Fuzzy robust regression models based on granularity and possibility distribution

Fuzzy regression analysis is an important regression analysis method to predict uncertain information in the real world. In this paper, the input data are crisp with randomness; the output data are trapezoid fuzzy number, and three different risk preferences and chaos optimization algorithm are introduced to establish fuzzy regression model. On the basis of the principle of the minimum total spread between the observed and the estimated values, risk-neutral, risk-averse, and risk-seeking fuzzy regression model are developed to obtain the parameters of fuzzy linear regression model. Chaos optimization algorithm is used to determine the digital characteristic of random variables. The mean absolute percentage error and variance of errors are adopted to compare the modeling results. A stock rating case is used to evaluate the fuzzy regression models. The comparisons with five existing methods show that our proposed method has satisfactory performance.

This study presents an integrated fuzzy regression and time-series technique to estimate and predict electricity demand. Furthermore, it is difficult to model uncertain behaviour of energy consumption with only conventional time-series and fuzzy regression, which could be an ideal substitute for such cases. After reviewing various fuzzy regression models and studying their advantages and shortcomings, the best model is selected. Also, the impact of data preprocessing and post-processing on the fuzzy regression performance is to study and to show that this method does not contribute to the efficiency of the model. In addition, another unique feature of this study is utilisation of autocorrelation function to define input variables versus trial and error method. At last, the comparison of actual data with fuzzy regression and ARIMA model, using Granger?Newbold test, is achieved. Monthly electricity consumption of Iran from 1995 to 2005 is considered as the case of this study.

Combining nonlinear programming and least squares method, this paper proposes a two-stage mixed fuzzy linear regression model based on distance criterion. In order to ensure that the error of fuzzy estimated value and fuzzy observation value can be reduced when the explanatory variable is a clear number, the fuzzy regression model has a fuzzy adjustment term in addition to the clear regression coefficient. Firstly, based on the distance criterion, a nonlinear programming model is established to obtain the regression coefficient of the explanatory variables, and the fuzzy adjustment term is obtained based on the distance criterion and the least square method. Compared with the existing methods that cannot determine the sign of the coefficient, the method can accurately determine the sign of the regression coefficient. Finally, it is verified that the model has smaller mean square error and higher reliability than other models through a large number of numerical experiments and practical examples.

Error measures for fuzzy linear regression: Monte Carlo simulation approach

Since management and economic systems are complex, it is hard to handle data obtained in management and economic areas. Hitherto, in the fields, much research has focused on the structure and analysis of such data. H. Tanaka et al. proposed a fuzzy regression model to illustrate the potential possibilities inherent in the target system. J. C. Bezdek proposed a switching regression model based on a fuzzy clustering model to separate mixed samples coming from plural latent systems and apply regression models to the groups of samples coming from each system. It is hard to illustrate a rough and moderate possibility of the target system. In this paper, to deal with the possibility of a social system, we propose a new fuzzy robust regression model.

Tanaka suggested that the parameters of a linear regression model should be made fuzzy to bring about the swing of a system and created a fuzzy linear regression model. This model can be formulated in a linear programming problem that minimizes a span between the upper and lower limits under constraints that include all data. In recent years, all the attention has been focused on a fuzzy number that has an indifferent zone. A fuzzy number is defi ned by using a Type 2 membership function. This paper addresses the fact that a Type 2 membership function has the upper and lower limits and shows that a Type 2 membership function can be identifi ed by expanding a fuzzy linear regression model into a fuzzy linear polynomial regression model. Finally, after a proposed fuzzy polynomial model is identifi ed, a mathematical model will be created for a fuzzy decision-making method that has an indifferent zone.

An integrated fuzzy regression-data envelopment analysis algorithm for optimum oil consumption estimation with ambiguous data

