟨hal-01090604⟩
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