Robust Fuzzy Varying Coefficient Regression Analysis with Crisp Inputs and Gaussian Fuzzy Output

Yang, Zhihui; Yin, Yunqiang; Chen, Yizeng

doi:10.5626/jcse.2013.7.4.263

Cited by 16 publications

(3 citation statements)

References 26 publications

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“…While engineering and environmental research prevail as implementation areas, the second largest group is that of business administration and economics. Case studies in that respect range from workforce forecasting [43] to project evaluations [33], analysis of macroeconomic parameters [58; 42], analysis of gross domenstic product [75], and stock price forecasting [38].…”

Section: Linear Regression Analysis Problem Over Fuzzy Datamentioning

confidence: 99%

Outlier Detection Algorithms Over Fuzzy Data with Weighted Least Squares

Nikolova

Rodríguez

Symes

et al. 2021

Int. J. Fuzzy Syst.

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In the classical leave-one-out procedure for outlier detection in regression analysis, we exclude an observation, then construct a model on the remaining data. If the difference between predicted and observed value is high we declare this value an outlier. As a rule, those procedures utilize single comparison testing. The problem becomes much harder when the observations can be associated with a given degree of membership to an underlying population and the outlier detection should be generalized to operate over fuzzy data. We present a new approach for outlier that operates over fuzzy data using two inter-related algorithms. Due to the way outliers enter the observation sample, they may be of various order of magnitude. To account for this, we divided the outlier detection procedure into cycles. Furthermore, each cycle consists of two phases. In Phase 1 we apply a leave-one-out procedure for each nonoutlier in the data set. In Phase 2, all previously declared outliers are subjected to Benjamini-Hochberg step-up multiple testing procedure controlling the false discovery rate, and the non-confirmed outliers can return to the data set. Finally, we construct a regression model over the resulting set of non-outliers. In that way we ensure that a reliable and high-quality regression model is obtained in Phase 1 because the leaveone-out procedure comparatively easily purges the dubious observations due to the single comparison testing. In the same time, the confirmation of the outlier status in relation to the newly obtained high-quality regression model is much harder due to the multiple testing procedure applied hence only the true outliers remain outside the data sample. The two phases in each cycle are a good trade-off between the desire to construct a high-quality model (i.e. over informative data points) and the desire to use as much data points as possible (thus leaving as much observations as possible in the data sample). The number of cycles is user-defined, but the procedures can finalize the analysis in case a cycle with no new outliers is detected. We offer one illustrative example and two other practical case studies (from real-life thrombosis studies) that demonstrate the application and strengths of our algorithms. In the concluding section, we discuss several limitations of our approach and also offer directions for future research. Keywords: regression analysis, leave-one-out method, degree of membership, multiple testing, Benjamini-Hochberg step-up multiple testing, false-discovery rate Highlights: -We develop algorithms for outlier rejection over fuzzy samples using weighted least squares that operate in a given number of cycles -Each cycle has two phases -use single testing leave-one-out procedure for initial purging of data, then confirm the previous outlier status with multiple testing -We offer one illustrative example and two examples from a case study in thrombosis research to show the strength of our cycle-based approach

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Section: Linear Regression Analysis Problem Over Fuzzy Datamentioning

confidence: 99%

Outlier Detection Algorithms Over Fuzzy Data with Weighted Least Squares

Nikolova

Rodríguez

Symes

et al. 2021

Int. J. Fuzzy Syst.

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“…Wang et al [45] proposed a fuzzy non-parametric model with crisp input and LRfuzzy output based on the local linear smoothing technique with a cross-validation procedure to select the optimal value of the smoothing parameter to fit the model. Additionally, Hesamian and Akbari [47] and Yang and Yin [47] proposed some fuzzy multiple regression model with fuzzy varying coefficients based on exact predictors and fuzzy responses.…”

Section: Introductionmentioning

confidence: 99%

A Fuzzy Linear Regression Model With Functional Predictors And Fuzzy Responses

Hesamian¹,

Mg²

2021

Preprint

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A novel functional regression model was introduced, where the predictor was a curve linked to a scalar fuzzy response variable. An absolute error-based penalized method with SCAD loss function was proposed to evaluate the unknown components of the model. For this purpose, a concept of fuzzy-valued function was developed and discussed. Then, a fuzzy large number notion was proposed to estimate the fuzzyvalued function. Some common goodness-of-fit criteria were also used to examine the performance of the proposed method. Efficiency of the proposed method was then evaluated through two numerical examples, including a simulation study and an applied example in the scope of watershed management. The proposed method was also compared with several common fuzzy regression models in cases where the functional data was converted to scalar ones.

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“…Wang et al (2007) proposed a fuzzy nonparametric model with crisp input and L R-fuzzy output on the basis of the local linear smoothing technique with a cross-validation procedure to select the optimal value of the smoothing parameter to fit the model. Additionally, Yang and Yin (2013) proposed some fuzzy multiple regression models with fuzzy varying coefficients which rely on exact predictors and fuzzy responses.…”

Section: Introductionmentioning

confidence: 99%

A fuzzy functional linear regression model with functional predictors and fuzzy responses

Hesamian

Akbari

2021

Soft Comput

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A novel functional regression model was introduced in this research in which, the predictor is a curve linked to a scalar fuzzy response variable. An absolute error-based penalized method with SCAD loss function was also proposed to evaluate the unknown components of the model. For this purpose, a concept of fuzzy-valued function was developed and discussed. Then, a fuzzy large number notion was proposed to estimate the fuzzy-valued function. The performance of the proposed method was examined by some common goodness-of-fit criteria. The efficiency of the proposed method was then evaluated through two numerical examples; a simulation study and an applied example in the scope of watershed management. The proposed method was also compared with several common fuzzy regression models in cases where the functional data were converted to scalar ones.

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Robust Fuzzy Varying Coefficient Regression Analysis with Crisp Inputs and Gaussian Fuzzy Output

Cited by 16 publications

References 26 publications

Outlier Detection Algorithms Over Fuzzy Data with Weighted Least Squares

Outlier Detection Algorithms Over Fuzzy Data with Weighted Least Squares

A Fuzzy Linear Regression Model With Functional Predictors And Fuzzy Responses

A fuzzy functional linear regression model with functional predictors and fuzzy responses

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