Fuzzy Linear Regression Using Gaussian Fuzzy Numbers

2020 ◽  
Vol 30 (5) ◽  
pp. 386-390
Author(s):  
Seongeun Lim ◽  
Jin Hee Yoon
Keyword(s):  
Linear Regression ◽  
Fuzzy Numbers ◽  
Fuzzy Linear Regression

A fuzzy multiple linear regression model based on meteorological factors for air quality index forecast

2021 ◽  
pp. 1-25
Author(s):  
Yujie Gu ◽  
Yuxiu Zhao ◽  
Jian Zhou ◽  
Hui Li ◽  
Yujie Wang
Keyword(s):  
Air Quality ◽  
Linear Regression ◽  
Linear Regression Model ◽  
Regression Models ◽  
Quality Index ◽  
Fuzzy Numbers ◽  
Meteorological Factors ◽  
Multiple Linear Regression Model ◽  
Linear Regression Models ◽  
Fuzzy Linear Regression

Air quality index (AQI) is an indicator usually issued on a daily basis to inform the public how good or bad air quality recently is or how it will become over the next few days, which is of utmost importance in our life. To provide a more practicable way for AQI prediction, so that residents can clear about air conditions and make further plans, five imperative meteorological indicators are elaborately selected. Accordingly, taking these indicators as independent variables, a fuzzy multiple linear regression model with Gaussian fuzzy coefficients is proposed and reformulated, based on the linearity of Gaussian fuzzy numbers and Tanaka’s minimum fuzziness criterion. Subsequently, historical data in Shanghai from March 2016 to February 2018 are extracted from the government database and divided into two parts, where the first half is statistically analyzed and used for formulating four seasonal fuzzy linear regression models in views of the special climate environment of Shanghai, and the second half is used for prediction to validate the performance of the proposed model. Furthermore, considering that there is beyond dispute that triangular fuzzy number is more prevalent and crucial in the field of fuzzy studies for years, plenty of comparisons between the models based on the two types of fuzzy numbers are carried out by means of the three measures including the membership degree, the fuzziness and the credibility. The results demonstrate the powerful effectiveness and efficiency of the fuzzy linear regression models for AQI prediction, and the superiority of Gaussian fuzzy numbers over triangular fuzzy numbers in presenting the relationships between the meteorological factors and AQI.

scholarly journals Privacy-Preserving Two-Party Computation of Parameters of a Fuzzy Linear Regression

2021 ◽  
pp. 11-19
Author(s):  
Elena Volkova ◽  
◽  
Vladimir Gisin ◽  
Keyword(s):  
Linear Programming ◽  
Linear Regression ◽  
Programming Problem ◽  
Linear Programming Problem ◽  
Fuzzy Numbers ◽  
Optimization Problems ◽  
Observation Data ◽  
Fuzzy Linear Regression ◽  
Explanatory Variables ◽  
Common Criterion

Purpose: describe two-party computation of fuzzy linear regression with horizontal partitioning of data, while maintaining data confidentiality. Methods: the computation is designed using a transformational approach. The optimization problems of each of the two participants are transformed and combined into a common problem. The solution to this problem can be found by one of the participants. Results: A protocol is proposed that allows two users to obtain a fuzzy linear regression model based on the combined data. Each of the users has a set of data about the results of observations, containing the values of the explanatory variables and the values of the response variable. The data structure is shared: both users use the same set of explanatory variables and a common criterion. Regression coefficients are searched for as symmetric triangular fuzzy numbers by solving the corresponding linear programming problem. It is assumed that both users are semihonest (honest but curious, or passive and curious), i.e. they execute the protocol, but can try to extract information about the source data of the partner by applying arbitrary processing methods to the received data that are not provided for by the protocol. The protocol describes the transformed linear programming problem. The solution of this problem can be found by one of the users. The number of observations of each user is known to both users. The observation data remains confidential. The correctness of the protocol is proved and its security is justified. Keywords: fuzzy numbers, collaborative solution of a linear programming problem, two-way computation, transformational approach, cloud computing, federated machine learning.

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

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
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.

scholarly journals A Learn Of Fuzzy Regression Model and its Applications

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.

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

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.  

FUZZY LINEAR REGRESSION ANALYSIS FROM THE POINT OF VIEW RISK

2004 ◽  
Vol 12 (05) ◽  
pp. 635-649 ◽  
Author(s):  
MOHAMMAD MODARRES ◽  
EBRAHIM NASRABADI ◽  
MOHAMMAD MEHDI NASRABADI
Keyword(s):  
Linear Regression ◽  
Regression Models ◽  
Fuzzy Numbers ◽  
Linear Regression Analysis ◽  
Point Of View ◽  
Risk Averse ◽  
Linear Regression Models ◽  
Fuzzy Linear Regression ◽  
Risk Seeking ◽  
The Difference

In this paper, fuzzy linear regression models with fuzzy/crisp output, fuzzy/crisp input are considered. In this regard, we define risk-neutral, risk-averse and risk-seeking fuzzy linear regression models. In order to do that, two equality indices are applied to express the degree of equality between a pair of fuzzy numbers. We also develop three mathematical models to obtain the parameters of fuzzy linear regression models. Minimizing the difference between the total spread of the observed and estimated values is the objective of these models. The advantage of our proposed models is the simplicity in programming and computation.

scholarly journals The Use of Fuzzy Estimators for the Construction of a Prediction Model Concerning an Environmental Ecosystem

2019 ◽  
Vol 11 (18) ◽  
pp. 5039
Author(s):  
Georgia Ellina ◽  
Garyfalos Papaschinopoulos ◽  
Basil Papadopoulos
Keyword(s):  
Experimental Data ◽  
Fuzzy Logic ◽  
Linear Regression ◽  
Prediction Model ◽  
Shallow Lakes ◽  
Water Body ◽  
Fuzzy Numbers ◽  
Fuzzy Linear Regression ◽  
Fuzzy Implications ◽  
Close Interval

As a variable system, the Lake of Kastoria is a good example regarding the pattern of the Mediterranean shallow lakes. The focus of this study is on the investigation of this lake’s eutrophication, analyzing the relation of the basic factors that affect this phenomenon using fuzzy logic. In the method we suggest, while there are many fuzzy implications that can be used since the proposition can take values in the close interval [0,1], we investigate the most appropriate implication for the studied water body. We propose a method evaluating fuzzy implications by constructing triangular non-asymptotic fuzzy numbers for each of the studied parameters coming from experimental data. This is achieved with the use of fuzzy estimators and fuzzy linear regression. In this way, we achieve a better understanding of the mechanisms and functions that regulate this ecosystem.

Algorithm 1017

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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