Narrow Results

This paper presents the comparative study for fuzzy regression model using linear programming and fuzzy regression model using genetic algorithms. Two cases were considered: crisp X – crisp Y and crisp X – fuzzy Y. Simulation was carried out with a tool developed in MATLAB.

This paper presents a new method of estimating fuzzy multivariable linear and nonlinear regression models using triangular fuzzy numbers. This estimation method is obtained by implementing a dual version of the ridge regression procedure for linear models. It allows us to perform fuzzy nonlinear regression by constructing a fuzzy linear regression in a high dimensional feature space for the data set with crisp inputs and fuzzy output. Experimental results are then presented, which indicate the performance of this algorithm.

In this paper, fuzzy linear regression models with fuzzy/crisp output, fuzzy/crisp input are considered. In this regard, we define risk-neutral, risk-averse and risk-seeking fuzzy linear regression models. In order to do that, two equality indices are applied to express the degree of equality between a pair of fuzzy numbers. We also develop three mathematical models to obtain the parameters of fuzzy linear regression models. Minimizing the difference between the total spread of the observed and estimated values is the objective of these models. The advantage of our proposed models is the simplicity in programming and computation.

To handle large variation data, an interval piecewise regression method with automatic change-point detection by quadratic programming is proposed as an alternative to Tanaka and Lee's method. Their unified quadratic programming approach can alleviate the phenomenon where some coefficients tend to become crisp in possibilistic regression by linear programming and also obtain the possibility and necessity models at one time. However, that method can not guarantee the existence of a necessity model if a proper regression model is not assumed especially with large variations in data. Using automatic change-point detection, the proposed method guarantees obtaining the necessity model with better measure of fitness by considering variability in data. Without piecewise terms in estimated model, the proposed method is the same as Tanaka and Lee's model. Therefore, the proposed method is an alternative method to handle data with the large variations, which not only reduces the number of crisp coefficients of the possibility model in linear programming, but also simultaneously obtains the fuzzy regression models, including possibility and necessity models with better fitness. Two examples are presented to demonstrate the proposed method.

Although fuzzy regression is widely employed to solve many problems in practice, what seems to be lacking is the problem of multicollinearity. In this paper, the fuzzy centers principal component analysis is proposed to first derive the fuzzy principal component scores. Then the fuzzy principal component regression (FPCR) is formed to overcome the problem of multicollinearity in the fuzzy regression model. In addition, a numerical example is used to demonstrate the proposed method and compare with other methods. On the basis of the results, we can conclude that the proposed method can provide a correct fuzzy regression model and avoid the problem of multicollinearity.

When the outliers exist in the data set, fuzzy regression gives incorrect results. A few number of researchers considered this problem and proposed linear-programming-based methods and fuzzy least-squares methods to deal with the outliers problem. In this paper, we develop a new model along with a linear-programming-based approach for computation of fuzzy regression models. The problem of outliers is modeled with this approach. Two examples are illustrated to compare the performance of proposed approach with those given in literature. Results from numerical examples show that our approach gives good solutions.

Some neural network related methods have been applied to nonlinear fuzzy regression analysis by several investigators. The performance of these methods will significantly worsen when the outliers exist in the training data set. In this paper, we propose a training algorithm for fuzzy neural networks with general fuzzy number weights, biases, inputs and outputs for computation of nonlinear fuzzy regression models. First, we define a cost function that is based on the concept of possibility of fuzzy equality between the fuzzy output of fuzzy neural network and the corresponding fuzzy target. Next, a training algorithm is derived from the cost function in a similar manner as the back-propagation algorithm. Last, we examine the ability of our approach by computer simulations on numerical examples. Simulation results show that the proposed algorithm is able to reduce the outlier effects.

Since fuzzy linear regression was introduced by Tanaka et al., fuzzy regression analysis has been widely studied and applied in various areas. Diamond proposed the fuzzy least squares method to eliminate disadvantages in the Tanaka et al method. In this paper, we propose a modified fuzzy least squares regression analysis. When independent variables are crisp, the dependent variable is a fuzzy number and outliers are present in the data set. In the proposed method, the residuals are ranked as the comparison of fuzzy sets, and the weight matrix is defined by the membership function of the residuals. To illustrate how the proposed method is applied, two examples are discussed and compared in methods from the literature. Results from the numerical examples using the proposed method give good solutions.

