scholarly journals FUZZY PRINCIPAL COMPONENT REGRESSION (FPCR) FOR FUZZY INPUT AND OUTPUT DATA

2006 ◽  
Vol 14 (01) ◽  
pp. 87-100 ◽  
Author(s):  
JIH-JENG HUANG ◽  
GWO-HSHIUNG TZENG ◽  
CHORNG-SHYONG ONG
Keyword(s):  
Principal Component Analysis ◽  
Regression Model ◽  
Principal Component Regression ◽  
Principal Component ◽  
Fuzzy Regression ◽  
Output Data ◽  
Input And Output ◽  
Fuzzy Input ◽  
Fuzzy Regression Model ◽  
Component Scores

Although fuzzy regression is widely employed to solve many problems in practice, what seems to be lacking is the problem of multicollinearity. In this paper, the fuzzy centers principal component analysis is proposed to first derive the fuzzy principal component scores. Then the fuzzy principal component regression (FPCR) is formed to overcome the problem of multicollinearity in the fuzzy regression model. In addition, a numerical example is used to demonstrate the proposed method and compare with other methods. On the basis of the results, we can conclude that the proposed method can provide a correct fuzzy regression model and avoid the problem of multicollinearity.

Fuzzy Regression Model Based on Geometric Centroid and Incentre Points and Application to Performance Evaluation

2020 ◽  
Vol 28 (02) ◽  
pp. 269-288
Author(s):  
Yanbing Gong ◽  
Lin Xiang ◽  
Gaofeng Liu
Keyword(s):  
Regression Model ◽  
Least Squares ◽  
Least Squares Method ◽  
Estimation Error ◽  
Triangular Fuzzy Number ◽  
Fuzzy Regression ◽  
Distance Method ◽  
Fuzzy Input ◽  
Fuzzy Regression Model ◽  
Fuzzy Linear Regression Model

Fuzzy regression model is developed to construct the relationship between independent variable and dependent variable in a fuzzy environment. In order to increase the explanatory performance of fuzzy regression model, the least-squares method usually is applied to determine the numeric coefficients based on the concept of distance. In this paper, we consider the fuzzy linear regression model with fuzzy input, fuzzy output and crisp parameters and introduce a new distance based on the geometric centroid and incentre points (GCIP) of triangular fuzzy number, merge least-squares method with the new GCIP distance and propose least-squares GCIP distance method. Finally, an example of employee job performance is given to illustrate the effectiveness and feasibility of the method. Comparisons with existing methods show that total estimation error using the same distance criterion, the explanatory performance of the GCIP method is satisfactory, and the calculation is relatively simple.

scholarly journals On Optimal and Asymptotic Properties of a Fuzzy L2 Estimator

Mathematics ◽  
2020 ◽  
Vol 8 (11) ◽  
pp. 1956
Author(s):  
Jin Hee Yoon ◽  
Przemyslaw Grzegorzewski
Keyword(s):  
Regression Model ◽  
Asymptotic Properties ◽  
Asymptotic Relative Efficiency ◽  
Confidence Regions ◽  
Fuzzy Regression ◽  
Monte Carlo Simulation Study ◽  
Fuzzy Input ◽  
Fuzzy Regression Model ◽  
Algebraic Properties ◽  
Best Linear Unbiased

A fuzzy least squares estimator in the multiple with fuzzy-input–fuzzy-output linear regression model is considered. The paper provides a formula for the L2 estimator of the fuzzy regression model. This paper proposes several operations for fuzzy numbers and fuzzy matrices with fuzzy components and discussed some algebraic properties that are needed to use for proving theorems. Using the proposed operations, the formula for the variance, provided and this paper, proves that the estimators have several important optimal properties and asymptotic properties: they are Best Linear Unbiased Estimator (BLUE), asymptotic normality and strong consistency. The confidence regions of the coefficient parameters and the asymptotic relative efficiency (ARE) are also discussed. In addition, several examples are provided including a Monte Carlo simulation study showing the validity of the proposed theorems.

scholarly journals USNWR College Rankings Reexamined

2005 ◽  
Vol 2 (12) ◽  
Author(s):  
Thomas J. Webster ◽  
Rosette J. Mare
Keyword(s):  
Principal Component Analysis ◽  
Regression Model ◽  
Peer Assessment ◽  
Principal Component Regression ◽  
Principal Component ◽  
Act Scores ◽  
Relative Contribution ◽  
Ranking Criterion ◽  
National University ◽  
World Report

