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/).
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 -