Fuzzy QSARs for predicting log Koc of persistent organic pollutants

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.

Fuzzy regression analysis using fuzzy linear models with symmetric triangular fuzzy number coefficients has been formulated earlier. The goal of this regression is to find the output for all data sets. In this research, we have formulated a newer fuzzy linear regression model that uses symmetric triangular coefficient. The uniqueness of our model lies in the fact that this can be extended to use nonsymmetric fuzzy triangular coefficient that eradicates the drawbacks of existing fuzzy linear regression models.

Development of reservoir operation policies considering variable agricultural water demands

On assessing the H value in fuzzy linear regression

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 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.

Fuzzy regression for perceptual image quality assessment

So far, many studies on the load forecasting have been made to improve the prediction accuracy using various methods such as regression, artificial neural network (ANN) and neural network-fuzzy methods. In order to reduce the load forecasting error, the concept of fuzzy regression analysis is employed to load forecasting problem. The difference between regressed forecasting results and actual results is analyzed using fuzzy concept. Error correction was then applied based on fuzzy sense of error involved in prediction. Forecasted results need expert inference for which fuzzy proves to be beneficial. Results analyzed clearly support the viewpoint. The fuzzy linear regression model is made from the load data of the previous years and the coefficients of the model are found by solving the mixed linear programming problem. The fuzzy correction in predicted results improved the error from 1 to 3 %.

Applications of Soft Computing to Human-centered Information Systems

When we attempt to model a complex system including a human as an important component, it may be difficult to represent the system by a deterministic mathematical model. The main reason of this difficulty is that the system itself inherently has some fuzziness concerning subjective judgement of a human. In this paper, we propose a fuzzy nonlinear regression method with RFLN (RCE-based fuzzy learning network), which is capable of extracting knowledge of the experts automatically. RFLN is an extended RCE (restricted Coulomb energy) model, hence it needs few iterations in learning and its additional learning is easy. The proposed method has higher flexibility than fuzzy linear regression models. We propose learning algorithms to identify a nonlinear interval model which approximately includes all the given input-output data. The proposed method has characteristics of faster learning and of easier additional learning. The effectiveness of the method is shown by numerical experiments.

Modeling of thermal comfort in air conditioned rooms by fuzzy regression analysis

The purpose of this paper is to present how a fuzzy process control chart is constructed for a process with fuzzy outcomes. In this paper, the fuzzy outcomes of the process are due to subjective quality ratings by experts. Fuzzy process control consists of an off-line stage and an on-line stage. In the off-line stage, experts give quality ratings of objects based on a numerical scale, and then these ratings are fuzzified as fuzzy numbers. Collective knowledge of experts in quality rating is acquired through fuzzy regression analysis. In the on-line stage, a computer vision system is set up to obtain the dimensions of objects, and then the fuzzy regression model maps these dimensions to fuzzy quality ratings in the form of fuzzy numbers. Finally, these fuzzy quality ratings are plotted on the fuzzy control chart. Out-of-control conditions are formulated based on possibility theory. This fuzzy control chart is analog to the x~ and R charts in statistical process control.

Tanaka et al. formulated the problem of determining the linear regression expression with fuzzy parameters as a fuzzy regression analysis problem, using the data for the input‐output relation. This paper discusses such a fuzzy regression analysis, and proposes a method which identifies the fuzzy parameters using the interval regression expression.First, a method is proposed which identifies the fuzzy parameters with symmetrical triangular form from the interval regression expression. Then a method is proposed which identifies the fuzzy parameters with asymmetrical trapezoid form from two interval regression expressions. Using numerical examples, a method is illustrated which identifies the asymmetrical trapezoid fuzzy parameters from the usual point data and the fuzzy data.The method proposed herein employs the interval regression expression based on the interval operations, which leads to the merit that the procedure is simple and easy to understand compared with the conventional method employing the operations of fuzzy numbers. The fuzzy regression expression with asymmetrical trapezoid fuzzy parameters is a generalization of the fuzzy regression expression with symmetrical fuzzy parameters obtained by the conventional method.

In some practical situations, it is not possible to categorize samples into one of two response categories because of the vague nature of the response variable. Statistical logistic regression models are, therefore, not appropriate for modeling such response variables. Moreover, the small sample size in most cases limits the use of statistical logistic regression models. Fuzzy logistic regression models, instead, can overcome these problems. In order to investigate the use of fuzzy logistic regression, the present study is designed and implemented to evaluate the relationship between dietary pattern and a set of risk factors of interest. Since it is not possible to define a healthy dietary pattern precisely, therefore, the possibility of having the healthy diet is reported for each subject as a number between zero and one. The conventional logistic model is not appropriate and fails in dealing with such imprecise data; hence, a possibilistic approach is used to model the available data and to estimate the fuzzy parameters of the model. For evaluating the model, a goodness-of-fit index and an appropriate predictive capability criterion with cross validation technique is developed. The logistic model investigated here is found to be general and inclusive enough to be recommended for modeling vague observations or ambiguous relations in any field of medical sciences.

This paper tests three formulations of linear programming problems used to derive a fuzzy linear regression model, which are based on three different indices representing the necessity and of sufficiency equivalence relations between fuzzy numbers. It is shown that those formulations are extensions of three traditional formulations for fuzzy data. The trade‐off between “fit” (between the model and the observed data) and the “fuzziness” (of the model) is considered to be a multiobjective decisionmaking problem. This leads to the formulation of a multiobjective programming problem for deriving the fuzzy linear regression model. Corresponding to this situation, an interactive decision‐making procedure is proposed, which is applied to the problem of estimating the pork demand.