Multiple Optimal Solutions and the Best Lipschitz Constants Between an Aggregation Function and Associated Idempotized Aggregation Function

Multiple Optimal Solutions and the Best Lipschitz Constants Between an Aggregation Function and Associated Idempotized Aggregation Function

This paper presents and compares the optimal solutions and the theoretical and empirical best Lipschitz constants between an aggregation function and associated idempotized aggregation function. According to an exhaustive search we performed, the multiple optimal solutions and the empirical best Lip...

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Bibliographic Details
Main Authors: Hui-Chin Tang, Wei-Ting Chen
Format: Article
Language:English
Published: MDPI AG 2021-04-01
Series:Axioms
Subjects:
aggregation
Lipschitz
computation
idempotent
Online Access:https://www.mdpi.com/2075-1680/10/2/52
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spelling doaj-bb37a3b08d6e4aeb816571baafdaf92d2021-04-02T23:04:43ZengMDPI AGAxioms2075-16802021-04-0110525210.3390/axioms10020052Multiple Optimal Solutions and the Best Lipschitz Constants Between an Aggregation Function and Associated Idempotized Aggregation FunctionHui-Chin Tang0Wei-Ting Chen1Department of Industrial Engineering and Management, National Kaohsiung University of Science and Technology, Kaohsiung 80778, TaiwanDepartment of Industrial Engineering and Management, National Kaohsiung University of Science and Technology, Kaohsiung 80778, TaiwanThis paper presents and compares the optimal solutions and the theoretical and empirical best Lipschitz constants between an aggregation function and associated idempotized aggregation function. According to an exhaustive search we performed, the multiple optimal solutions and the empirical best Lipschitz constants are presented explicitly. The results indicate that differences of the multiple optimal solutions exist among the Minkowski norm, the number of steps, and the type of aggregation function. We demonstrate that these differences can affect the theoretical and empirical best Lipschitz constants of an aggregation function.https://www.mdpi.com/2075-1680/10/2/52aggregationLipschitzcomputationidempotent
collection DOAJ
language English
format Article
sources DOAJ
author Hui-Chin Tang
Wei-Ting Chen
spellingShingle Hui-Chin Tang
Wei-Ting Chen
Multiple Optimal Solutions and the Best Lipschitz Constants Between an Aggregation Function and Associated Idempotized Aggregation Function
Axioms
aggregation
Lipschitz
computation
idempotent
author_facet Hui-Chin Tang
Wei-Ting Chen
author_sort Hui-Chin Tang
title Multiple Optimal Solutions and the Best Lipschitz Constants Between an Aggregation Function and Associated Idempotized Aggregation Function
title_short Multiple Optimal Solutions and the Best Lipschitz Constants Between an Aggregation Function and Associated Idempotized Aggregation Function
title_full Multiple Optimal Solutions and the Best Lipschitz Constants Between an Aggregation Function and Associated Idempotized Aggregation Function
title_fullStr Multiple Optimal Solutions and the Best Lipschitz Constants Between an Aggregation Function and Associated Idempotized Aggregation Function
title_full_unstemmed Multiple Optimal Solutions and the Best Lipschitz Constants Between an Aggregation Function and Associated Idempotized Aggregation Function
title_sort multiple optimal solutions and the best lipschitz constants between an aggregation function and associated idempotized aggregation function
publisher MDPI AG
series Axioms
issn 2075-1680
publishDate 2021-04-01
description This paper presents and compares the optimal solutions and the theoretical and empirical best Lipschitz constants between an aggregation function and associated idempotized aggregation function. According to an exhaustive search we performed, the multiple optimal solutions and the empirical best Lipschitz constants are presented explicitly. The results indicate that differences of the multiple optimal solutions exist among the Minkowski norm, the number of steps, and the type of aggregation function. We demonstrate that these differences can affect the theoretical and empirical best Lipschitz constants of an aggregation function.
topic aggregation
Lipschitz
computation
idempotent
url https://www.mdpi.com/2075-1680/10/2/52
work_keys_str_mv AT huichintang multipleoptimalsolutionsandthebestlipschitzconstantsbetweenanaggregationfunctionandassociatedidempotizedaggregationfunction
AT weitingchen multipleoptimalsolutionsandthebestlipschitzconstantsbetweenanaggregationfunctionandassociatedidempotizedaggregationfunction
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