Choquet integral regression model based on Liu’s second order multivalent fuzzy measure

Hsiang Chuan Liu, Hsien Chang Tsai, Yen Kuei Yu, Yi Ting Mai

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

The well-known Sugeno’s Lambda-measure can only be used for real data fit to subadditive, additive, or super-additive fuzzy measures, which cannot be mixed with any fuzzy measure. To overcome this disadvantage, Grabisch extended the fuzzy density function from the first order to the second order, in order to propose his 2-additive fuzzy measure. We know that the 2-additive fuzzy measure is only a univalent fuzzy measure. Hsiang-Chuan Liu has proposed an improved multivalent fuzzy measure based on a 2-additive fuzzy measure, called Liu’s second order multivalent fuzzy measure. It is more sensitive and useful than a 2-additive fuzzy measure, since it is a generalization of the 2-additive fuzzy measure. However, the fuzzy density functions of all of the above mentioned fuzzy measures can only be used for unsupervised data. In this paper, we have proposed the corresponding ones for the supervised data. In order to compare the Choquet integral regression model with P-measure,?-measure, Liu’ multivalent fuzzy measure, 2-additive measure, and Liu’ second order multivalent fuzzy measure based on Liu’s supervised fuzzy density function, the traditional multiple regression model and the ridge regression model, a real data experiment by using a 5-fold cross validation Mean Square Error (MSE) is conducted. Results show that the Choquet integral regression model with Liu’ second order multivalent fuzzy measure has the best performance.

Original languageEnglish
Title of host publicationApplied System Innovation - Proceedings of the International Conference on Applied System Innovation, ICASI 2015
EditorsTeen-Hang Meen, Stephen D. Prior, Artde Donald Kin-Tak Lam
PublisherCRC Press/Balkema
Pages825-830
Number of pages6
ISBN (Print)9781138028937
DOIs
Publication statusPublished - 2016
EventInternational Conference on Applied System Innovation, ICASI 2015 - Osaka, Japan
Duration: 2015 May 222015 May 27

Publication series

NameApplied System Innovation - Proceedings of the International Conference on Applied System Innovation, ICASI 2015

Other

OtherInternational Conference on Applied System Innovation, ICASI 2015
CountryJapan
CityOsaka
Period15-05-2215-05-27

All Science Journal Classification (ASJC) codes

  • Business, Management and Accounting (miscellaneous)
  • Computer Networks and Communications
  • Computer Science Applications
  • Control and Optimization
  • Control and Systems Engineering
  • Social Sciences (miscellaneous)
  • Electrical and Electronic Engineering

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