### 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 language | English |
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Title of host publication | Applied System Innovation - Proceedings of the International Conference on Applied System Innovation, ICASI 2015 |

Editors | Artde Donald Kin-Tak Lam, Stephen D. Prior, Teen-Hang Meen |

Publisher | CRC Press/Balkema |

Pages | 825-830 |

Number of pages | 6 |

ISBN (Print) | 9781138028937 |

Publication status | Published - 2016 Jan 1 |

Event | International Conference on Applied System Innovation, ICASI 2015 - Osaka, Japan Duration: 2015 May 22 → 2015 May 27 |

### Publication series

Name | Applied System Innovation - Proceedings of the International Conference on Applied System Innovation, ICASI 2015 |
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### Other

Other | International Conference on Applied System Innovation, ICASI 2015 |
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Country | Japan |

City | Osaka |

Period | 15-05-22 → 15-05-27 |

### Fingerprint

### 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

*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.

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*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.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

TY - GEN

T1 - Choquet integral regression model based on Liu’s second order multivalent fuzzy measure

AU - Liu, Hsiang Chuan

AU - Tsai, Hsien-Chang

AU - Yu, Yen Kuei

AU - Mai, Yi Ting

PY - 2016/1/1

Y1 - 2016/1/1

N2 - 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.

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.

UR - http://www.scopus.com/inward/record.url?scp=85016737173&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85016737173&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:85016737173

SN - 9781138028937

T3 - Applied System Innovation - Proceedings of the International Conference on Applied System Innovation, ICASI 2015

SP - 825

EP - 830

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

A2 - Lam, Artde Donald Kin-Tak

A2 - Prior, Stephen D.

A2 - Meen, Teen-Hang

PB - CRC Press/Balkema

ER -