A revisited approach to linear fuzzy regression using trapezoidal fuzzy intervals

Bisserier, Amory; Boukezzoula, Reda; Galichet, Sylvie

doi:10.1016/j.ins.2010.06.017

Cited by 53 publications

(29 citation statements)

References 43 publications

(69 reference statements)

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“…Fuzzy regression analysis using triangular fuzzy numbers and trapezoidal fuzzy number have been studied in many works [9][10][11][12][13][14][15]. The theoretical studeis regarding fuzzy regression model have been investigated in [16][17][18].…”

Section: Fuzzy Regression Model Using Trapezoidal Fuzzy Numbersmentioning

confidence: 99%

Fuzzy Regression Model Using Trapezoidal Fuzzy Numbers for Re-auction Data

Kim¹,

Lee²,

Lee³

et al. 2016

IJFIS

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Re-auction happens when a bid winner defaults on the payment without making second in-line purchase declaration even after determining sales permission. This is a process of selling under the court's authority. Re-auctioning contract price of real estate is largely influenced by the real estate business, real estate value, and the number of bidders. This paper is designed to establish a statistical model that deals with the number of bidders participating especially in apartment re-auctioning. For these, diverse factors are taken into consideration, including ratio of minimum sales value from the point of selling to re-auctioning, number of bidders at the time of selling, investment value of the real estate, and so forth. As an attempt to consider ambiguous and vague factors, this paper presents a comparatively vague concept of real estate and bidders as trapezoid fuzzy number. Two different methods based on the least squares estimation are applied to fuzzy regression model in this paper. The first method is the estimating method applying substitution after obtaining the estimators of regression coefficients, and the other method is to estimate directly from the estimating procedure without substitution. These methods are provided in application for re-auction data, and appropriate performance measure is also provided to compare the accuracies.

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Section: Fuzzy Regression Model Using Trapezoidal Fuzzy Numbersmentioning

confidence: 99%

Fuzzy Regression Model Using Trapezoidal Fuzzy Numbers for Re-auction Data

Kim¹,

Lee²,

Lee³

et al. 2016

IJFIS

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“…In the planning process of a new product, the following consumer preference model described in (1) is essential in order to represent the functional relationship between consumer preferences and engineering characteristics for a new product [3]:…”

Section: Consumer Preference Modelsmentioning

confidence: 99%

“…Apart from new product development, the F-SR bridges the research gap in the existing fuzzy regression methods [1,5,10,25,31,38,49,50] which do not address the issue of selecting significant regressors with high-order or interaction terms for modelling. The effectiveness of the F-SR is evaluated based on a case study of a tea maker design and a solder paste dispenser design.…”

Section: Introductionmentioning

confidence: 99%

A Stepwise-Based Fuzzy Regression Procedure for Developing Customer Preference Models in New Product Development

Chan

Lam

Dillon

et al. 2015

IEEE Trans. Fuzzy Syst.

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Fuzzy regression methods have commonly been used to develop consumer preferences models which correlate the engineering characteristics with consumer preferences regarding a new product; the consumer preference models provide a platform whereby product developers can decide the engineering characteristics in order to satisfy consumer preferences prior to developing the products. Recent research shows that these fuzzy regression methods are commonly used to model customer preferences. However, these approaches have a common limitation in that they do not investigate the appropriate polynomial structure which includes significant regressors with only significant engineering characteristics; also, they cannot generate interaction or high-order regressors in the models. The inclusion of insignificant regressors is not an effective approach when developing the models. Exclusion of significant regressors may affect the generalization capability of the consumer preference models.In this paper, a novel fuzzy modelling method is proposed, namely fuzzy stepwise regression (F-SR), in order to develop a customer preference model which is structured with an appropriate polynomial which includes only significant regressors. Based on the appropriate polynomial structure, the fuzzy coefficients are determined using the fuzzy least square regression. The developed fuzzy regression model attempts to obtain a better generalization capability using a smaller number of regressors. The effectiveness of the F-SR is evaluated based on two design problems, namely a tea maker design and a solder paste dispenser design. Results show that better generalization capabilities can be obtained compared with the fuzzy regression methods commonly-used for new product development. Also, smaller-scale consumer preference models with fewer engineering characteristics can be obtained. Hence, a simpler and more effective product development platform can be provided.

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“…However, a large std value in the second stage can be due to either incorrect outlier detection, or non linearity of the dataset. There are different model fitting measurements in the lit erature of fuzzy linear regression such as Euclidean distance [11], distance criterion [12], compatibility measure [13], relative none-intersected area [14], and Hojati's measure [15] and etc. In this paper, we use Hojati's measure given in (5) due to the fact that this measurement is in the range of 0 to 1 which makes it easier for interpretation.…”

Section: A Two-stage Outlier Detection Approachmentioning

confidence: 99%

A least square approach for the detection and removal of outliers for fuzzy linear regressions

Mashinchi

Orgun

2010

2010 Second World Congress on Nature and Biologically Inspired Computing (NaBIC)

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Fuzzy linear analysis may lead to an incorrect interpretation of data in case of being incapable of dealing with outliers. Both basic probabilistic and least squares approaches are sensitive to outliers. In order to detect the outliers in data, we propose a two stage least squares approach which in contrast to the other proposed methods in the literature does not have any user defined variables. In the first stage of this approach, the outliers are detected and the clean dataset is prepared and then in the second stage a model is sought to fit the clean dataset. In both the first and second phases, the minimization of the model fitting measurement is achieved with hybrid optimization which gives us the flexibility of using any type of a model fitting measure regardless of being continuous or differentiable.

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A revisited approach to linear fuzzy regression using trapezoidal fuzzy intervals

Cited by 53 publications

References 43 publications

Fuzzy Regression Model Using Trapezoidal Fuzzy Numbers for Re-auction Data

Fuzzy Regression Model Using Trapezoidal Fuzzy Numbers for Re-auction Data

A Stepwise-Based Fuzzy Regression Procedure for Developing Customer Preference Models in New Product Development

A least square approach for the detection and removal of outliers for fuzzy linear regressions

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