• Title/Summary/Keyword: fuzzy regression model

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The Rank Transform Method in Nonparametric Fuzzy Regression Model

  • Choi, Seung-Hoe;Lee, Myung-Sook
    • Journal of the Korean Data and Information Science Society
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    • v.15 no.3
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    • pp.617-624
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    • 2004
  • In this article the fuzzy number rank and the fuzzy rank transformation method are introduced in order to analyse the non-parametric fuzzy regression model which cannot be described as a specific functional form such as the crisp data and fuzzy data as a independent and dependent variables respectively. The effectiveness of fuzzy rank transformation methods is compared with other methods through the numerical examples.

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Equivalence in Alpha-Level Linear Regression

  • Yoon, Jin-Hee;Jung, Hye-Young;Choi, Seung-Hoe
    • Communications for Statistical Applications and Methods
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    • v.17 no.4
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    • pp.611-624
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    • 2010
  • Several methods were suggested for constructing a fuzzy relationship between fuzzy independent and dependent variables. This paper reviews the use of the method by minimizing the square of the difference between an observed and a predicted fuzzy number in an ${\alpha}$-level linear regression model. We introduce a new distance between fuzzy numbers on the basis of a mode, a core point and a radius of an ${\alpha}$-level set of a fuzzy number an construct the fuzzy regression model using the proposed fuzzy distance. We also investigate sufficient condition for an equivalence in the ${\alpha}$-level regression model.

Thermal Error Modeling of a Horizontal Machining Center Using the Fuzzy Logic Strategy (퍼지논리를 이용한 수평 머시닝 센터의 열변형 오차 모델링)

  • Lee, Jae-Ha;Lee, Jin-Hyeon;Yang, Seung-Han
    • Transactions of the Korean Society of Mechanical Engineers A
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    • v.24 no.10 s.181
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    • pp.2589-2596
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    • 2000
  • As current manufacturing processes require high spindle speed and precise machining, increasing accuracy by reducing volumetric errors of the machine itself, particularly thermal errors, is very important. Thermal errors can be estimated by many empirical models, for example, an FEM model, a neural network model, a linear regression model, an engineering judgment model, etc. This paper discusses to make a modeling of thermal errors efficiently through backward elimination and fuzzy logic strategy. The model of a thermal error using fuzzy logic strategy overcomes limitation of accuracy in the linear regression model or the engineering judgment model. It shows that the fuzzy model has more better performance than linear regression model, though it has less number of thermal variables than the other. The fuzzy model does not need to have complex procedure such like multi-regression and to know the characteristics of the plant, and the parameters of the model can be mathematically calculated. Also, the fuzzy model can be applied to any machine, but it delivers greater accuracy and robustness.

ROBUST FUZZY LINEAR REGRESSION BASED ON M-ESTIMATORS

  • SOHN BANG-YONG
    • Journal of applied mathematics & informatics
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    • v.18 no.1_2
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    • pp.591-601
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    • 2005
  • The results of fuzzy linear regression are very sensitive to irregular data. When this points exist in a set of data, a fuzzy linear regression model can be incorrectly interpreted. The purpose of this paper is to detect irregular data and to propose robust fuzzy linear regression based on M-estimators with triangular fuzzy regression coefficients for crisp input-output data. Numerical example shows that irregular data can be detected by using the residuals based on M-estimators, and the proposed robust fuzzy linear regression is very resistant to this points.

ON THEIL'S METHOD IN FUZZY LINEAR REGRESSION MODELS

  • Choi, Seung Hoe;Jung, Hye-Young;Lee, Woo-Joo;Yoon, Jin Hee
    • Communications of the Korean Mathematical Society
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    • v.31 no.1
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    • pp.185-198
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    • 2016
  • Regression analysis is an analyzing method of regression model to explain the statistical relationship between explanatory variable and response variables. This paper propose a fuzzy regression analysis applying Theils method which is not sensitive to outliers. This method use medians of rate of increment based on randomly chosen pairs of each components of ${\alpha}$-level sets of fuzzy data in order to estimate the coefficients of fuzzy regression model. An example and two simulation results are given to show fuzzy Theils estimator is more robust than the fuzzy least squares estimator.

