Fuzzy Linear Regression Model Research Articles

Computation of Fuzzy Linear Regression Model using Simulation Data

Regression analysis is a powerful technique for determining the causal influence on population outcome, although it is susceptible to outliers. It also oversimplifies the real-world data and problem, as data is rarely linearly separable. This paper analyses the simulation data of a fuzzy linear regression model (FLRM) model, which can aid in minimizing the interference of unwanted information, hence improving the precision of results. The aim of the fuzzy linear regression model (FLRM) is used to determine the best prediction model with the lowest measurement error. The model provides a fundamental mathematical and statistical framework for acknowledging the data imprecision. This study has applied the fuzzy linear regression model (FLRM) to evaluate the data in 15 rows of respondent models. The study implemented measurement error of cross-validation technique which is mean square error (MSE) and root mean square error (RMSE), to enhance data accuracy. Microsoft Excel and Matlab were applied to obtain the result. The simulation result indicates that comparing models with two measurement errors should be used to determine the optimal results. MSE and RMSE value with six parameters of a degree of fitting H-value have been calculated in the study. It concludes that a degree of fitting H-value of 0.0 is proven as a good model with the lowest MSE and RMSE measurement errors.

Comparison of prediction fuzzy modeling towards high-risk symptoms of lung cancer

Lung cancer constituted 12.2% of newly diagnosed cancer cases globally in 2020. The high fatality rate of the condition is attributed to delayed diagnosis and inadequate symptom recognition. In Malaysia, the incidence of lung cancer is estimated to be 1 in 60 males and 1 in 138 females, with a median age of 70 years or above. Most lung cancer cases were detected during advanced stages, specifically stages III and IV, with a prevalence exceeding 90% for both genders. In Malaysia, most patients are diagnosed in stages III and IV, which are associated with a lower likelihood of long-term survival. Many cases are identified at a late stage, characterized by significant tumor expansion or the spread of cancer cells to areas that cannot be treated surgically. Malaysians are unaware of cancer symptoms; hence the situation is common. To improve survival and reduce mortality, Malaysians must recognize the symptoms of lung cancer. Fuzzy linear regression and multiple linear regression models have been compared to predict high-risk lung cancer symptoms in Malaysia. The fuzzy linear regression model analyses secondary data, eliminates irrelevant information and enhances precision in the results. Lung cancer patients at Al-Sultan Abdullah Hospital (UiTM Hospital) in Selangor provided data for this study. Data from 124 lung cancer patients were analyzed using Microsoft Excel, SPSS, and MATLAB. To improve data accuracy, the study used cross-validation measurement error (MSE and RMSE). According to data analysis, hemoptysis and chest pain are high-risk symptoms with MSE and RMSE values of 1.549 and 1.245, respectively.

Construction of Business Model of Unmanned Economy Under Digital Technology

In the ever-evolving landscape of modern business, the integration of advanced technologies is paramount for optimizing operations, ensuring efficiency, and staying competitive. The business model for the unmanned economy comprises the challenges related to supply chain and logistics. This paper proposed an architecture of LM-LSTM (Linear Regression and Long Short-Term Memory) model within the context of the Unmanned business model. The proposed model uses the mandami based fuzzy rule for the computation of the unmanned economy. Within the mandami fuzzy linear regression model is adopted for the computation and estimation of the variables related to the unmanned economy. The objective is to provide a comprehensive analysis of the impact of this predictive modeling system on various dimensions of the business. Through the generated rules the LSTM model is utilized for the classification and computation of the features related to supply chain, forecast demand and other parameters in an unmanned economy. The examination of 10 unmanned products in Chinese products are evaluated. The findings of LM-LSTM stated that Sales forecasting, one of the critical aspects of any business, has seen a remarkable improvement in accuracy, with an average Mean Absolute Error (MAE) of 3.00%. This accuracy ensures that products are produced and stocked according to actual demand, preventing costly overstocking or stockouts. The inventory management process has been streamlined, with tailored strategies for each product category. This adaptation has resulted in reduced stockouts, efficient parts sourcing, and minimal overstock situations. Supply chain optimization has significantly reduced lead times, enhancing customer satisfaction through timely product deliveries. Customer behavior analysis, facilitated by LM-LSTM, has led to a notable increase in sales across the product range, with an average increase of 91%. This enhanced customer engagement is coupled with substantial cost savings, with an overall reduction of 118%. Downtime has been minimized, contributing to smoother operations and improved customer service.

