Monte Carlo methods in fuzzy linear regression

Abdalla, Areeg; Buckley, James J.

doi:10.1007/s00500-006-0148-5

Cited by 25 publications

(18 citation statements)

References 8 publications

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“…Mehran et al (2005) reviewed relevant articles on fuzzy regression and provided a simple approach to determine the coefficients of a fuzzy linear relationship. Meanwhile, Abdalla and Buckley (2007) applied a new fuzzy Monte Carlo method to a certain fuzzy linear regression problem to estimate the best solution. In this case, the best solution is a vector of triangular fuzzy numbers for the fuzzy coefficients in the model, which minimises one of two error measures.…”

Section: Overview Of Related Workmentioning

confidence: 99%

A fuzzy regression approach to a hierarchical evaluation model for oil palm fruit grading

Arbaiy

Watada

2010

Fuzzy Optim Decis Making

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Measurement of quality is an important task in the evaluation of agricultural products and plays a pivotal role in agricultural production. The inspection process normally involves a visual examination according to the ripeness standards of crops, and this grading is subject to expert knowledge and interpretation. Therefore, the quality inspection process of fruits needs to be conducted properly to ensure that high-quality fruit bunches are selected for production. However, human subjective judgments during the evaluation make the fruit grading inexact. The objectives of this paper are to build a fuzzy hierarchical evaluation model that characterises the criteria of oil palm fruits to decide the fuzzy weights of these criteria based on a fuzzy regression model, and to help inspectors conduct a proper total evaluation. A numerical example is included to illustrate the computational process of the proposed model.

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Section: Overview Of Related Workmentioning

confidence: 99%

A fuzzy regression approach to a hierarchical evaluation model for oil palm fruit grading

Arbaiy

Watada

2010

Fuzzy Optim Decis Making

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“…Therefore, in order to obtain more information, the fuzzy relation among collected actual data in fuzzy regression was first introduced by Tanaka et al (1982). Many researches, for examples, Watada (1992) uses fuzzy regression to time series to analyze time series data; Chang (1997) showed that the fuzzy regression model could be better explained in seasonal analysis; Tsaur et al (2002) used two independent variables of preceding periodical data and index of time to show the pattern of the seasonal variation; Tsaur (2003) showed that the fuzzy regression model could be used to forecast the demand of internet users under different product life cycles; Abdalla and Buckley (2007) apply fuzzy Monte Carlo method to a certain fuzzy linear regression problem to estimate the best solution, and find that the best solution is a vector of triangular fuzzy numbers for the fuzzy coefficients in the model. Therefore, for analyzing limited time series data with the reliability and validity, the fuzzy set theory is hybridized into the grey model GM(1,1) to derive fuzzy grey model GM(1,1) (Tsaur and Liao 2007), fuzzy grey regression model (Tsaur 2008).…”

Section: Introductionmentioning

confidence: 99%

Insight of the fuzzy grey autoregressive model

Tsaur

2008

Soft Comput

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In our previous research, we proposed a fuzzy grey regression model for solving limited time series data. The present paper follows the previous research and proposes a fuzzy grey autoregressive model for considering that the current value is correlated with previous values. The proposed model combines the advantages of the grey system model, the fuzzy regression model and the autoregressive model. Two illustrated examples are provided in which the amount of internet subscribers in Taiwan and the global demand of LCD TVs are forecasted. The results of these practical applications show that the proposed model can be used to obtain smaller forecasting errors of MAPE and RMSE, and that it makes good forecasts for the next demand period of internet subscribers and LCD TV. Furthermore, this model makes it possible for decision makers to forecast the best and the worst estimates based on fewer observations.

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“…A different fuzzy linear regression model was studied in Abdalla and Buckley (2007a). In Abdalla and Buckley (2007a) the independent variables were crisp (not fuzzy), the dependent variable was a triangular fuzzy number and the unknown coefficients were also triangular fuzzy numbers.…”

Section: Introductionmentioning

confidence: 99%

“…In Abdalla and Buckley (2007a) the independent variables were crisp (not fuzzy), the dependent variable was a triangular fuzzy number and the unknown coefficients were also triangular fuzzy numbers. In Abdalla and Buckley (2007a), we used the same two error measures (defined below), compared our results using fuzzy Monte Carlo to the results in four other publications and in all cases, except one, obtained smaller error. This one case where our Monte Carlo method did not produce the smallest error is similar to that discussed in Sect.…”

Section: Introductionmentioning

confidence: 99%