Fuzzy Regression Model Research Articles

An improved lasso regression model for evaluating the efficiency of intervention actions in a system reliability analysis

A conventional LASSO (least absolute shrinkage and selection operator) regression model utilizing the Pythagorean fuzzy sets in a system reliability analysis is developed. Overall, the Pythagorean fuzzy multivariate regression analysis enables decision makers to correctly identify the relationships between a set of responses in the form of fuzzy or non-fuzzy interpretive variables. The interpretability of the model is significantly improved by the proposed Pythagorean fuzzy LASSO regression model (PFLRM). Thus, a system reliability analysis is considered as an application of the study to evaluate the efficiency and effectiveness of the proposed PFLRM. There is no doubt that a system reliability analysis is vital to improve the safety performance of chemical processing industries, where an extensive number of industrial accidents occur annually. These accidents have subsequently highlighted the failure of some of the intervention actions to keep the systems safely in operation. The results illustrate a better performance with higher accuracy with the proposed PFLRM compared with the existing number of fuzzy regression models, particularly in the availability of non-informative variables.

A general approach to fuzzy regression models based on different loss functions

In this paper, a new general approach is presented to fit a fuzzy regression model when the response variable and the parameters of model are as fuzzy numbers. In this approach, for estimating the parameters of fuzzy regression model, a new definition of objective function is introduced based on the different loss functions and under the averages of differences between the $$\alpha $$ -cuts of errors. The application of the proposed approach is studied using a simulated data set and some real data sets in the presence of different types of outliers.

A fuzzy multiple linear regression model based on meteorological factors for air quality index forecast

Air quality index (AQI) is an indicator usually issued on a daily basis to inform the public how good or bad air quality recently is or how it will become over the next few days, which is of utmost importance in our life. To provide a more practicable way for AQI prediction, so that residents can clear about air conditions and make further plans, five imperative meteorological indicators are elaborately selected. Accordingly, taking these indicators as independent variables, a fuzzy multiple linear regression model with Gaussian fuzzy coefficients is proposed and reformulated, based on the linearity of Gaussian fuzzy numbers and Tanaka’s minimum fuzziness criterion. Subsequently, historical data in Shanghai from March 2016 to February 2018 are extracted from the government database and divided into two parts, where the first half is statistically analyzed and used for formulating four seasonal fuzzy linear regression models in views of the special climate environment of Shanghai, and the second half is used for prediction to validate the performance of the proposed model. Furthermore, considering that there is beyond dispute that triangular fuzzy number is more prevalent and crucial in the field of fuzzy studies for years, plenty of comparisons between the models based on the two types of fuzzy numbers are carried out by means of the three measures including the membership degree, the fuzziness and the credibility. The results demonstrate the powerful effectiveness and efficiency of the fuzzy linear regression models for AQI prediction, and the superiority of Gaussian fuzzy numbers over triangular fuzzy numbers in presenting the relationships between the meteorological factors and AQI.

The fuzzy linear regression model for finding sales forcastion from financial leasing in China’s equipment manufacturing industries

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.

Financial asset yield series forecasting based on risk-neutral fuzzy bilinear regression and probabilistic neural network

Application of quantitative methods for forecasting purposes in financial markets has attracted significant attention from researchers and managers in recent years when conventional time series forecasting models can hardly develop the inherent rules of complex nonlinear dynamic financial systems. In this paper, based on the fuzzy technique integrated with the statistical tools and artificial neural network, a new hybrid forecasting system consisting of three stages is constructed to exhibit effectively improved forecasting accuracy of financial asset price. The sum of squared errors is minimized to determine the coefficients in fitting the fuzzy autoregression model stage for formulating sample groups to deal with data containing outliers. Fuzzy bilinear regression model introducing risk view based on quadratic programming algorithm that reflects the properties of both least squares and possibility approaches without expert knowledge is developed in the second stage. The main idea of the model considers the sub-models tracking the possible relations between the spread and the center, also linking the estimation deviation with risk degree of fitness of the model. In the third stage, fuzzy bilinear regression forecasting combining with the optimal architecture of probabilistic neural network classifiers indicates that the proposed method has great contribution to control over-wide interval financial data with a certain confidence level. Statistical validation and performance analysis using historical financial asset yield series on Shanghai Stock Exchange composite index all exhibit the effectiveness and stability of the proposed hybrid forecasting formulation compared with other forecasting methods.

