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
EditorsArtde Donald Kin-Tak Lam, Stephen D. Prior, Teen-Hang Meen
PublisherCRC Press/Balkema
Pages825-830
Number of pages6
ISBN (Print)9781138028937
Publication statusPublished - 2016 Jan 1
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

Fingerprint

Choquet Integral
Fuzzy Measure
Regression Model
Model-based
regression
Probability density function
Fuzzy Function
Density Function
Fuzzy measure
Choquet integral
Regression model
experiment
Mean square error
performance
Ridge Regression
Multiple Regression
Multiple Models
Cross-validation

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

Cite this

Liu, H. C., Tsai, H-C., Yu, Y. K., & Mai, Y. T. (2016). Choquet integral regression model based on Liu’s second order multivalent fuzzy measure. In A. D. K-T. Lam, S. D. Prior, & T-H. Meen (Eds.), Applied System Innovation - Proceedings of the International Conference on Applied System Innovation, ICASI 2015 (pp. 825-830). (Applied System Innovation - Proceedings of the International Conference on Applied System Innovation, ICASI 2015). CRC Press/Balkema.
Liu, Hsiang Chuan ; Tsai, Hsien-Chang ; Yu, Yen Kuei ; Mai, Yi Ting. / Choquet integral regression model based on Liu’s second order multivalent fuzzy measure. Applied System Innovation - Proceedings of the International Conference on Applied System Innovation, ICASI 2015. editor / Artde Donald Kin-Tak Lam ; Stephen D. Prior ; Teen-Hang Meen. CRC Press/Balkema, 2016. pp. 825-830 (Applied System Innovation - Proceedings of the International Conference on Applied System Innovation, ICASI 2015).
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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.",
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Liu, HC, Tsai, H-C, Yu, YK & Mai, YT 2016, Choquet integral regression model based on Liu’s second order multivalent fuzzy measure. in ADK-T Lam, SD Prior & T-H Meen (eds), Applied System Innovation - Proceedings of the International Conference on Applied System Innovation, ICASI 2015. Applied System Innovation - Proceedings of the International Conference on Applied System Innovation, ICASI 2015, CRC Press/Balkema, pp. 825-830, International Conference on Applied System Innovation, ICASI 2015, Osaka, Japan, 15-05-22.

Choquet integral regression model based on Liu’s second order multivalent fuzzy measure. / Liu, Hsiang Chuan; Tsai, Hsien-Chang; Yu, Yen Kuei; Mai, Yi Ting.

Applied System Innovation - Proceedings of the International Conference on Applied System Innovation, ICASI 2015. ed. / Artde Donald Kin-Tak Lam; Stephen D. Prior; Teen-Hang Meen. CRC Press/Balkema, 2016. p. 825-830 (Applied System Innovation - Proceedings of the International Conference on Applied System Innovation, ICASI 2015).

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

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AB - 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.

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M3 - Conference contribution

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Liu HC, Tsai H-C, Yu YK, Mai YT. Choquet integral regression model based on Liu’s second order multivalent fuzzy measure. In Lam ADK-T, Prior SD, Meen T-H, editors, Applied System Innovation - Proceedings of the International Conference on Applied System Innovation, ICASI 2015. CRC Press/Balkema. 2016. p. 825-830. (Applied System Innovation - Proceedings of the International Conference on Applied System Innovation, ICASI 2015).