### Abstract

The well known fuzzy measures, λ-measure and P-measure, have only one formulaic solution. Two multivalent fuzzy measures with infinitely many solutions, L-measure and d-measure, were proposed by our previous works, but the former do not include the additive measure as the latter and the latter has not so many measure solutions as the former, therefore, a composed fuzzy measure of above two measures, called LΔ -measure was proposed by our additional previous work. However, all of abovementioned fuzzy measures do not contain the largest measure, B-measure, which all not completed measures. In this paper, an improved completed fuzzy measure composed of maximized L-measure and λ-measure, denoted L_{mΔ} -measure,is proposed. For evaluating the Choquet integral regression models with our proposed fuzzy measure and other different ones, two real data experiments by using a 5-fold cross-validation mean square error (MSE) were conducted. The performances of Choquet integral regression models with fuzzy measure based L_{mΔ} -measure, L_{mΔ} -measure, L_{Δ} -measure, L-measure, Δ-measure, λ-measure, and P-measure, respectively, a ridge regression model, and a multiple linear regression model are compared. Both of two experimental results show that the Choquet integral regression models with respect to our new measure based on λ-support outperforms others forecasting models.

Original language | English |
---|---|

Pages (from-to) | 474-483 |

Number of pages | 10 |

Journal | WSEAS Transactions on Information Science and Applications |

Volume | 7 |

Issue number | 4 |

Publication status | Published - 2010 Apr 1 |

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### All Science Journal Classification (ASJC) codes

- Information Systems
- Computer Science Applications

### Cite this

*WSEAS Transactions on Information Science and Applications*,

*7*(4), 474-483.

}

*WSEAS Transactions on Information Science and Applications*, vol. 7, no. 4, pp. 474-483.

**Composed fuzzy measure of maximized L-measure and delta-measure.** / Liu, Hsiang Chuan; Tsai, Hsien-Chang; Jheng, Yu Du; Liu, Tung Sheng.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Composed fuzzy measure of maximized L-measure and delta-measure

AU - Liu, Hsiang Chuan

AU - Tsai, Hsien-Chang

AU - Jheng, Yu Du

AU - Liu, Tung Sheng

PY - 2010/4/1

Y1 - 2010/4/1

N2 - The well known fuzzy measures, λ-measure and P-measure, have only one formulaic solution. Two multivalent fuzzy measures with infinitely many solutions, L-measure and d-measure, were proposed by our previous works, but the former do not include the additive measure as the latter and the latter has not so many measure solutions as the former, therefore, a composed fuzzy measure of above two measures, called LΔ -measure was proposed by our additional previous work. However, all of abovementioned fuzzy measures do not contain the largest measure, B-measure, which all not completed measures. In this paper, an improved completed fuzzy measure composed of maximized L-measure and λ-measure, denoted LmΔ -measure,is proposed. For evaluating the Choquet integral regression models with our proposed fuzzy measure and other different ones, two real data experiments by using a 5-fold cross-validation mean square error (MSE) were conducted. The performances of Choquet integral regression models with fuzzy measure based LmΔ -measure, LmΔ -measure, LΔ -measure, L-measure, Δ-measure, λ-measure, and P-measure, respectively, a ridge regression model, and a multiple linear regression model are compared. Both of two experimental results show that the Choquet integral regression models with respect to our new measure based on λ-support outperforms others forecasting models.

AB - The well known fuzzy measures, λ-measure and P-measure, have only one formulaic solution. Two multivalent fuzzy measures with infinitely many solutions, L-measure and d-measure, were proposed by our previous works, but the former do not include the additive measure as the latter and the latter has not so many measure solutions as the former, therefore, a composed fuzzy measure of above two measures, called LΔ -measure was proposed by our additional previous work. However, all of abovementioned fuzzy measures do not contain the largest measure, B-measure, which all not completed measures. In this paper, an improved completed fuzzy measure composed of maximized L-measure and λ-measure, denoted LmΔ -measure,is proposed. For evaluating the Choquet integral regression models with our proposed fuzzy measure and other different ones, two real data experiments by using a 5-fold cross-validation mean square error (MSE) were conducted. The performances of Choquet integral regression models with fuzzy measure based LmΔ -measure, LmΔ -measure, LΔ -measure, L-measure, Δ-measure, λ-measure, and P-measure, respectively, a ridge regression model, and a multiple linear regression model are compared. Both of two experimental results show that the Choquet integral regression models with respect to our new measure based on λ-support outperforms others forecasting models.

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M3 - Article

VL - 7

SP - 474

EP - 483

JO - WSEAS Transactions on Information Science and Applications

JF - WSEAS Transactions on Information Science and Applications

SN - 1790-0832

IS - 4

ER -