Marine economic industrial structure based on fuzzy entropy and least square regression model

China’s economy is in the critical period of transformation from a traditional land economy to a marine economy. China is rich in marine resources, facing important development opportunities and challenges. The adjustment of marine economic industrial structure is of great significance to promote the development of China’s marine economy. To intuitively analyze and clearly understand the effect of industrial structure adjustment of marine economy in recent years in China, using the data of China’s marine industry from 2008 to 2018, fuzzy entropy theory, and least square regression model, the influence of the scientificity and advancement of marine economic industrial structure adjustment on marine economic was analyzed. Results show that the fitting degree of the model is good and significant, with every 1% increase in the scientificity and height of marine economic industrial structure adjustment, the marine economy increases by 1.88% and 2.80%, respectively. The development of marine science and technology can promote the rise of the marine economy.

Конфиденциальное двустороннее вычисление параметров нечеткой линейной регрессионной модели

Purpose: describe two-party computation of fuzzy linear regression with horizontal partitioning of data, while maintaining data confidentiality. Methods: the computation is designed using a transformational approach. The optimization problems of each of the two participants are transformed and combined into a common problem. The solution to this problem can be found by one of the participants. Results: A protocol is proposed that allows two users to obtain a fuzzy linear regression model based on the combined data. Each of the users has a set of data about the results of observations, containing the values of the explanatory variables and the values of the response variable. The data structure is shared: both users use the same set of explanatory variables and a common criterion. Regression coefficients are searched for as symmetric triangular fuzzy numbers by solving the corresponding linear programming problem. It is assumed that both users are semihonest (honest but curious, or passive and curious), i.e. they execute the protocol, but can try to extract information about the source data of the partner by applying arbitrary processing methods to the received data that are not provided for by the protocol. The protocol describes the transformed linear programming problem. The solution of this problem can be found by one of the users. The number of observations of each user is known to both users. The observation data remains confidential. The correctness of the protocol is proved and its security is justified. Keywords: fuzzy numbers, collaborative solution of a linear programming problem, two-way computation, transformational approach, cloud computing, federated machine learning.

Fuzzy regression model for forecasting impact of venture capital network and underwriter network on IPO premium

In recent years, social network analysis is one of the top 20 fields of artificial intelligence. Based on the network signal theory, this study examines the influence of the dual network embeddedness on the premiums of Chinese initial public offerings (IPOs). In this paper we proposed fuzzy regression model for forecasting the impact of venture capital network and underwriter network on IPO premium based on some hypothesis. We find that: (1) Enterprises embedded in the central position of venture capital network will increase the IPO secondary market premium; (2) Secondly, employing underwriter in the central position of underwriting network will increase the IPO secondary market premium; (3) As venture capital are getting closer to the central position of venture capital network, the influence of underwriter network centrality in underwriting network on the increase of IPO secondary market reaction will gradually weaken. The research shows that occupying central position both in venture capital syndication network and underwriting network have the functions of sending signals, then increase the IPO secondary market premium, but the functions of different network signals will replace each other.

Monitoring fuzzy linear quality profiles: A comparative study

Quality profiles representing the quality of a process or product as the functional relationship between one or more dependent variables and one or more explanatory variables are nowadays widely recognized in statistical process control (SPC) applications by both researchers and practitioners. On the other hand, in many real-world cases, evaluation of process or product characteristics is carried out with ambiguity or conducted using linguistic values. The theory of fuzzy sets provides an appropriate approach to deal with uncertainty due to ambiguity in human subjective evaluations or vagueness in linguistic variables. The purpose of this study is to introduce two novel methods based on fuzzy regression modeling for monitoring fuzzy linear profiles in phase II of SPC. To accomplish this, fuzzified Hoteling’s T2 statistic and fuzzy hypothesis testing are used. Moreover, a simulation study is used to compare the performance of the proposed methods compared with previous methods, based on the average run length (ARL) criterion in order to assess the detectability of charts with regard to the step shifts in profile parameters. Finally, the results of a real-world example in the tile and ceramic industry are presented.