Forecasting Model Selection with Variables Impact to Predict Electricity Demand at Rajshahi City of Bangladesh

The purpose of this study is to forecast electricity demand by using the best-selected method which untangles all the factors that affect electricity demand. Three different methods traditional methods (Multiple Regression Model), modified-traditional methods (ARMA), and soft computing method (Fuzzy Linear Regression Model) are selected for prediction. Environmental parameters like temperature, humidity, and wind speed are included as variables as Rajshahi has very impactful weather. The impact of each variable was calculated from their standardized values to know the effect of environmental parameters. The accuracy of the three forecasting models is compared by different statistical measures of errors. Using Mean Absolute Percentage Error (MAPE), the errors of the Multiple Regression Model, ARMA, and Fuzzy Linear Regression (FLR) Model are 6.85%, 22.24%, and 4.45%. The other three measures of error also give the FLR gives the best results. Finally, the electricity demand of Rajshahi City for the next five years is forecasted using the Fuzzy Linear Regression Model.

Fuzzy Bridge Regression Model Estimating via Simulation

The main problem when dealing with fuzzy data variables is that it cannot be formed by a model that represents the data through the method of Fuzzy Least Squares Estimator (FLSE) which gives false estimates of the invalidity of the method in the case of the existence of the problem of multicollinearity. To overcome this problem, the Fuzzy Bridge Regression Estimator (FBRE) Method was relied upon to estimate a fuzzy linear regression model by triangular fuzzy numbers. Moreover, the detection of the problem of multicollinearity in the fuzzy data can be done by using Variance Inflation Factor when the inputs variable of the model crisp, output variable, and parameters are fuzzed. The results were compared using standard mean squares error via simulated experiments and taking different sample sizes (20, 40, 80, and 160). The model's superiority was shown by achieving the least value of the mean squares error (MSE(, which indicated by the fuzzy bridge regression model.

An adjustment degree of fitting on fuzzy linear regression model toward manufacturing income

Regression analysis is a popular tool used in data analysis, whereas fuzzy regression is usually used for analyzing uncertain and imprecise data. In the industrial area, the company usually has problems in predicting the future manufacturing income. Therefore, a new approach model is needed to solve the future company prediction income. This article analyzed the manufacturing income by using the multiple linear regression (MLR) model and fuzzy linear regression (FLR) model proposed by Tanaka and Zolfaghari, involving 9 explanatory variables. In order to find the optimum of the FLR model, the degree of fitting (H) was adjusted between 0 to 1. The performance of three methods has been measured by using mean square error (MSE), mean absolute error (MAE) and mean absolute percentage error (MAPE). The analysis proved that FLR with Zolfaghari’s model with the degree of fitting of 0.025 outperformed the MLR and FLR with Tanaka’s model with the smallest error value. In conclusion, the manufacturing income is directly proportional to 6 independent variables. Furthermore, the manufacturing income is inversely proportional to 3 independent variables. This model is suitable in predicting future manufacturing income.

Hesitant t-spherical fuzzy linear regression model based decision making approach using gradient descent method

Hesitant fuzzy set based linear regression model is used to solve decision making problems, where each element is assessed with multiple membership grades. However, in order to handle uncertainty properly, non-membership and abstinence degrees of each elements are also considered as equally significant, which are not captured by hesitant fuzzy set. To resolve these limitations of hesitant fuzzy set based model, this paper proposes hesitant t-spherical fuzzy linear regression model, where hesitant t-spherical fuzzy set can efficiently handle both non-membership and abstinence degrees along with membership degree. The regression model is used to determine the imprecise functional relationship between the dependent and independent variables which are represented using hesitant t-spherical fuzzy set. We apply gradient descent technique to estimate the optimal coefficients of the variables used in the proposed regression model. Finally, the residuals of the regression are computed for the purpose of decision making. The proposed approach has been illustrated using three real life applications (robot selection, revenue generation, and material selection) and compared with the existing approaches. Moreover, we have used sensitivity analysis and weighted spearman’s rank correlation coefficient metrics to demonstrate that the outcome of the proposed model is more consistent and reliable to rank its best alternative compared to existing approaches, which shows its capability to solve real life uncertain decision-making problems.

The Use of Fuzzy Linear Regression Modeling to Predict High-risk Symptoms of Lung Cancer in Malaysia

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.

