Maximal directions of monotonicity of an aggregation function

De Baets B.; De Meyer H.

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Maximal directions of monotonicity of an aggregation function

机译：Maximal directions of monotonicity of an aggregation function

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We introduce the concept of maximal directions of increasingness (resp. decreasingness) of an aggregation function. In the bivariate case, we derive these maximal directions with respect to points on the main diagonal of the unit square for a symmetric aggregation function that has either piecewise convex or piecewise concave level curves and is differentiable up to second order. With any bivariate aggregation function of the latter type we associate another bivariate aggregation function that has the same maximal directions of increasingness (resp. decreasingness) while having straight lines as level curves. We explore under which conditions the latter aggregation function is a semi-copula, a quasi-copula or a copula. As a by-product we establish a new construction method for aggregation functions with given diagonal section. (c) 2021 Elsevier B.V. All rights reserved.

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《Fuzzy sets and systems》 |2022年第15期|54-78|共25页
作者
De Baets B.; De Meyer H.;
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作者单位

Univ Ghent, Dept Data Anal & Math Modelling, KERMIT, Coupure Links 653, B-9000 Ghent, Belgium;

Univ Ghent, Dept Appl Math Comp Sci & Stat, Krijgslaan 281, B-9000 Ghent, Belgium;

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收录信息美国《科学引文索引》(SCI);美国《工程索引》(EI);
原文格式 PDF
正文语种英语
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关键词
Aggregation function; Concave; convex level curve; Copula; Directional monotonicity; Maximal direction of monotonicity;

Maximal directions of monotonicity of an aggregation function

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