Identification of fuzzy parameters by interval regression models

Applications of Soft Computing to Human-centered Information Systems

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.

Fuzzy QSARs for predicting log Koc of persistent organic pollutants

Error measures for fuzzy linear regression: Monte Carlo simulation approach

IntroductionThis is the first of four chapters on fuzzy regression. This chapter and Chapter 14 are about fuzzy linear regression and Chapters 12 and 13 consider fuzzy nonlinear regression. In this chapter the independent (predictor, explanatory) variables are crisp but the dependent (response) variable is fuzzy. In Chapter 14 both the independent variables and the dependent variable are fuzzy. This chapter is based on [1].Fuzzy linear regression has become a very large area of research. Put “fuzzy regression” into your search engine and you can get too many web sites to visit.“Fuzzy linear regression” will eliminate a lot of web sites but the list is still quite long. We have selected a few recent and key references on fuzzy linear regression which are: (1) books (or articles in these books) ([4],[8],[14]); and (2) papers ([2],[3],[5],[9],[10],[12],[13],[15],[19]-[24],[27]-[32]).As far as the authors know our research is the only research on using Monte Carlo techniques in fuzzy linear regression. However, there have been other approaches employing random search (genetic algorithms) and others using neural nets. If we put “genetic algorithms” and “fuzzy linear regression” into the search engine there are less than 200 references. A recent reference is [11]. We feel that one problem with using a GA is that it can converge to a local minimum and to avoid this you need to start it with many different randomly generated initial populations. Also, we believe that our Monte Carlo method is easier to apply than a genetic algorithm, once you have a quasi-random number generator in your computer. Next we searched for “neural nets” and “fuzzy linear regression” getting less than 100 references. A key reference on this topic is [6].

Development of reservoir operation policies considering variable agricultural water demands

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.

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.

In this study, the uncertain free vibration of structures with hybrid (random and fuzzy) parameters is investigated. The non-deterministic Young’s modulus of structural elements is modeled as random variables while the uncertain mass density is represented by fuzzy parameters with associated membership functions. By implementing the α -sublevel strategy, the stochastic fuzzy eigenvalue problem is rigorously transformed into a series of stochastic interval analysis of natural frequencies. In this context, the Unified Interval Stochastic Sampling (UISS) is adopted such that the statistical characteristics of the upper and lower bounds of natural frequencies at each α -sublevel can be calculated. Subsequently, the membership functions of mean and standard deviations are respectively established for the extreme bounds of eigenvalues. Benefiting from the stochastic samples offered by the UISS method, the probability profiles of the uncertain natural frequencies at each α -sublevel can be identified by utilizing either parametric or nonparametric statistical inference methods. The accuracy and effectiveness of the proposed approach is demonstrated by analyzing a practically motivated 3D structure with comparison to the results obtained by the conventional Monte Carlo simulation method.

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 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.

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

On assessing the H value in fuzzy linear regression

Fuzzy regression, a nonparametric method, can be quite useful in estimating the relationships among variables where the available data are very limited and imprecise. It can also serve as a sound methodology that can be applied to a variety of management and engineering problems where variables are interacting in an uncertain, qualitative, and fuzzy way. A close examination of the fuzzy regression algorithm reveals that the resulting possibility distribution of fuzzy parameters, which makes this technique attractive in a fuzzy environment, is dependent upon an h parameter value. The h value, which is between 0 and 1, is referred to as the degree of fit of the estimated fuzzy linear model to the given data, and is subjectively selected by a decision maker (DM) as an input to the model. The selection of a proper value of h is important in fuzzy regression, because it determines the range of the posibility ditributions of the fuzzy parameters. In this paper, we discuss the interdependent relationship among the h value, membership function shape, and the spreads of fuzzy parameters in fuzzy linear regression with fuzzy input-output using shape-preserving operations.