Choquet Integral with Respect to High Order Extensional L- Measure

2010 ◽  
Vol 44-47 ◽  
pp. 3579-3583 ◽  
Author(s):  
Hsiang Chuan Liu ◽  
Wei Sung Chen ◽  
Chin Chun Chen ◽  
Yu Du Jheng ◽  
Der Bang Wu
Keyword(s):  
Regression Model ◽  
Choquet Integral ◽  
Real Data ◽  
Multiple Regression Model ◽  
High Order ◽  
Data Set ◽  
Model Based ◽  
Result Show ◽  
Two Measures ◽  
Fold Cross Validation

In this paper, a generalized multivalent fuzzy measure of extensional L-measure, called high order extensional L-measure, is proposed. It is proved that if the value of order index is equal to one, this new measure is just the extensional L-measure, and the larger the value of order index is, the more sensitive it is. A real data set with 5- fold cross-validation MSE is conducted, for comparing the performances of the Choquet integral regression model based on this new measure with other four measures, P-measure and λ-measure, and authors’ two measures, L-measure and extensional L-measure, and two traditional regression model, multiple regression model and ridge regression model, the result show that the Choquet integral regression model based on this new measure has the best performance.

A Simulation Study on Choquet Integral with Respect to Extensional L- Measure

2010 ◽  
Vol 44-47 ◽  
pp. 3647-3651
Author(s):  
Hsu Chan Yao ◽  
Hsiang Chuan Liu ◽  
Yu Du Jheng
Keyword(s):  
Regression Model ◽  
Simulation Study ◽  
Choquet Integral ◽  
Multiple Linear Regression Model ◽  
Real Data ◽  
Experiment Data ◽  
Data Set ◽  
Monte Carlo Simulation Study ◽  
Fuzzy Measures ◽  
Fold Cross Validation

In this paper, an Monte Carlo simulation study method with 5- fold cross-validation MSE is used, a simulation experiment data and a real data set are conducted, for comparing the performances of a multiple linear regression model, a ridge regression model, and the Choquet integral regression model with respect to two well-known fuzzy measures, P-measure and λ-measure, and two new fuzzy measures proposed by authors’ previous works, L-measure and extensional L-measure, respectively. Both of the results show that the Choquet integral regression model with respect to extensional L-measure has the best performance.

High Order Lambda Measure Based Choquet Integral Composition Forecasting Model

2013 ◽  
Vol 284-287 ◽  
pp. 3111-3114
Author(s):  
Hsiang Chuan Liu ◽  
Wei Sung Chen ◽  
Ben Chang Shia ◽  
Chia Chen Lee ◽  
Shang Ling Ou ◽  
...  
Keyword(s):  
Time Series ◽  
Linear Regression ◽  
Cross Validation ◽  
Choquet Integral ◽  
Real Data ◽  
High Order ◽  
Forecasting Model ◽  
Mean Square ◽  
Weighted Composition ◽  
Fold Cross Validation

In this paper, a novel fuzzy measure, high order lambda measure, was proposed, based on the Choquet integral with respect to this new measure, a novel composition forecasting model which composed the GM(1,1) forecasting model, the time series model and the exponential smoothing model was also proposed. For evaluating the efficiency of this improved composition forecasting model, an experiment with a real data by using the 5 fold cross validation mean square error was conducted. The performances of Choquet integral composition forecasting model with the P-measure, Lambda-measure, L-measure and high order lambda measure, respectively, a ridge regression composition forecasting model and a multiple linear regression composition forecasting model and the traditional linear weighted composition forecasting model were compared. The experimental results showed that the Choquet integral composition forecasting model with respect to the high order lambda measure has the best performance.

Multilevel Zero-inflated Censored Beta Regression Modeling for Proportions and Rate Data with Extra-zeros

2019 ◽  
Author(s):  
Leili Tapak ◽  
Omid Hamidi ◽  
Majid Sadeghifar ◽  
Hassan Doosti ◽  
Ghobad Moradi
Keyword(s):  
Regression Model ◽  
Simulation Study ◽  
Real Data ◽  
P Value ◽  
Parameter Estimates ◽  
Beta Regression ◽  
Rate Data ◽  
Data Set ◽  
Proposed Model ◽  
Beta Regression Model

