Proceedings of the 7th conference of the European Society for Fuzzy Logic and Technology (EUSFLAT-11)

On the convergence of HLMS Algorithm

Authors
Murillo Javier, Serge Guillaume, Elizabeth Tapia, Bulacio Pilar
Corresponding Author
Murillo Javier
Available Online August 2011.
DOI
10.2991/eusflat.2011.147How to use a DOI?
Keywords
multicriteria, fuzzy integrals, HLMS, convergence
Abstract

In multicriteria decision making, the study of attribute contributions is crucial to attain correct decisions. Fuzzy measures allow a complete description of the joint behavior of attribute subsets. However, the determination of fuzzy measures is often hard. A common way to identify fuzzy measures is HLMS (Heuristic Least Mean Squares) algorithm. In this paper, the convergence of the HLMS algorithm is analyzed. First, we show that the learning rate parameter ( ) dominates the convergence of HLMS. Second, we provide an upper bound for that guarantees HLMS convergence. In addition, a toy example shows the descriptive power of fuzzy measures versus the poverty of individual measures.

Copyright
© 2011, the Authors. Published by Atlantis Press.
Open Access
This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

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Volume Title
Proceedings of the 7th conference of the European Society for Fuzzy Logic and Technology (EUSFLAT-11)
Series
Advances in Intelligent Systems Research
Publication Date
August 2011
ISBN
978-90-78677-00-0
ISSN
1951-6851
DOI
10.2991/eusflat.2011.147How to use a DOI?
Copyright
© 2011, the Authors. Published by Atlantis Press.
Open Access
This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

Cite this article

TY  - CONF
AU  - Murillo Javier
AU  - Serge Guillaume
AU  - Elizabeth Tapia
AU  - Bulacio Pilar
PY  - 2011/08
DA  - 2011/08
TI  - On the convergence of HLMS Algorithm
BT  - Proceedings of the 7th conference of the European Society for Fuzzy Logic and Technology (EUSFLAT-11)
PB  - Atlantis Press
SP  - 817
EP  - 821
SN  - 1951-6851
UR  - https://doi.org/10.2991/eusflat.2011.147
DO  - 10.2991/eusflat.2011.147
ID  - Javier2011/08
ER  -