A simple method for computation of fuzzy linear regression

Hojati, Mehran; Bector, C. R.; Smimou, K.

doi:10.1016/j.ejor.2004.01.039

Cited by 156 publications

(93 citation statements)

References 13 publications

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“…Probable basis function (PBF) neural network forms one of the essential type of neural networks. In this paper, we proposed simple but powerful method for fuzzy regression analysis using PBF neural network, since the proposed method employ PBF neural network which have higher flexibility and a wider application field than the existing LP based and FLS fuzzy regression methods [12][13][14][15][16]. The effectiveness of our method was demonstrated by three examples and a computational experience.…”

mentioning

confidence: 86%

Numerical Solution of Fuzzy linear Regression using Fuzzy Neural Network Based on Probability Function

Ezadi¹,

Askari²

2017

Journal of Fuzzy Set Valued Analysis

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In this work, we consider the development of a fuzzy neural network based on probability function for Estimated output of fuzzy regression models with test real input and fuzzy output. The proposed approach is a fuzzification of the outputs and weights of conventional fuzzy neural network based on probability function. The error of the proposed method is based on total square error is minimized by optimization method in order to be able to obtain the optimal weights of the neural network. The advantage of the proposed approach is its simplicity and computation as well as its performance. To compare the performance of the proposed method with the other traditional methods given in the literature several numerical examples are presented.

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confidence: 86%

Numerical Solution of Fuzzy linear Regression using Fuzzy Neural Network Based on Probability Function

Ezadi¹,

Askari²

2017

Journal of Fuzzy Set Valued Analysis

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“…In general, fuzzy regression methods are divided into two categories: the first one is based on linear programming (LP) approach and the second one is based on the fuzzy least squares (FLS) approach. The first class which minimizes the total vagueness of the estimated values for the output includes Tanaka et al's [46] method and its extensions [20,33,40,45,46]. The sec-ond class includes FLS methods to minimize the total square of errors in the estimated values [15,16,31,48].…”

Section: Fuzzy Regression Methodsmentioning

confidence: 99%

“…Yang and Lin [48] proposed two estimation methods along with an FLS approach for considered FLR models with fuzzy inputs, fuzzy outputs and fuzzy parameters. Hojati et al [20] proposed a simple goal programming-like approach for computation of FR for two cases: crisp inputs-fuzzy outputs and fuzzy inputs-fuzzy outputs. Chen and Dang [10] proposed a three-phase method to construct the FR model with variable spreads to resolve the problem of increasing spreads.…”

Section: Introductionmentioning

confidence: 99%

“…In general, there are two main approaches in FR analysis: linear programmingbased methods and FLS-based methods. The first one is based on minimizing fuzziness as an optimal criterion [4][5][6]8,20,33,[36][37][38][40][41][42]45,47], whereas the second one is based on least squares (LS) of errors as a fitting criterion [3,9,15,16,[25][26][27]31,48].…”

Section: Introductionmentioning

confidence: 99%

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Fuzzy radial basis function network for fuzzy regression with fuzzy input and fuzzy output

Pehlivan

Apaydin

2016

Complex Intell. Syst.

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In this study, fuzzy regression (FR) models with fuzzy inputs and outputs are discussed. Some of the FR methods based on linear programming and fuzzy least squares in the literature are explained. Within this study, we propose a Fuzzy Radial Basis Function (FRBF) Network to obtain the estimations for FR model in the case that inputs and outputs are symmetric/nonsymmetric triangular fuzzy numbers. Proposed FRBF Network approach is a fuzzification of the inputs, outputs and weights of traditional RBF Network and it can be used as an alternative to FR methods. The FRBF Network approach is constructed on the basis of minimizing the square of the total difference between observed and estimated outputs. A simple training algorithm from the cost function of the FRBF Network through Backpropagation algorithm is developed in this study. The advantage of our proposed approach is its simplicity and easy computation as well as its performance. To compare the performance of the proposed method with those given in the literature, three numerical examples are presented.

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“…On the one hand, Hojati et al (2005) [23] proposed to evaluate the estimators of fuzzy outputs and parameters, by setting α -set in fuzzy multiplication, but the estimators of fuzzy outputs depend on the value of α , which is unknown. On the other, a shape preserving operator, W T was proved, by Hong (2001) [24], to be the only T-norm which induces a shape preserving mul-tiplication of LL-fuzzy numbers.…”

Section: Introductionmentioning

confidence: 99%

Regression Analysis of a Kind of Trapezoidal Fuzzy Numbers Based on a Shape Preserving Operator

Sun¹,

Lü²

2017

JDAIP

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Fuzzy regression provides more approaches for us to deal with imprecise or vague problems. Traditional fuzzy regression is established on triangular fuzzy numbers, which can be represented by trapezoidal numbers. The independent variables, coefficients of independent variables and dependent variable in the regression model are fuzzy numbers in different times and W T , the shape preserving operator, is the only T-norm which induces a shape preserving multiplication of LL-type of fuzzy numbers. So, in this paper, we propose a new fuzzy regression model based on LL-type of trapezoidal fuzzy numbers and W T . Firstly, we introduce the basic fuzzy set theories, the basic arithmetic propositions of the shape preserving operator and a new distance measure between trapezoidal numbers. Secondly, we investigate the specific model algorithms for FIFCFO model (fuzzy input-fuzzy coefficient-fuzzy output model) and introduce three advantages of fit criteria, Error Index, Similarity Measure and Distance Criterion. Thirdly, we use a design set and two reference sets to make a comparison between our proposed model and the reference models and determine their goodness with the above three criteria. Finally, we draw the conclusion that our proposed model is reasonable and has better prediction accuracy, but short of robust, comparing to the reference models by the three goodness of fit criteria. So, we can expand our traditional fuzzy regression model to our proposed new model.

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A simple method for computation of fuzzy linear regression

Cited by 156 publications

References 13 publications

Numerical Solution of Fuzzy linear Regression using Fuzzy Neural Network Based on Probability Function

Numerical Solution of Fuzzy linear Regression using Fuzzy Neural Network Based on Probability Function

Fuzzy radial basis function network for fuzzy regression with fuzzy input and fuzzy output

Regression Analysis of a Kind of Trapezoidal Fuzzy Numbers Based on a Shape Preserving Operator

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