On order invariant synthesizing functions.
type: Item
instance of: scholarly article
title: On order invariant synthesizing functions.
zbMATH Open document ID: 1038.91072
author: Jean-Luc Marichal
published in: Journal of Mathematical Psychology
publication date: 2003-04-27T00:00:00Z
review text: The author offers several characterizations of lattice polynomials [see \textit{G. Birkhoff}, Lattice theory, AMS, Providence (1967; Zbl 0153.02501) and \textit{S. Ovchinnikov}, Order 14, 365--371 (1998; Zbl 0910.06001)]. The author calls them Boolean max-min functions -- they are indeed composed of a set function with 0 or 1 as values and of several maximum and minimum functions. Essential characterizing properties are, in addition to continuity, order invariance and, eventually, idempotence \((M(x,\dots ,x)=x)\). Order statistics, medians, and projection functions are considered as particular cases and characterized in corollaries.
Mathematics Subject Classification ID: 91C05
Mathematics Subject Classification ID: 39B22
zbMATH DE Number: 1901017
zbMATH Keywords: synthesizing functions
zbMATH Keywords: order invariance
zbMATH Keywords: lattice polynomials
reviewed by: János Aczél
MaRDI profile type: Publication
full work available at URL: jmps.2002.1418
OpenAlex ID: W2142707851
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DOI: 10.1006/JMPS.2002.1418
description: scientific article; zbMATH DE number 1901017