Abstract Objectives Zero-inflated proportion or rate data nested in clusters due to the sampling structure can be found in many disciplines. Sometimes, the rate response may not be observed for some study units because of some limitations (false negative) like failure in recording data and the zeros are observed instead of the actual value of the rate/proportions (low incidence). In this study, we proposed a multilevel zero-inflated censored Beta regression model that can address zero-inflation rate data with low incidence.Methods We assumed that the random effects are independent and normally distributed. The performance of the proposed approach was evaluated by application on a three level real data set and a simulation study. We applied the proposed model to analyze brucellosis diagnosis rate data and investigate the effects of climatic and geographical position. For comparison, we also applied the standard zero-inflated censored Beta regression model that does not account for correlation.Results Results showed the proposed model performed better than zero-inflated censored Beta based on AIC criterion. Height (p-value <0.0001), temperature (p-value <0.0001) and precipitation (p-value = 0.0006) significantly affected brucellosis rates. While, precipitation in ZICBETA model was not statistically significant (p-value =0.385). Simulation study also showed that the estimations obtained by maximum likelihood approach had reasonable in terms of mean square error.Conclusions The results showed that the proposed method can capture the correlations in the real data set and yields accurate parameter estimates.

A CHOQUET INTEGRAL REGRESSION MODEL BASED ON A NEW FUZZY MEASURE

2007 ◽  
pp. 1349-1355 ◽  
Author(s):  
HSIANG-CHUAN LIU ◽  
WEN-CHIH LIN ◽  
WEI-SHENG WENG
Keyword(s):  
Regression Model ◽  
Choquet Integral ◽  
Fuzzy Measure ◽  
Model Based

scholarly journals Predicting the cure rate of breast cancer using a new regression model with four regression structures

2017 ◽  
Vol 27 (11) ◽  
pp. 3207-3223 ◽  
Author(s):  
Thiago G Ramires ◽  
Gauss M Cordeiro ◽  
Michael W Kattan ◽  
Niel Hens ◽  
Edwin MM Ortega
Keyword(s):  
Breast Carcinoma ◽  
Regression Model ◽  
Additive Model ◽  
Real Data ◽  
Cure Rate ◽  
Time Model ◽  
Data Set ◽  
Explanatory Variables ◽  
Diagnostic Measures ◽  
Cure Fraction

Cure fraction models are useful to model lifetime data with long-term survivors. We propose a flexible four-parameter cure rate survival model called the log-sinh Cauchy promotion time model for predicting breast carcinoma survival in women who underwent mastectomy. The model can estimate simultaneously the effects of the explanatory variables on the timing acceleration/deceleration of a given event, the surviving fraction, the heterogeneity, and the possible existence of bimodality in the data. In order to examine the performance of the proposed model, simulations are presented to verify the robust aspects of this flexible class against outlying and influential observations. Furthermore, we determine some diagnostic measures and the one-step approximations of the estimates in the case-deletion model. The new model was implemented in the generalized additive model for location, scale and shape package of the R software, which is presented throughout the paper by way of a brief tutorial on its use. The potential of the new regression model to accurately predict breast carcinoma mortality is illustrated using a real data set.

scholarly journals Evaluation of a Multiple Regression Model for Noisy and Missing Data

2018 ◽  
Vol 8 (4) ◽  
pp. 2220
Author(s):  
Chanintorn Jittawiriyanukoon
Keyword(s):  
Big Data ◽  
Missing Data ◽  
Data Collection ◽  
Regression Model ◽  
Multiple Regression ◽  
Mean Squared Error ◽  
Real Data ◽  
Multiple Regression Model ◽  
Average Percentage ◽  
Standard Data

<span>The standard data collection problems may involve noiseless data while on the other hand large organizations commonly experience noisy and missing data, probably concerning data collected from individuals. As noisy and missing data will be significantly worrisome for occasions of the vast data collection then the investigation of different filtering techniques for big data environment would be remarkable. A multiple regression model where big data is employed for experimenting will be presented. Approximation for datasets with noisy and missing data is also proposed. The statistical root mean squared error (RMSE) associated with correlation coefficient (COEF) will be analyzed to prove the accuracy of estimators. Finally, results predicted by massive online analysis (MOA) will be compared to those real data collected from the following different time. These theoretical predictions with noisy and missing data estimation by simulation, revealing consistency with the real data are illustrated. Deletion mechanism (DEL) outperforms with the lowest average percentage of error.</span>

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

2016 ◽  
pp. 825-829
Author(s):  
Hsiang-Chuan Liu ◽  
Hsien-Chang Tsai ◽  
Yen-Kuei Yu ◽  
Yi-Ting Mai
Keyword(s):  
Regression Model ◽  
Choquet Integral ◽  
Second Order ◽  
Fuzzy Measure ◽  
Model Based
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