Fuzzy Regression Analysis using Trapezoidal Fuzzy Numbers

As a widely used method, regression analysis plays an increasingly important role in creating statistical models and making forecasts in the field of economics and finance. The use of traditional regression for modeling socio-economic processes is not sufficiently substantiated in some situations. Currently, a new direction is being actively developed, associated with fuzzy regression analysis and its application as an alternative to classical methods for modeling economic phenomena. Fuzzy regression methods are based on the theory of fuzzy sets. A number of methods and their modifications are proposed for constructing fuzzy regression models, but most of them use triangular fuzzy symmetric numbers. In this paper, we propose a new method for constructing linear fuzzy regression using trapezoidal fuzzy numbers. The method is based on dividing the sample using a regression model which is estimated by using the ordinary least squares. Two fuzzy regressions using triangular numbers are estimated from the formed samples, on the basis of which a fuzzy model with trapezoidal fuzzy numbers is constructed. Basing on the proposed method, a linear fuzzy model of the gross regional product as an indicator of the economic development of the Republic of Tatarstan of Russia is constructed depending on a number of factors. A comparative assessment of the quality of fuzzy regression models using triangular and trapezoidal numbers was performed.

Optimization of integrated fuzzy decision tree and regression models for selection of oil spill response method in the Arctic

The challenging oil spill response in the Arctic calls for effective response decision support tools. In this study, a framework comprising the development of various integrated fuzzy decision tree and regression (FDTR) models as well as model optimization was developed to facilitate the selection of suitable response methods for oil spill accidents in Arctic waters. The FDTR models took into account the influential attributes affecting the effectiveness of oil spill response in harsh Arctic environments. Different FDTR models were developed based on the combinations of three regression analyses, including linear, non-linear, and Gaussian process regression (GPR) and four information evaluation measures for splitting a decision tree, including information gain, deviance, GINI impurities (GINI), and misclassification error. Non-dominated sorting differential evolution (NSDE) optimization was employed to enhance the predictive performance of the FDTR models. The prediction performance of the FDTR models was compared using an oil spill dataset. Using this framework, the average prediction accuracy and the number of rules (representing the robustness) of FDTRs were increased by 14% and decreased by 57%, respectively. A set of optimal prediction models to promptly select an appropriate response method can be obtained using this framework. Among all models, GPR-GINI performed the best concerning optimal values of objective functions.

Optimized recurrent neural network with fuzzy classifier for data prediction using hybrid optimization algorithm: Scope towards diverse applications

Today, data processing has become a challenging task due to the significant increase in the amount of data collected using various sensors. To put up knowledge and forecast the data, the existing data mining techniques compute all numerical attributes in the memory simultaneously. However, the over-abundance of entire factors in the data makes accurate prediction infeasible. This paper attempts to implement a new data prediction model using an optimized machine learning algorithm. The proposed data prediction model involves four main phases: (a) data acquisition, (b) feature extraction, (c) data normalization, and (d) prediction. Initially, few data from the UCI repository like Bike Sharing Dataset, Carbon Nanotubes, Concrete Compressive Strength, Electrical Grid Stability Simulated Data, and SkillCraft-1 Master Table are collected. Further, the feature extraction process extracts the first-order statistics like mean, median, standard deviation, the maximum value of entire data, and the minimum value of entire data, and the second-order statistics like kurtosis, skewness, energy, and entropy. Next, the data or feature normalization is done to arrange the data within a certain limit. The normalized features are then subjected to a hybrid prediction system by integrating the Recurrent Neural Network (RNN) and Fuzzy Regression model. As a modification, the number of hidden neurons in the RNN and membership limits of the Fuzzy Regression model are optimized by a hybrid optimization algorithm by merging the concepts of Whale Optimization Algorithm (WOA) and Cat Swarm Optimization (CSO), which is called the Whale Updated Seek Mode-based CSO (WS-CSO) algorithm. Then, the efficiency of the optimized hybrid classifier for all-time prediction of data in different applications is confirmed based on its valuable performance and comparative analysis.

