Boscovich Fuzzy Regression Line

We introduce a new fuzzy linear regression method. The method is capable of approximating fuzzy relationships between an independent and a dependent variable. The independent and dependent variables are expected to be a real value and triangular fuzzy numbers, respectively. We demonstrate on twenty datasets that the method is reliable, and it is less sensitive to outliers, compare with possibilistic-based fuzzy regression methods. Unlike other commonly used fuzzy regression methods, the presented method is simple for implementation and it has linear time-complexity. The method guarantees non-negativity of model parameter spreads.

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A new method to the fuzzy linear regression with triangular fuzzy numbers

IEEE Annual Meeting of the Fuzzy Information, 2004. Processing NAFIPS '04. ◽

10.1109/nafips.2004.1336304 ◽

2004 ◽

Author(s):

Zhang-xia Zhu ◽

Bing-yuan Cao

Keyword(s):

Linear Regression ◽

Fuzzy Numbers ◽

New Method ◽

Triangular Fuzzy Numbers ◽

Fuzzy Linear Regression

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RIDGE REGRESSION PROCEDURES FOR FUZZY MODELS USING TRIANGULAR FUZZY NUMBERS

International Journal of Uncertainty Fuzziness and Knowledge-Based Systems ◽

10.1142/s0218488504002746 ◽

2004 ◽

Vol 12 (02) ◽

pp. 145-159 ◽

Cited By ~ 11

Author(s):

DUG HUN HONG ◽

CHANGHA HWANG

Keyword(s):

Nonlinear Regression ◽

Ridge Regression ◽

Fuzzy Numbers ◽

Linear Models ◽

Estimation Method ◽

Feature Space ◽

Triangular Fuzzy Numbers ◽

Fuzzy Linear Regression ◽

Data Set ◽

Nonlinear Regression Models

This paper presents a new method of estimating fuzzy multivariable linear and nonlinear regression models using triangular fuzzy numbers. This estimation method is obtained by implementing a dual version of the ridge regression procedure for linear models. It allows us to perform fuzzy nonlinear regression by constructing a fuzzy linear regression in a high dimensional feature space for the data set with crisp inputs and fuzzy output. Experimental results are then presented, which indicate the performance of this algorithm.

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Bounds Pricing Method of Currency Options Based on Triangular Fuzzy Numbers, Fuzzy Programming and Fuzzy Regression

2009 International Association of Computer Science and Information Technology - Spring Conference ◽

10.1109/iacsit-sc.2009.109 ◽

2009 ◽

Author(s):

Fan-Yong Liu

Keyword(s):

Fuzzy Numbers ◽

Fuzzy Programming ◽

Fuzzy Regression ◽

Triangular Fuzzy Numbers ◽

Currency Options

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A Systematic Approach to OptimizinghValue for Fuzzy Linear Regression with Symmetric Triangular Fuzzy Numbers

Mathematical Problems in Engineering ◽

10.1155/2013/210164 ◽

2013 ◽

Vol 2013 ◽

pp. 1-9 ◽

Cited By ~ 9

Author(s):

Xilong Liu ◽

Yizeng Chen

Keyword(s):

Linear Regression ◽

Systematic Approach ◽

Fuzzy Numbers ◽

Programming Model ◽

Numerical Study ◽

Triangular Fuzzy Numbers ◽

Fuzzy Linear Regression ◽

The Real ◽

Optimal Value ◽

Sample Data

A systematic approach is proposed to optimizehvalue for fuzzy linear regression (FLR) analysis using minimum fuzziness criteria with symmetric triangular fuzzy numbers (TFNs). Firstly, a new concept of credibility is defined to evaluate the performance of FLR models with differenthvalues when a set of sample data pairs is given. Secondly, based on the defined concept of credibility, a programming model is formulated to optimize the value ofh. Finally, both the numerical study and the real application show that the approach proposed in this paper is effective and efficient; that is, optimal value forhcan be determined definitely with respect to a set of given sample data pairs.