This paper extends Webster's [2001] analysis of the accuracy of the weighting scheme utilized by U.S. News & World Report (USNWR) to rank colleges and universities according to "widely accepted indicators of national excellence," which he found to be plagued by severe and pervasive multicollinearity.  As in the Webster study, we employ principal component analysis to assess the relative contributions of thirteen criteria used by USNWR in 2004 to rank "top schools" in the national university category.  Although USNWR continues to assign the greatest weight to peer assessment, this study confirms Webster's findings that average SAT/ACT scores of enrolled students is the most significant ranking criterion.  This paper also extends Webster's study by examining the reliability of the USNWR rankings, which have come under repeated criticism for their lack of consistency.  When compared with simulations generated from an estimated principal component regression model, the 2004 USNWR rankings are found to be increasingly more unreliable for lower ranked institutions.  The source of this inconsistency appears to be peer assessment, which is the only subjective criterion used in the USNWR ranking methodology.  This suggests that the rankings might be improved by lowering (or removing entirely) the relative contribution of peer assessment from the USNWR ranking methodology.

scholarly journals Reconstruction of critical coalbed methane logs with principal component regression model: A case study

2020 ◽  
Vol 38 (4) ◽  
pp. 1178-1193
Author(s):  
Wan Li ◽  
Tongjun Chen ◽  
Xiong Song ◽  
Tianqi Gong ◽  
Mengyue Liu
Keyword(s):  
Principal Component Analysis ◽  
Wavelet Analysis ◽  
Regression Model ◽  
Coalbed Methane ◽  
Multivariate Regression ◽  
Principal Component Regression ◽  
Principal Component ◽  
Component Analysis ◽  
Methane Content ◽  
Sonic Logs

Wireline logging plays a critical role in coalbed methane exploration. However, the lack of crucial log data, such as neutron and sonic logs, makes coalbed methane exploration difficult. In this paper, we propose a principal component regression model incorporating a multiscale wavelet analysis, a histogram calibration, a principal component analysis, and a multivariate regression to reconstruct essential neutron and sonic logs from conventional logs (i.e., density, resistivity, gamma ray, spontaneous potential, and caliper logs). Our proposed model does not need core-related correlation, and there is no local optimization. We have applied the model to evaluate coalbed methane content in a real case. Firstly, we use the multiscale wavelet analysis and histogram calibration to improve logs’ reliability and lateral comparability. Then, we apply principal component analysis to transform the well-correlated wireline logs into linearly independent components and regress reconstruction functions for neutron and sonic logs with multivariate regression. The reconstructed logs are like the measured logs in trend, mean, and scale. Finally, we apply the reconstructed neutron logs to predict the coalbed methane-content distribution. The predicted distribution is not only following the regional distribution characteristics of coalbed methane enrichment zones but also validated by the coalbed methane production data. In summary, the successful applications of wireline-log reconstruction and regional coalbed methane-content prediction have demonstrated the reliability of the proposed principal component regression model.

scholarly journals Subspace Method Aided Data-Driven Fault Detection Based on Principal Component Analysis

2017 ◽  
Vol 2017 ◽  
pp. 1-8
Author(s):  
Lingling Ma ◽  
Xiangshun Li
Keyword(s):  
Principal Component Analysis ◽  
Fault Detection ◽  
Principal Component ◽  
Component Analysis ◽  
Data Driven ◽  
Subspace Method ◽  
Output Data ◽  
Tennessee Eastman Process ◽  
System Models ◽  
Input And Output

The model-based fault detection technique, which needs to identify the system models, has been well established. The objective of this paper is to develop an alternative procedure instead of identifying the system models. In this paper, subspace method aided data-driven fault detection based on principal component analysis (PCA) is proposed. The basic idea is to use PCA to identify the system observability matrices from input and output data and construct residual generators. The advantage of the proposed method is that we just need to identify the parameterized matrices related to residuals rather than the system models, which reduces the computational steps of the system. The proposed approach is illustrated by a simulation study on the Tennessee Eastman process.

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