Theory and application of the composed fuzzy measure of L-measure and delta-measures

Accession number:20094112368240

Title: Theory and application of the composed fuzzy measure of L- measure and delta-measures

Authors: Liu, Hsiang-Chuan (1); Chen, Chin-Chun (2); Wu, Der-Bang (2); Sheu, Tian-Wei (2)

Author affiliation:(1) Department of Bioinformatics, Asia University, Taichung, 41345, Taiwan; (2) National Taichung University, Taichung, 40306, Taiwan; (3) Department of General Education, Min-Hwei College, Tainan 736, Taiwan; (4) Graduate Institute of Educational Measurement and Department of Mathematics Education, National Taichung University, Taichung, 40306, Taiwan; (5) Graduate Institute of Educational Measurement, National Taichung University,

Taichung, 40306, Taiwan

Corresponding author:Liu, H.-C.

(lhc@asia.edu.tw)

Source title: WSEAS Transactions on Systems and Control Abbreviated source title:WSEAS Trans. Syst. Control

Volume:4 Issue:8

Issue date:August 2009 Publication year:2009 Pages:359-368

Language:English ISSN:19918763

Document type:Journal article (JA)

Publisher:World Scientific and Engineering Academy and Society, Ag.

Ioannou Theologou 17-23, Zographou, Athens, 15773, Greece

Abstract:The well known fuzzy measures, λ-measure and P- measure, have only one formulaic solution. Two multivalent fuzzy measures with infinitely many solutions were proposed by our previous works, called L-measure and δ-measure, but the former do not include the additive measure as the latter and the latter has not so many measure solutions as the former. Due to the above drawbacks, in this paper, an improved fuzzy measure

composed of above both, denoted L<inf>&delta;</inf> -measure, is proposed. For evaluating the Choquet integral regression models with our proposed fuzzy measure and other different ones, a real

data experiment by using a 5-fold cross-validation mean square error (MSE) is conducted. The performances of Choquet integral regression models with fuzzy measure based L<inf>&delta;</inf>

-measure, L-measure, &delta;-measure, &lambda;-measure, and P- measure, respectively, a ridge regression model, and a multiple linear regression model are compared. Experimental result shows that the Choquet integral regression models with respect to

extensional L-measure based on &gamma;-support outperforms others forecasting models.

Number of references:16

Main heading:Integral equations

Controlled terms: Linear regression - Mean square error

Uncontrolled terms: Choquet integral regression model - Composed fuzzy measure - Delta-measure - Gamma-support - Lambda-measure - P-measure

Classification code:731.1 Control Systems - 921.2 Calculus - 922.2 Mathematical Statistics

Database:Compendex

Compilation and indexing terms, Copyright 2009 Elsevier Inc.