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A Learn Of Fuzzy Regression Model and its Applications

International Journal of Recent Technology and Engineering - 2 ◽

10.35940/ijrte.b2415.078219 ◽

2019 ◽

Vol 8 (2) ◽

pp. 2967-2971

Keyword(s):

Linear Regression ◽

Regression Model ◽

Linear Regression Model ◽

Fuzzy Numbers ◽

Fuzzy Regression ◽

Regression Coefficients ◽

Fuzzy Linear Regression ◽

Fuzzy Regression Model ◽

Fuzzy Linear Regression Model

Many statistics report shown in fuzzy module into clear problems using the centroid system, consequently we will research the usual linear regression model which is modified from the fuzzy linear regression model. The models enter and generate fuzzy numbers, and the regression coefficients are clear numbers. Hybrid algorithms are considered to fit the fuzzy regression model. So that the validity and quality of the suggested methods can be guaranteed. Therefore,the parameter estimation and have an impact on evaluation situated on knowledge deletion. By way of the gain knowledge of example and evaluation with other model, it may be concluded that the model in this paper is utilized without difficulty and better.

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Multivariate Matrix for Fuzzy Linear Regression Model to Analyse The Taxation in Malaysia

International Journal of Engineering & Technology ◽

10.14419/ijet.v7i4.33.23490 ◽

2018 ◽

Vol 7 (4.33) ◽

pp. 78

Author(s):

Noor Hidayah Mohamed Isa ◽

Mahmod Othman ◽

Samsul Ariffin Abdul Karim

Keyword(s):

Linear Regression ◽

World Bank ◽

Fuzzy Numbers ◽

Tax Revenue ◽

Triangular Fuzzy Numbers ◽

Fuzzy Linear Regression ◽

Independent Variables ◽

Fuzzy Linear Regression Model ◽

Merchandise Trade ◽

The Relationship

A multivariate matrix is proposed to find the best factor for fuzzy linear regression (FLR) with symmetric triangular fuzzy numbers (TFNs). The goal of this paper is to select the best factor influence tax revenue among four variables. Eighteen years’ data of the variables from IndexMundi and World Bank Data. It is found that the model is successfully explained between independent variables and response variable. It is notices that sixty-six percent of the variance of tax revenue is explained by Gross Domestic Product, Inflation, Unemployment and Merchandise Trade. The introduction of multivariate matrix for fuzzy linear regression in taxation is a first attempt to analyses the relationship the tax revenue with the independent variables.

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Algorithm 1017

ACM Transactions on Mathematical Software ◽

10.1145/3451389 ◽

2021 ◽

Vol 47 (3) ◽

pp. 1-18

Author(s):

Pavel Škrabánek ◽

Natália Martínková

Keyword(s):

Linear Regression ◽

Goodness Of Fit ◽

Fuzzy Numbers ◽

Linear Models ◽

Total Error ◽

Estimation Method ◽

Fuzzy Regression ◽

Model Parameters ◽

Statistical Regression ◽

Fuzzy Linear Regression

Fuzzy regression provides an alternative to statistical regression when the model is indefinite, the relationships between model parameters are vague, the sample size is low, or the data are hierarchically structured. Such cases allow to consider the choice of a regression model based on the fuzzy set theory. In fuzzyreg, we implement fuzzy linear regression methods that differ in the expectations of observational data types, outlier handling, and parameter estimation method. We provide a wrapper function that prepares data for fitting fuzzy linear models with the respective methods from a syntax established in R for fitting regression models. The function fuzzylm thus provides a novel functionality for R through standardized operations with fuzzy numbers. Additional functions allow for conversion of real-value variables to be fuzzy numbers, printing, summarizing, model plotting, and calculation of model predictions from new data using supporting functions that perform arithmetic operations with triangular fuzzy numbers. Goodness of fit and total error of the fit measures allow model comparisons. The package contains a dataset named bats with measurements of temperatures of hibernating bats and the mean annual surface temperature reflecting the climate at the sampling sites. The predictions from fuzzy linear models fitted to this dataset correspond well to the observed biological phenomenon. Fuzzy linear regression has great potential in predictive modeling where the data structure prevents statistical analysis and the modeled process exhibits inherent fuzziness.

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