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.

A Novel Composition Forecasting Model Based on Choquet Integral with Respect to L-Measure and O-Density

2012 ◽  
Vol 472-475 ◽  
pp. 1245-1248
Author(s):  
Hsiang Chuan Liu ◽  
Bai Cheng Jeng ◽  
Yen Kuei Yu ◽  
Shang Ling Ou ◽  
Yih Chang Ou ◽  
...  
Keyword(s):  
Linear Regression ◽  
Multiple Linear Regression ◽  
Mean Square Error ◽  
Ridge Regression ◽  
Choquet Integral ◽  
Real Data ◽  
Forecasting Model ◽  
Mean Square ◽  
Forecasting Models ◽  
Weighted Composition

In this paper, based on L-measure and O-density, a novel composition forecasting model is proposed. For evaluating this new composition forecasting model, a real data experiment by using the sequential mean square error was conducted. Based on O-density, the performances of Choquet integral composition forecasting model with the L-measure, Lambda-measure and P-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. Experimental results show that the Choquet integral composition forecasting model with respect to the L-measure outperforms other 5 composition forecasting models.

scholarly journals A Novel Fuzzy Time Series Forecasting Model Based on Multiple Linear Regression and Time Series Clustering

2020 ◽  
Vol 2020 ◽  
pp. 1-17
Author(s):  
Yanpeng Zhang ◽  
Hua Qu ◽  
Weipeng Wang ◽  
Jihong Zhao
Keyword(s):  
Time Series ◽  
Linear Regression ◽  
Multiple Linear Regression ◽  
Time Series Forecasting ◽  
High Order ◽  
Fuzzy Time Series ◽  
Forecasting Model ◽  
Time Series Clustering ◽  
Proposed Model ◽  
High Order Time

Time series forecasting models based on a linear relationship model show great performance. However, these models cannot handle the the data that are incomplete, imprecise, and ambiguous as the interval-based fuzzy time series models since the process of fuzzification is abandoned. This article proposes a novel fuzzy time series forecasting model based on multiple linear regression and time series clustering for forecasting market prices. The proposed model employs a preprocessing to transform the set of fuzzy high-order time series into a set of high-order time series, with synthetic minority oversampling technique. After that, a high-order time series clustering algorithm based on the multiple linear regression model is proposed to cluster dataset of fuzzy time series and to build the linear regression model for each cluster. Then, we make forecasting by calculating the weighted sum of linear regression models’ results. Also, a learning algorithm is proposed to train the whole model, which applies artificial neural network to learn the weights of linear models. The interval-based fuzzification ensures the capability to deal with the uncertainties, and linear model and artificial neural network enable the proposed model to learn both of linear and nonlinear characteristics. The experiment results show that the proposed model improves the average forecasting accuracy rate and is more suitable for dealing with these uncertainties.

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.

scholarly journals A Neutrosophic Forecasting Model for Time Series Based on First-Order State and Information Entropy of High-Order Fluctuation

Entropy ◽  
2019 ◽  
Vol 21 (5) ◽  
pp. 455 ◽  
Author(s):  
Hongjun Guan ◽  
Zongli Dai ◽  
Shuang Guan ◽  
Aiwu Zhao
Keyword(s):  
Time Series ◽  
Information Entropy ◽  
Stock Exchange ◽  
Time Series Forecasting ◽  
High Order ◽  
Stock Index ◽  
Neutrosophic Set ◽  
Forecasting Model ◽  
Forecasting Models ◽  
Proposed Model

In time series forecasting, information presentation directly affects prediction efficiency. Most existing time series forecasting models follow logical rules according to the relationships between neighboring states, without considering the inconsistency of fluctuations for a related period. In this paper, we propose a new perspective to study the problem of prediction, in which inconsistency is quantified and regarded as a key characteristic of prediction rules. First, a time series is converted to a fluctuation time series by comparing each of the current data with corresponding previous data. Then, the upward trend of each of fluctuation data is mapped to the truth-membership of a neutrosophic set, while a falsity-membership is used for the downward trend. Information entropy of high-order fluctuation time series is introduced to describe the inconsistency of historical fluctuations and is mapped to the indeterminacy-membership of the neutrosophic set. Finally, an existing similarity measurement method for the neutrosophic set is introduced to find similar states during the forecasting stage. Then, a weighted arithmetic averaging (WAA) aggregation operator is introduced to obtain the forecasting result according to the corresponding similarity. Compared to existing forecasting models, the neutrosophic forecasting model based on information entropy (NFM-IE) can represent both fluctuation trend and fluctuation consistency information. In order to test its performance, we used the proposed model to forecast some realistic time series, such as the Taiwan Stock Exchange Capitalization Weighted Stock Index (TAIEX), the Shanghai Stock Exchange Composite Index (SHSECI), and the Hang Seng Index (HSI). The experimental results show that the proposed model can stably predict for different datasets. Simultaneously, comparing the prediction error to other approaches proves that the model has outstanding prediction accuracy and universality.