Self-Organizing Fuzzy Modeling Based on Hyperplane-Shaped Clusters (다차원 평면 클러스터를 이용한 자기 구성 퍼지 모델링)

  • Koh, Taek-Beom
    • Journal of Institute of Control, Robotics and Systems
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    • v.7 no.12
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    • pp.985-992
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    • 2001
  • This paper proposes a self-organizing fuzzy modeling(SOFUM)which an create a new hyperplane shaped cluster and adjust parameters of the fuzzy model in repetition. The suggested algorithm SOFUM is composed of four steps: coarse tuning. fine tuning cluster creation and optimization of learning rates. In the coarse tuning fuzzy C-regression model(FCRM) clustering and weighted recursive least squared (WRLS) algorithm are used and in the fine tuning gradient descent algorithm is used to adjust parameters of the fuzzy model precisely. In the cluster creation, a new hyperplane shaped cluster is created by applying multiple regression to input/output data with relatively large fuzzy entropy based on parameter tunings of fuzzy model. And learning rates are optimized by utilizing meiosis-genetic algorithm in the optimization of learning rates To check the effectiveness of the suggested algorithm two examples are examined and the performance of the identified fuzzy model is demonstrated via computer simulation.

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LEAST ABSOLUTE DEVIATION ESTIMATOR IN FUZZY REGRESSION

  • KIM KYUNG JOONG;KIM DONG HO;CHOI SEUNG HOE
    • Journal of applied mathematics & informatics
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    • v.18 no.1_2
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    • pp.649-656
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    • 2005
  • In this paper we consider a fuzzy least absolute deviation method in order to construct fuzzy linear regression model with fuzzy input and fuzzy output. We also consider two numerical examples to evaluate an effectiveness of the fuzzy least absolute deviation method and the fuzzy least squares method.

Fuzzy linear regression model and its application (퍼지 선형회귀모형과 응용)

  • 이성호;홍덕헌
    • The Korean Journal of Applied Statistics
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    • v.10 no.2
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    • pp.403-411
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    • 1997
  • Fuzzy linear regression model introduced by Tanaka et al. 91982) has been proposed and developed as alternative to statistical linear regression when our understanding of a phenomenon is imprecise or vague. In this paper we review fuzzy linear regression model and its parameter estimation and examine its strengths and weaknesses through case study. In addition another fuzzy linear model is introduced and applied to an economic study.

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

  • Yang, Zhihui;Yin, Yunqiang;Chen, Yizeng
    • Journal of Computing Science and Engineering
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    • v.7 no.4
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    • pp.263-271
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    • 2013
  • This study presents a fuzzy varying coefficient regression model after deleting the outliers to improve the feasibility and effectiveness of the fuzzy regression model. The objective of our methodology is to allow the fuzzy regression coefficients to vary with a covariate, and simultaneously avoid the impact of data contaminated by outliers. In this paper, fuzzy regression coefficients are represented by Gaussian fuzzy numbers. We also formulate suitable goodness of fit to evaluate the performance of the proposed methodology. An example is given to demonstrate the effectiveness of our methodology.

Fuzzy Semiparametric Support Vector Regression for Seasonal Time Series Analysis

  • Shim, Joo-Yong;Hwang, Chang-Ha;Hong, Dug-Hun
    • Communications for Statistical Applications and Methods
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    • v.16 no.2
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    • pp.335-348
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    • 2009
  • Fuzzy regression is used as a complement or an alternative to represent the relation between variables among the forecasting models especially when the data is insufficient to evaluate the relation. Such phenomenon often occurs in seasonal time series data which require large amount of data to describe the underlying pattern. Semiparametric model is useful tool in the case where domain knowledge exists about the function to be estimated or emphasis is put onto understandability of the model. In this paper we propose fuzzy semiparametric support vector regression so that it can provide good performance on forecasting of the seasonal time series by incorporating into fuzzy support vector regression the basis functions which indicate the seasonal variation of time series. In order to indicate the performance of this method, we present two examples of predicting the seasonal time series. Experimental results show that the proposed method is very attractive for the seasonal time series in fuzzy environments.