Migrativity of aggregation functions

被引：86

作者：

Bustince, H. ^{[1
]}

Montero, J. ^{[2
]}

Mesiar, R. ^{[3
,4
]}

机构：

[1] Univ Publ Navarra, Dept Automat & Computac, Pamplona, Spain

[2] Univ Complutense, Fac Matemat, E-28040 Madrid, Spain

[3] Slovak Univ Technol Bratislava, Dept Math & Descript Geometry, SK-81368 Bratislava, Slovakia

[4] Acad Sci Czech Republ, Inst Informat Theory & Automat, CZ-18208 Prague, Czech Republic

来源：

FUZZY SETS AND SYSTEMS | 2009年 / 160卷 / 06期

关键词：

Aggregation functions; Migrativity; Associativity; Bisymmetry; t-Norms; Uninorms; Nullnorms;

D O I：

10.1016/j.fss.2008.09.018

中图分类号：

TP301 [理论、方法];

学科分类号：

081202 ;

摘要：

In this paper we introduce a slight modification of the definition of migrativity for aggregation functions that allows useful characterization of this property. Among other things, in this context we prove that there are not-conorms, uninorms or nullnorms that satisfy migrativity (with the product being the only migrative t-norm, as already shown by other authors) and that the only migrative idempotent aggregation function is the geometric mean. The k-Lipschitz migrative aggregation functions are also characterized and the product is shown to be the only 1-Lipschitz migrative aggregation function. Similarly, it is the only associative migrative aggregation function possessing a neutral element. Finally, the associativity and bisymmetry of migrative aggregation functions are discussed. (C) 2008 Elsevier B.V. All rights reserved.

引用

页码：766 / 777

页数：12