Fuzzy regression based on asymmetric support vector machines

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.

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 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.

Error measures for fuzzy linear regression: Monte Carlo simulation approach

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.

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 characteristic of the fuzzy regression model is to enwrap all the given samples. An interval of fuzzy regression model is created by considering how far a sample is from the central values. That means when samples are widely scattered the size of an interval of the fuzzy model is widened. That is, the fuzziness of the fuzzy regression model is decided by the range of sample distribution. Therefore, many research results on a fuzzy regression model in order to describe the possibility of the target system have been reported. We have proposed two fuzzy robust regression models which remove influences of improper data such as unusual data and outliers. In this paper, we describe the model building of our fuzzy robust regressions by removing influences of improper data.

Fuzzy linear regression analysis for fuzzy input-output data

Applications of Soft Computing to Human-centered Information Systems

In many statistical process control (SPC) applications, the quality of a process or product is represented by a relationship or the so-called quality profile, between a quality characteristic and one or more explanatory variables. The process quality characteristics are sometimes measured with a reasonable degree of approximation. Often, especially when qualitative assessments arise, evaluation of quality characteristics is carried out ambiguously or using linguistic qualifiers. The fuzzy sets theory has proved to be a well-established approach for dealing with uncertainty due to the approximate measurement, ambiguity in subjective evaluations, or vagueness in linguistic variables. Our main purpose was to present and compare four methods of monitoring nonlinear fuzzy profiles, for which different nonlinear fuzzy regression modeling approaches are considered. The first two methods are “a data-driven fuzzy rule-based” and “an extended least square support vector machine (LS-SVM),” for which the profile is characterized without considering a predefined mathematical relationship. However, for the other two methods, a specific form of the profile was needed. The third method, namely “a modified fuzzy regression model,” was initially invented for linear models. Besides, the fourth method employs “the fuzzy least square method” based on linearizing transformation. The exponentially weighted moving average (EWMA) control statistic was used to derive the control statistic to be plotted on the univariate as well as multivariate control charts. An extensive simulation study was conducted to compare the performance of the methods, and the average run length (ARL) criterion was considered to assess the detect-ability of control charts against various out-of-control conditions. Our comparison results indicated that the multivariate EWMA (MEWMA) chart based on the LS-SVM method outperforms the rest in detecting process shifts with smaller values of ARL when the process undergoes out-of-control conditions.

Lung cancer is the most prevalent cancer in the world, accounting for 12.2% of all newly diagnosed cases in 2020 and has the highest mortality rate due to its late diagnosis and poor symptom detection. Currently, there are 4,319 lung cancer deaths in Malaysia, representing 2.57 percent of all mortality in 2020. The late diagnosis of lung cancer is common, which makes survival more difficult. In Malaysia, however, most cases are detected when the tumors have become too large, or cancer has spread to other body areas that cannot be removed surgically. This is a frequent situation due to the lack of public awareness among Malaysians regarding cancer-related symptoms. Malaysians must be acknowledged the high-risk symptoms of lung cancer to enhance the survival rate and reduce the mortality rate. This study aims to use a fuzzy linear regression model with heights of triangular fuzzy by Tanaka (1982), H-value ranging from 0.0 to 1.0, to predict high-risk symptoms of lung cancer in Malaysia. The secondary data is analyzed using the fuzzy linear regression model by collecting data from patients with lung cancer at Al-Sultan Abdullah Hospital (UiTM Hospital), Selangor. The results found that haemoptysis and chest pain has been proven to be the highest risk, among other symptoms obtained from the data analysis. It has been discovered that the H-value of 0.0 has the least measurement error, with mean square error (MSE) and root mean square error (RMSE) values of 1.455 and 1.206, respectively.

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.

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.

In 1965 L.A. Zadeh presented a fuzzy set. After then, fuzzy clustering method was proposed in early stage. L.A. Zadeh presented the concept of similarity for a fuzzy set in 1981. Ruspini proposed a clustering method based on fuzzy decomposition. Dunn and Bezdek wrote a clustering based on IDODATA algorithm in terms of fuzzy concept. Many methods for fuzzy multivariate analysis were presented .For example, there are several approaches to multivariant analysis such as dynamic programming, M. Sugeno’s measure, similarity concepts and clustering. M. Roubens and M.P. Windham discussed about the validity of clustering. Regarding hierarchical clustering, N. Osumi et al discussed it using fuzzy concepts. J. Watada et al proposed a heuristic hierarchical clustering which is employing similarity concepts of L.A. Zadeh’s. There are many papers which discuss fuzzy clustering.In 1979 H. Tanaka et al proposed fuzzy linear regression model. This development broke through fuzzy multivariate analysis because no methods are proposed except clustering and hierarchical clustering till then. There are also various applications of fuzzy multicariant analyses. Furthermore, various data analyses were proposed based on the fuzzy linear regression model. For example, J. Watada et al developed Fuzzy time-series analysis and I. Hayashi developed GMDH method.This paper summarizes the 40 year history of Fuzzy Multivariate Methods.KeywordsFuzzy Multivariate AnalysisFuzzy StatisticsFuzzy Linear Programming

With the development of technology and artificial intelligence(AI), financial leasing is used frequently in China’s equipment manufacturing industries, especially after 2008, which attracts our attention. This paper focuses on the problem. A theoretical model is provided in the paper to explain the motivation that why financial leasing is used in equipment manufacturing industries. In this paper, we employ multi-level fuzzy linear regression model to analyze data of manufacturing equipment industry of China in order to discover impact between sales revenue and financial leasing. We also discover credit sale forecasting using this model. We discover that economic leasing has a constructive important effect on sales revenue in total samples, which is consistent with the theoretical framework. However, the results are different in sub-industries, which shows that economic leasing has a constructive and important effect on sales profits in some sub-industries, but some of them are not. Furthermore, we also find that asset characteristics has a substantial effect on financial leasing decision. The outcome demonstrates that the more precise the asset, the easier it can be leased.