Commutativity and self-duality: Two tales of one equation

被引：11

作者：

Maes, Koen C. ^{[1
]}

De Baets, Bernard ^{[1
]}

机构：

[1] Univ Ghent, Dept Appl Math Biometr & Proc Control, B-9000 Ghent, Belgium

来源：

INTERNATIONAL JOURNAL OF APPROXIMATE REASONING | 2009年 / 50卷 / 01期

关键词：

Aggregation function; Commutativity; Self-duality; Orthosymmetry; Phi-Inverse; Contour lines; AGGREGATION OPERATORS; MONOTONE-FUNCTIONS; CONSTRUCTION;

D O I：

10.1016/j.ijar.2008.08.002

中图分类号：

TP18 [人工智能理论];

学科分类号：

081104 ; 0812 ; 0835 ; 1405 ;

摘要：

The mathematical expressions for the commutativity or self-duality of an increasing [0,1](2) -> [0,1] function F involve the transposition of its arguments. We unite both properties in a single functional equation. The solutions of this functional equation are discussed. Special attention goes to the geometrical construction of these solutions and their characterization in terms of contour lines. Furthermore, it is shown how 'rotating' the arguments of F allows to convert the results into properties for [0,1](2) -> [0,1] functions having monotone partial functions. (c) 2008 Elsevier Inc. All rights reserved.

引用

页码：189 / 199

页数：11

共 17 条

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Maes, K. C.
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Maes, Koen C.
De Baets, Bernard
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