Fuzzy linear regression with fuzzy intervals

Peters, Georg

doi:10.1016/0165-0114(94)90144-9

Cited by 286 publications

(140 citation statements)

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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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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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“…To evaluate the effectiveness of the proposed intelligent fuzzy regression for modeling the relationship between affective variables and design variables, we use mobile phone design. Results of the modeling were compared with those based on the existing fuzzy regression methods (Tanaka et al 1982, Peters 1994) and statistical regression (Seber 2003).…”

Section: Proposed Methodsmentioning

confidence: 99%

“…The modeling results based on intelligent fuzzy regression are compared with those based on statistical regression (Seber 2003), Peters' fuzzy regression (Peters 1994) and Takagi's fuzzy regression (Takagi and Sugeno 1985). Evaluation of the effectiveness of the models is carried out by investigating the mean of training errors as shown below:…”

Section: Model Developmentmentioning

confidence: 99%

An intelligent fuzzy regression approach for affective product design that captures nonlinearity and fuzziness

Chan

Kwong

Dillon

et al. 2011

Journal of Engineering Design

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Affective product design aims at incorporating customers' affective needs into design variables of a new product so as to optimize customers' affective satisfaction. Faced with fierce competition in marketplaces, companies try to determine the settings in order to maximize customers' affective satisfaction with products. To achieve this, a set of customer survey data is required in order to develop a model which relates customers' affective responses to the design variables of a new product. Customer survey data is usually fuzzy since human feeling is usually fuzzy, and the relationship between customers' affective responses and design variables is usually nonlinear. However, previous research on modelling the relationship between affective response and design variables has not addressed the development of explicit models involving either nonlinearity or fuzziness. In this paper, an intelligent fuzzy regression approach is proposed to generate models which represent this nonlinear and fuzzy relationship between affective responses and design variables. In order to do this,  K.Y. Chan is the corresponding author. His email address is Kit.Chan@curtin.edu.au.we extend the existing work on fuzzy regression by first utilizing an evolutionary algorithm to construct branches of a tree representing structures of a model where the nonlinearity of the model can be addressed. The fuzzy regression algorithm is then used to determine the fuzzy coefficients of the model. The models thus developed are explicit, and consist of fuzzy, nonlinear terms which relate affective responses to design variables. A case study of affective product design of mobile phones is used to illustrate the proposed method. h refers to the degree to which the fuzzy linear model fits the data sets in developing the fuzzy model. Keywords: Fuzzy regression, evolutionary algorithm, affective product design

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“…Peters-fuzzy regression (Peters-FR) (Peters 1994), have been used to develop the customer preference models. The customer preference models developed by the three methods and the mean absolute errors obtained by the developed models are summarized in The results indicate that the proposed FORM can obtain the smallest mean absolute errors compared with the other two tested fuzzy regression methods.…”

Section: Development Of Customer Preference Modelsmentioning

confidence: 99%

A fuzzy ordinary regression method for modeling customer preference in tea maker design

Chan

Kwong

Law³

2014

Neurocomputing

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; The telephone number is (618) 92662945 and the fax number is 618 92662819.2 C.K. Kwong's email address is c.k.kwong@polyu.edu.hk. The telephone number is (852) 27666610 and the fax number is (852) 23625267.3 M.C. Law's email address is daniel@gewcorp.com. The telephone number is (852) 2343 8211 and the fax number is (852) 23431647. Abstract-Faced with fierce competition in marketplaces, manufacturers need to determine the appropriate settings of engineering characteristics of the new products so that the best customer preferences of the products can be obtained. To achieve this, functional models relating customer preferences to engineering characteristics need to be developed. As information regarding functional relationships between customer preferences are generally subjective or heuristic in nature, development of the customer preference models involve two uncertainties, namely fuzziness and randomness. Existing approaches use only fuzzy-based technologies to address the uncertainty caused by fuzziness. They are not designed to address the randomness of the observed data which is caused by a limited knowledge of the variability of influences between customer preferences and engineering characteristics. In this article, a fuzzy ordinary regression method is proposed to develop the customer preference models which are capable of addressing the two uncertainties of crispness and fuzziness of the customer preferences. A case study of a tea maker design which involves both uncertainties is used to demonstrate the effectiveness of the proposed method.

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Fuzzy linear regression with fuzzy intervals

Cited by 286 publications

References 5 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

An intelligent fuzzy regression approach for affective product design that captures nonlinearity and fuzziness

A fuzzy ordinary regression method for modeling customer preference in tea maker design

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