A fuzzy logic framework to handle uncertainty in remote sensing‐based hydrological data for water budget improvement across mid‐ and small‐scale basins

AbstractIn recent years, the efficacy of remote sensing (RS) products for water budget (WB) analysis has been widely tested and implemented in global and regional basins. Although RS products provide high temporal and spatial resolution images with near‐global coverage, uncertainty is still a significant problem. Fuzzy logic is a powerful technique for dealing with uncertainty in different engineering problems. In this study, the annual residual error () in the WB equation arising from the uncertainties of the RS products was minimized by applying fuzzy correction coefficients to each WB component. For analysis, three different fuzzy linear regression (FLR) models with 14 different sub‐models were used in the two basins having different spatial characteristics, namely Sakarya and Cyprus basins. Although FLR sub‐models produce similar findings in the Sakarya basin, they generated more complex results in the Cyprus basin. This is mainly due to the higher uncertainty of the RS products in the Cyprus basin. The Cyprus basin is too small for some low‐resolution RS‐based products to resolve, and it has a higher leakage error due to across ocean/land boundary. In addition, the general performance of sub‐models is better in the Sakarya basin than that in the Cyprus basin. The best fuzzy sub‐models reduced the error up to 68% and 52% in terms of mean absolute error compared with the non‐fuzzy model in the Sakarya and Cyprus basins, respectively. Further evaluations showed that the best sub‐model precipitation well captured the temporal patterns of gauge observations in both basins. Moreover, they have the best consistency with gauge observations in terms of root mean square error, Kling‐Gupta efficiency, and percent bias in both basins. The results proved that this study will provide valuable insights into WB analysis in ungauged basins by incorporating the fuzzy logic approach into hydrological RS products.

A fuzzy linear regression model with autoregressive fuzzy errors based on exact predictors and fuzzy responses

A fuzzy linear regression model with autoregressive fuzzy errors based on exact predictors and fuzzy responses

Making Group Decisions within the Framework of a Probabilistic Hesitant Fuzzy Linear Regression Model.

A fuzzy set extension known as the hesitant fuzzy set (HFS) has increased in popularity for decision making in recent years, especially when experts have had trouble evaluating several alternatives by employing a single value for assessment when working in a fuzzy environment. However, it has a significant problem in its uses, i.e., considerable data loss. The probabilistic hesitant fuzzy set (PHFS) has been proposed to improve the HFS. It provides probability values to the HFS and has the ability to retain more information than the HFS. Previously, fuzzy regression models such as the fuzzy linear regression model (FLRM) and hesitant fuzzy linear regression model were used for decision making; however, these models do not provide information about the distribution. To address this issue, we proposed a probabilistic hesitant fuzzy linear regression model (PHFLRM) that incorporates distribution information to account for multi-criteria decision-making (MCDM) problems. The PHFLRM observes the input–output (IPOP) variables as probabilistic hesitant fuzzy elements (PHFEs) and uses a linear programming model (LPM) to estimate the parameters. A case study is used to illustrate the proposed methodology. Additionally, an MCDM technique called the technique for order preference by similarity to ideal solution (TOPSIS) is employed to compare the PHFLRM findings with those obtained using TOPSIS. Lastly, Spearman’s rank correlation test assesses the statistical significance of two rankings sets.

Introducing a trapezoidal interval type-2 fuzzy regression model

The uncertainty is an important attribute about data that can arise from different sources including randomness and fuzziness, therefore in uncertain environments, especially, in modeling, planning, decision-making, and control under uncertainty, most data available contain some degree of fuzziness, randomness, or both, and at the same time, some of this data may be anomalous (outliers). In this regard, the new fuzzy regression approaches by creating a functional relationship between response and explanatory variables can provide efficient tools to explanation, prediction and possibly control of randomness, fuzziness, and outliers in the data obtained from uncertain environments. In the present study, we propose a new two-stage fuzzy linear regression model based on a new interval type-2 (IT2) fuzzy least absolute deviation (FLAD) method so that regression coefficients and dependent variables are trapezoidal IT2 fuzzy numbers and independent variables are crisp. In the first stage, to estimate the IT2 fuzzy regression coefficients and provide an initial model (by original dataset), we introduce two new distance measures for comparison of IT2 fuzzy numbers and propose a novel framework for solving fuzzy mathematical programming problems. In the second stage, we introduce a new procedure to determine the mild and extreme fuzzy outlier cutoffs and apply them to remove the outliers, and then provide the final model based on a clean dataset. Furthermore, to evaluate the performance of the proposed methodology, we introduce and employ suitable goodness of fit indices. Finally, to illustrate the theoretical results of the proposed method and explain how it can be used to derive the regression model with IT2 trapezoidal fuzzy data, as well as compare the performance of the proposed model with some well-known models using training data designed by Tanaka et al. [55], we provide two numerical examples.