A Generalized Bridge Regression in Fuzzy Environment and Its Numerical Solution by a Capable Recurrent Neural Network

Bridge regression is a special family of penalized regressions using a penalty function ∑ A j γ with γ ≥ 1 that for γ = 1 and γ = 2 , it concludes lasso and ridge regression, respectively. In case where the output variable in the regression model was imprecise, we developed a bridge regression model in a fuzzy environment. We also exhibited penalized fuzzy estimates for this model when the input variables were crisp. So, we perform the presented optimization problem for the model that leads to a multiobjective program. Also, we try to determine the shrinkage parameter and the tuning parameter from the same optimization problem. In order to estimate fuzzy coefficients of the proposed model, we introduce a hybrid scheme based on recurrent neural networks. The suggested neural network model is constructed based on some concepts of convex optimization and stability theory which guarantees to find the approximate parameters of the proposed model. We use a simulation study to depict the performance of the proposed bridge technique in the presence of multicollinear data. Furthermore, real data analysis is used to show the performance of the proposed method. A comparison between the fuzzy bridge regression model and several other shrinkage models is made with three different well-known fuzzy criteria. In this study, we visualize the performance of the model by Taylor’s diagram and Bubble plot. Also, we examine the predictive ability of the model, thus, obtained by cross validation. The numerical results clearly showed higher accuracy of the proposed fuzzy bridge method compared to the other existing fuzzy regression models: fuzzy bridge regression model, multiobjective optimization, recurrent neural network, stability convergence, and goodness-of-fit measure.

A robust multiple regression model based on fuzzy random variables

In the present paper, a novel robust multiple regression model with fuzzy intercepts and non-fuzzy regression coefficients was proposed. A two-stage robust procedure adopted with fuzzy random variables and α-values of LR-fuzzy was also introduced to estimate the components of the model. Some common goodness-of-fit criteria were also used to evaluate the performance of the proposed method. The effectiveness of the proposed method was compared to some common fuzzy robust regression models through three numerical examples including a simulation study. The numerical results indicated the lower sensitivity of the proposed model to outliers and its higher precision compared to the other existing robust regression methods.

On Optimal and Asymptotic Properties of a Fuzzy L2 Estimator

A fuzzy least squares estimator in the multiple with fuzzy-input–fuzzy-output linear regression model is considered. The paper provides a formula for the L2 estimator of the fuzzy regression model. This paper proposes several operations for fuzzy numbers and fuzzy matrices with fuzzy components and discussed some algebraic properties that are needed to use for proving theorems. Using the proposed operations, the formula for the variance, provided and this paper, proves that the estimators have several important optimal properties and asymptotic properties: they are Best Linear Unbiased Estimator (BLUE), asymptotic normality and strong consistency. The confidence regions of the coefficient parameters and the asymptotic relative efficiency (ARE) are also discussed. In addition, several examples are provided including a Monte Carlo simulation study showing the validity of the proposed theorems.

A Combinatorial Algorithm for Fuzzy Parameter Estimation with Application to Uncertain Measurements

This paper presents a new method for regression model prediction in an uncertain environment. In practical engineering problems, in order to develop regression or ANN model for making predictions, the average of set of repeated observed values are introduced to the model as an input variable. Therefore, the estimated response of the process is also the average of a set of output values where the variation around the mean is not determinate. However, to provide unbiased and precise estimations, the predictions are required to be correct on average and the spread of date be specified. To address this issue, we proposed a method based on the fuzzy inference system, and genetic and linear programming algorithms. We consider the crisp inputs and the symmetrical triangular fuzzy output. The proposed algorithm is applied to fit the fuzzy regression model. In addition, we apply a simulation example and a practical example in the field of machining process to assess the performance of the proposed method in dealing with practical problems in which the output variables have the nature of uncertainty and impression. Finally, we compare the performance of the suggested method with other methods. Based on the examples, the proposed method is verified for prediction. The results show that the proposed method reduces the error values to a minimum level and is more accurate than the Linear Programming (LP) and fuzzy weights with linear programming (FWLP) methods.