Fuzzy regression based on asymmetric support vector machines

Linear regression has been widely used for many years to forecast various socio-economic variables in marketing, management, sales, energy and so on. Demand and price are commonly estimated by means of regression models. However, where there is high uncertainty in the model, fuzzy regressions are applied. In this paper, a fuzzy-based approach is applied for transport energy demand forecasting using socio-economic and transport related indicators. The model is based on Gross Domestic Product (GDP), population and the number of vehicles as three inputs to the main model. Energy data from 1993 to 2005 are used to estimate each of the three inputs. By three individual fuzzy linear regression (FLR) models, a multi-level FLR model is designed. The input variables are transport energy demand in the last year, the number of vehicles, population and ratio of GDP overpopulation. The output variable is energy demand of the transportation sector in Iran. The inputs to the ending level are obtained as outputs of the starting levels. The estimation fuzzy problem for the model is formulated as a linear optimization problem. Comparison of the model predictions with data of the testing period shows validity of the proposed model. Furthermore, having obtained the fuzzy parameters, the transport energy demand is predicted for 2006 to 2020. It is noticeable that, without any price shock or efficiency improvement in the transportation sector, the energy consumption may reach to a threatening level of about 592 MBOE by 2020. Key words: Forecasting, multi-level fuzzy linear regression, transport energy demand, case study.

This paper introduces an integrated algorithm for forecasting electricity consumption (EL) based on fuzzy regression, time series and principal component analysis (PCA) in uncertain markets such as Iran. The algorithm is examined by mean absolute percentage error, analysis of variance (ANOVA) and Duncan Multiple Range Test. PCA is used to identify the input variables for the fuzzy regression and time series models. Monthly EL in Iran is used to show the superiority of the algorithm. Moreover, it is shown that the selected fuzzy regression model has better estimated values for total EL than time series. The algorithm provides as good results as intelligent methods. However, it is shown that the algorithm does not require utilization of preprocessing methods but genetic algorithm, artificial neural network and fuzzy inference system require preprocessing which could be a cumbersome task to deal with ambiguous data. The unique features of the proposed algorithm are three fold. First, two type of fuzzy regressions with and without preprocessed data are prescribed by the algorithm in order to minimize the bias. Second, it uses PCA approach instead of trial and error method for selecting the most important input variables. Third, ANOVA is used to statistically compare fuzzy regression and time series with actual data.

A knowledge management (KM) system has a different schema that one of them has been studied in the present study. One of version of KM is based on artificial intelligence (AI) methods. KM based on AI has been investigated in the present work based on natural gas consumption estimation domain. Developing accurate and flexible model to natural gas consumption estimation is a strategic step in policy and decision-making process in energy sector. This paper provides a stage algorithm during that it gains optimal fuzzy regression model for studding natural gas consumption in sixteen countries according to data in years 1989 till 2007. Different countries have selected from Africa, America, Asia, Europe and Middle East based on high, middle and low GDP index and for every one of them nine fuzzy regression models have executed and the results and error of each model have calculated. Preprocess has been done on the initial data to gain better results which the min-max method has been used for this purpose. Two criterions have been used to determining suitable and appropriate fuzzy regression model in each country. Firstly, fuzzy regression models with MAPE value below 10 is deleted from the assessment and remained fuzzy regression models are compared with ANOVA. Upon logic that given algorithm sketches for some countries none of used models are proper while for other countries optimal model is gained in first or second filter of algorithm. To show the applicability and superiority of the proposed flexible Fuzzy regression model the data for oil consumption in Japan, Thailand, Bangladesh from Asia and Norway, Italy, Bulgaria from Europe and Qatar, Iran, Iraq from Middle East and The united state, Mexico, Bolivia from North America and Libya, Tunisia, Nigeria from Africa during 1989 to 2007 are used.

Using fuzzy linear regression models, an estimation method to detect the human reasoning state in machine operation is discussed. Simple experiments of human operation using computer display show that the change of the human internal state at the reasoning in the operations is reflected in the system parameters of the fuzzy linear regression models. Fuzzy linear regression models are constructed using some fundamental operation data, and fuzziness parameters are calculated by traditional linear programming approaches. The characteristics of the human reasoning state are represented by the fuzziness parameters, and advantages of the proposed approaches, in human reliability are demonstrated by the example of vehicle driving operations.

This article introduces a general fuzzy regression model, which separates the response function on a mode and spreads of an α-level set for an observed fuzzy number, to estimate a fuzzy relation between two fuzzy random variables. We construct the general fuzzy regression model using least squares estimation and best response functions on the mode and spread of an α-level set for the fuzzy number when the response variable is an LR-fuzzy number and independent variables are crisp numbers. Then we derive a crisp mean and variance of the predicted fuzzy number, and compare the accuracy of our proposed fuzzy regression model with other fuzzy regression models suggested by many authors.

Applications of Soft Computing to Human-centered Information Systems

Hesitant t-spherical fuzzy linear regression model based decision making approach using gradient descent method