Forecasting stock market price by using fuzzified Choquet integral based fuzzy measures with genetic algorithm for parameter optimization

2020 ◽  
Vol 54 (2) ◽  
pp. 597-614
Author(s):  
Shanoli Samui Pal ◽  
Samarjit Kar
Keyword(s):  
Genetic Algorithm ◽  
Time Series ◽  
Linear Regression ◽  
Regression Model ◽  
Choquet Integral ◽  
Time Series Forecasting ◽  
Fuzzy Measure ◽  
Model Parameters ◽  
Forecasting Models ◽  
Non Linear

In this paper, fuzzified Choquet integral and fuzzy-valued integrand with respect to separate measures like fuzzy measure, signed fuzzy measure and intuitionistic fuzzy measure are used to develop regression model for forecasting. Fuzzified Choquet integral is used to build a regression model for forecasting time series with multiple attributes as predictor attributes. Linear regression based forecasting models are suffering from low accuracy and unable to approximate the non-linearity in time series. Whereas Choquet integral can be used as a general non-linear regression model with respect to non classical measures. In the Choquet integral based regression model parameters are optimized by using a real coded genetic algorithm (GA). In these forecasting models, fuzzified integrands denote the participation of an individual attribute or a group of attributes to predict the current situation. Here, more generalized Choquet integral, i.e., fuzzified Choquet integral is used in case of non-linear time series forecasting models. Three different real stock exchange data are used to predict the time series forecasting model. It is observed that the accuracy of prediction models highly depends on the non-linearity of the time series.

Credible Intervals for Precision and Recall Based on a K-Fold Cross-Validated Beta Distribution

2016 ◽  
Vol 28 (8) ◽  
pp. 1694-1722 ◽  
Author(s):  
Yu Wang ◽  
Jihong Li
Keyword(s):  
Confidence Intervals ◽  
Cross Validation ◽  
Real Data ◽  
Credible Interval ◽  
Interval Length ◽  
Data Sets ◽  
Credible Intervals ◽  
Degree Of Confidence ◽  
T Distribution ◽  
Fold Cross Validation

In typical machine learning applications such as information retrieval, precision and recall are two commonly used measures for assessing an algorithm's performance. Symmetrical confidence intervals based on K-fold cross-validated t distributions are widely used for the inference of precision and recall measures. As we confirmed through simulated experiments, however, these confidence intervals often exhibit lower degrees of confidence, which may easily lead to liberal inference results. Thus, it is crucial to construct faithful confidence (credible) intervals for precision and recall with a high degree of confidence and a short interval length. In this study, we propose two posterior credible intervals for precision and recall based on K-fold cross-validated beta distributions. The first credible interval for precision (or recall) is constructed based on the beta posterior distribution inferred by all K data sets corresponding to K confusion matrices from a K-fold cross-validation. Second, considering that each data set corresponding to a confusion matrix from a K-fold cross-validation can be used to infer a beta posterior distribution of precision (or recall), the second proposed credible interval for precision (or recall) is constructed based on the average of K beta posterior distributions. Experimental results on simulated and real data sets demonstrate that the first credible interval proposed in this study almost always resulted in degrees of confidence greater than 95%. With an acceptable degree of confidence, both of our two proposed credible intervals have shorter interval lengths than those based on a corrected K-fold cross-validated t distribution. Meanwhile, the average ranks of these two credible intervals are superior to that of the confidence interval based on a K-fold cross-validated t distribution for the degree of confidence and are superior to that of the confidence interval based on a corrected K-fold cross-validated t distribution for the interval length in all 27 cases of simulated and real data experiments. However, the confidence intervals based on the K-fold and corrected K-fold cross-validated t distributions are in the two extremes. Thus, when focusing on the reliability of the inference for precision and recall, the proposed methods are preferable, especially for the first credible interval.

Multi-factor high-order intuitionistic fuzzy time series forecasting model

2016 ◽  
Vol 27 (5) ◽  
pp. 1054-1062 ◽  
Author(s):  
Ya'nan Wang ◽  
◽  
Yingjie Lei ◽  
Yang Lei ◽  
Xiaoshi Fan
Keyword(s):  
Time Series ◽  
Time Series Forecasting ◽  
High Order ◽  
Fuzzy Time Series ◽  
Forecasting Model ◽  
Intuitionistic Fuzzy

A weighted coefficient model for estimation of Australian daily soil temperature at depths of 5cm to 100cm based on air temperature and rainfall

Soil Research ◽  
2011 ◽  
Vol 49 (4) ◽  
pp. 305 ◽  
Author(s):  
Brian Horton ◽  
Ross Corkrey
Keyword(s):  
Soil Temperature ◽  
Air Temperature ◽  
Cross Validation ◽  
Soil Depth ◽  
Mean Square ◽  
Air Temperatures ◽  
Proposed Model ◽  
Soil Temperatures ◽  
Weather Stations ◽  
Fold Cross Validation

Soil temperatures are related to air temperature and rainfall on the current day and preceding days, and this can be expressed in a non-linear relationship to provide a weighted value for the effect of air temperature or rainfall based on days lag and soil depth. The weighted minimum and maximum air temperatures and weighted rainfall can then be combined with latitude and a seasonal function to estimate soil temperature at any depth in the range 5–100 cm. The model had a root mean square deviation of 1.21–1.85°C for minimum, average, and maximum soil temperature for all weather stations in Australia (mainland and Tasmania), except for maximum soil temperature at 5 and 10 cm, where the model was less precise (3.39° and 2.52°, respectively). Data for this analysis were obtained from 32–40 Bureau of Meteorology weather stations throughout Australia and the proposed model was validated using 5-fold cross-validation.

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