A fuzzy nonlinear univariate regression model with exact predictors and fuzzy responses

In this paper, a fuzzy nonlinear univariate regression model with nonfuzzy predictors and fuzzy responses is proposed. For this purpose, both nonlinear parametric and nonparametric methods were utilized. The left and right spreads of unknown fuzzy smooth function were estimated via a popular kernel-based curve-fitting method, while the center was estimated using both parametric and nonparametric curve-fitting methods. In fact, two techniques were suggested and compared in terms of estimating the center of fuzzy smooth function: (1) nonparametric method (similar to the left and right spreads) and (2) parametric method adopted with a common nonlinear regression model called truncated spline regression. Each stage was separately estimated the unknown components were addressed via the conventional statistical regression methods. The proposed method managed to provide a simple and fast estimation/prediction approach for the fuzzy univariate regression analysis for any types of LR-fuzzy numbers. Some common goodness-of-fit criteria were also employed to evaluate the performance of the proposed method. The effectiveness of the developed method was further illustrated through three numerical examples including a simulation study based on a common kernel. The proposed method was also compared with several common fuzzy linear/nonlinear regression models. The numerical evaluations indicated that the proposed parametric method for centers exhibited more accurate results as compared with the nonparametric method.

Risk-adjusted control charts based on LR-fuzzy data

Control charts are widely used in industrial processes as well as in health sciences and particularly for monitoring the performance of cardiac surgeon or a group of surgeons based on the preoperative risk of patients. Since the preoperative risk is a vague and nonprecise variable and the anesthesiologists after checking how many risk factors a patient has, determine the risk of mortality before the surgery as a linguistic term such as low, medium, high or others like that, it is better to be considered as a fuzzy number, which can be determined by using fuzzy regression models. In this condition, we need a special chart to monitor the performance of surgeons based on these fuzzy data. In this article, we propose risk-adjusted control charts based on LR-fuzzy data and then test our conclusions on real data.

Fuzzy Linear regression based on approximate Bayesian computation

Fuzzy linear regression with crisp inputs and fuzzy output data constitutes an important modeling problem. Basic strategies used to solve this problem, i.e., the possibilistic method and the least squares method, together with their extensions, have some drawbacks. The possibilistic methods put emphasis on an inclusion property while the least squares methods focus on a central tendency property. Therefore, many researchers work on combining these two methods to obtain a better performance. In this paper, in contrast to most existing techniques which treat fuzzy linear regression as an optimization problem, we set the problem of constructing a fuzzy linear regression model in Bayesian statistics and propose a new fuzzy linear regression method based on approximate Bayesian computation (ABC). The method applies the likelihood-free inference algorithm ABC to generate independent samples of unknown model coefficients from Bayesian posterior distribution. This overcomes difficulty of defining likelihood function in fuzzy environment. By adjusting a prior distribution and a threshold of the ABC algorithm, the proposed approach can flexibly balance the inclusion property of the possibilistic methods and the central tendency property of the least squares methods. The convergence property of the proposed ABC algorithm is verified by a numerical example. Two measuring criteria, i.e., a distance metric and a degree of fitting index, which indicate the central tendency property and the inclusion property, respectively, are introduced to evaluate the quality of regression results. Three numerical examples are applied to show the performances of the proposed method. The numerical results are also compared with those obtained by some classical and recently proposed approaches. Additionally, a practical engineering application example is used to illustrate effectiveness of the proposed method.

Fuzzy regression model of the impact of technology on living standards

This paper proposes a model of the impact of technology on the standard of living based on fuzzy linear regression. The Human Development Index (HDI) was chosen as a dependent variable as an indicator of the health and well-being of the population. The explanatory variables are the Network Readiness Index (NRI), which measures the impact of information and communication technologies (ICT) on society and the development of the nation, and the Global Innovation Index (GII), which measures the driving forces of economic growth. The analysis is based on data for 2019 for four groups of countries with different levels of GDP per capita. For developed countries, the positive and balanced impact of innovation and ICT on living standards has been confirmed. For two groups of developing countries (upper and lower middle income), the GII coefficient was found to be negative. A more in-depth analysis showed that this is due to the state of political and social institutions. This fact means that without a simultaneous increase in the maturity of institutions, stimulation of other areas of innovative development (education, knowledge and technology, infrastructure) leads to a decrease in the quality of life.