A fuzzy functional linear regression model with functional predictors and fuzzy responses

A fuzzy functional linear regression model with functional predictors and fuzzy responses

Hesitant Fuzzy Linear Regression Model for Decision Making

An expert may experience difficulties in decision making when evaluating alternatives through a single assessment value in a hesitant environment. A fuzzy linear regression model (FLRM) is used for decision-making purposes, but this model is entirely unreasonable in the presence of hesitant fuzzy information. In order to overcome this issue, in this paper, we define a hesitant fuzzy linear regression model (HFLRM) to account for multicriteria decision-making (MCDM) problems in a hesitant environment. The HFLRM provides an alternative approach to statistical regression for modelling situations where input–output variables are observed as hesitant fuzzy elements (HFEs). The parameters of HFLRM are symmetric triangular fuzzy numbers (STFNs) estimated through solving the linear programming (LP) model. An application example is presented to measure the effectiveness and significance of our proposed methodology by solving a MCDM problem. Moreover, the results obtained employing HFLRM are compared with the MCDM tool called technique for order preference by similarity to ideal solution (TOPSIS). Finally, Spearman’s rank correlation test is used to measure the significance for two sets of ranking.

Efficiency Comparison of the Parameters Estimation by a Fuzzy Linear Regression Model

The fuzzy regression method can be used for fitting the fuzzy data for the construction of the simple linear regression model. This paper aims to study the performance and compare the adaptive fuzzy method and traditional fuzzy method by using the criteria of mean square error (MSE) and the coefficient of determine R 2. A Monte Carlo simulation with 5,000 iterations was performed to achieve the objective of research. In simulations, the independent variable has a gamma distribution with the parameters are α = 4, 5, 6 and β = 1. We carried out simulations to examine the performance of MSE from the adaptive fuzzy regression model and the traditional fuzzy regression model. The results showed that the transformation of independent variable with gamma distribution to be a normal distribution make the simple linear regression by the adaptive fuzzy method outperforms the traditional fuzzy method. In terms of MSE, the adaptive fuzzy method performed better than the traditional fuzzy method. In addition, the values of coefficient of determine from the adaptive fuzzy method and the traditional fuzzy method are slightly different.

Fuzzy Linear Regression Model Based on Adaptive Lasso Method

Fuzzy Linear Regression Model Based on Adaptive Lasso Method

Unit hydrograph identification based on fuzzy regression analysis

A methodology has been developed to treat the uncertainties of the unit hydrograph rainfall-runoff transformation based on the fuzzy linear regression model. The components of the unit hydrograph are proposed to be symmetric triangular fuzzy numbers. The main idea is to develop a fuzzified version of the widely—used unit hydrograph. The input of the model is the effective rainfall (which is a set of crisp numbers) and the output is the runoff (which is a set of fuzzy numbers). The problem of determining the fuzzy components of the unit hydrograph is transformed into a linear optimization approach based on the fuzzy linear regression of Tanaka. The condition applied is that the data must be included in the fuzzy band of discharge produced by the fuzzy unit hydrograph. However, some modifications of the widely-used fuzzy regression are proposed in order to be compatible with the unit hydrograph implementation. The model was tested based on twenty real rainfall-runoff events, the conclusion being that it works well in the case of an individual storm event. However, the consideration of many storms seems to be required in order to increase the applicability of the produced fuzzy hydrograph to other storms in such a way that the fuzziness is increased. Several measures of suitability are proposed in order to check the efficiency of the proposed method. Several other useful comments according to the comparison with other unit hydrograph considerations are made.

Quantile Fuzzy Varying Coefficient Regression based on kernel function

The fuzzy varying coefficient regression model is a generalized version of fuzzy linear regression model. This kind of model is flexible and adaptable than fuzzy linear regression model. In this paper, we introduce a fuzzy varying coefficient regression model based on the quantile loss function and under the kernel function. Based on the presented goodness of fit indices, we show that the proposed approach is robust under the outlier data. Some applications of this approach are studied on some data sets and a simulated data set.

Comparative Assessment of Multiple Linear Regression and Fuzzy Linear Regression Models

Comparative Assessment of Multiple Linear Regression and Fuzzy Linear Regression Models

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.