Fuzzy models have been increasingly used in decision-making in the energy sector to deal with many uncertainties such as lack of data and climate change. This paper presents a global energetic efficiency analysis based on the time series data of 91 countries from 1960 to 2010, using an integrated two-stage fuzzy approach. More precisely, Fuzzy DEA models for traditional constant and varying returns to scale assumptions are employed in a first stage to assess the relative efficiency of these countries over the course of time. In the second stage, fuzzy regressions based on different rule-based systems are used to predict the impact of a set of demographic and socio-economic variables on energy efficiency. Energetic efficiency appears to be explained by the countervailing forces of urbanization, wealth inequality, and social development. Thus, a transition to a more energetic efficient lower carbon society will depend on how we address certain socio-political factors, such as pursuing a more sustainable urbanization, reducing inequalities and taking into consideration socio-environmental aspects in trade agreements.

We first argue that a very important class of fuzzy functions in multivariate non-linear fuzzy regression is the multivariate fuzzy polynomials. Given some data, generated by a multivariate fuzzy function, our evolutionary algorithm searches our library of multivariate fuzzy polynomials for the one that best fits this data. Tests of our multivariate non-linear fuzzy regression package are given when the multivariate fuzzy function is a multivariate fuzzy polynomial and all the fuzzy numbers are non-negative.

Fuzzy regression model is an alternative to evaluate the relation between independent variables and dependent variable among the forecasting models when the data are not sufficient to identify the relation. Such phenomenon is significant especially for seasonal variation data for which large amount of data are required to show the pattern. However, few researches have been done on this issue. Because of its increasing importance in industries, in this study, we propose a method of applying fuzzy regression model for this purpose. By using two independent variables of preceding periodical data and index of time, the developed model not only shows the pattern of the seasonal variation, but also the yearly trend. From the results of the illustration, the average forecasting error is below 1.85% which, in comparison to the most commonly used Quadratic Trend Analysis of 2.91% and the Double Exponential Smoothing Model of 4.29%, has a better performance.

Quantitative models explaining and forecasting the growth of new technology like the Internet in global business operation appear infrequently in the literature. This paper introduces two artificial intelligence (AI) models such as the neural network and fuzzy regression along with an augmented diffusion model to study and predict the Internet growth in several OECD nations. First, a linear version of an augmented diffusion model is designed. An augmented diffusion model is constructed by including an economic indicator, gross domestic product per capita, into the model. In the next step, two soft AI models are calibrated from the augmented diffusion model. Performance measures of predictions from these models on new samples show that these soft models provide improved forecast accuracy over the augmented diffusion model. The results confirm the major contribution of this research in predicting global Internet growth.

The main purpose of this introductory chapter is to give an overview of the following 130 papers, which discuss financial econometrics, mathematics, statistics, and machine learning. There are eight sections in this introductory chapter. Section 1 is the introduction, Section 2 discusses financial econometrics, Section 3 explores financial mathematics, and Section 4 discusses financial statistics. Section 5 of this introductory chapter discusses financial technology and machine learning, Section 6 explores applications of financial econometrics, mathematics, statistics, and machine learning, and Section 7 gives an overview in terms of chapter and keyword classification of the handbook. Finally, Section 8 is a summary and includes some remarks.

This study analyzes the differences in financial performance between sustainable firms and nonsustainable firms through the use of a fuzzy Jensen’s alpha to measure abnormal returns. The sample consisted of 28 of the 35 firms from various sectors that composed the Mexican Price and Quotation Index (IPC) from 2008 to 2011. We compared two different methodologies to measure the Jensen’s alpha values, namely, ordinary least squares and Fuzzy Regression. Our results demonstrate that sustainable firms have greater possibilities of obtaining abnormal returns and evince less uncertainty than non-sustainable firms. Finally, we mention the Corporate Social Responsibility (CSR) trends in the Mexican capital market to emphasize the importance of the disclosure of non-financial issues as part of the process of generating long-term sustainability profits.