Fuzzy Regression Model Research Articles

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.

A fuzzy nonparametric regression model based on an extended center and range method

When dealing with nonparametric regression problems, kernel-based methods are often employed. In this paper, we investigate nonparametric regression problems with fuzzy responses and exact predictors by implementing an extended center and range method within a three-stage procedure. For this purpose, we utilize the Nadaraya–Watson estimator for estimating the unknown fuzzy smooth function. In each stage, the unknown bandwidth is determined with the help of a generalized cross validation criterion. To evaluate and to compare the performance of our proposed fuzzy nonparametric regression model with established regression models, different goodness-of-fit criteria are considered. Finally, we investigate the practical applicability and show the superiority of the proposed regression model by means of a simulation study and real data applications.

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.

A fuzzy Bayesian regression model with Gaussian process prior based on exact predictors and fuzzy responses

A fuzzy Bayesian regression model with Gaussian process prior based on exact predictors and fuzzy responses

New approach based on a fuzzy regression model for a photovoltaic system

New approach based on a fuzzy regression model for a photovoltaic system

Prediction of the Production Quality During Flat Bottom Drilling of Low Lead Brass Alloy Using Fuzzy Logic and Regression Models

The approved restrictive rules on the containment of Lead element in the chemical composition of the brass alloys which are utilized in drinking water and pumping systems have resulted in developing of new material generations. Neglection or limitation of this element has faced the industry with some serious problems such as lower machinability as compared to the conventional ones. Furthermore, since the most application of the manufactured components from these alloys corresponds to the fluids transfer, the permeability property between the parts and their surface becomes prominent. In other words, any burrs or extra material which are left on the surfaces of manufactured components will make assembly troublesome, causing seals to tear, and permeability problems in the user's hands. In this study, the quality of the machined blind holes with flat bottom drills with various geometries including radial, axial rake angle as well as the cutting edge-radius have been investigated for machining of low-lead brass alloy. Moreover, it has attempted to develop fuzzy logic and regression models in order to predict the machined holes burr height and surface quality. The model predictions have been compared with the experimental data. The obtained results have demonstrated that the developed models are able in predicting of the product quality.

Fuzzy Semi-Parametric Logistic Quantile Regression Model

In this paper, the fuzzy semi-parametric logistic quantile regression model was studied in the absence of special conditions in the classical regression models. This model becomes more flexible to deal with data for outlier's values and in the absence of a linear regression condition when the data of the dependent variable are restricted and fuzzy data and some of the variables are nonparametric, and the dependent variable in this model represents the fuzzy triangular number.
 The estimation of the semi-parametric logistic quantile regression model has been applied to simulated data when the sample size is (25, 50, 75, 100) and with a repetition of 1000. Where the model is estimated in two steps, the first step is to estimate the parametric part, and the second step is to estimate the non-parametric part by the Nadaraya-Watson estimator through different kernel functions. Depending on the mean squares error and the measure of goodness of fit, the results indicated the best estimate of a model with the Kernel-Cassian function when the quantile of the fuzzy conditional distribution equals 0.2 for all sample sizes .

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.

Refinement of fatigue curve parameters using fuzzy set theory and tomography images processing of censored composite samples

The fatigue curve is important in engineering practice. Since the task of constructing a fatigue curve is characterized, among other things, by the presence of qualitative (not numerical), inaccurate and incomplete information, the question arises of the appropriateness of applying the theory of fuzzy sets. To clarify information on censored, namely, removed from testing upon reaching the test base specimens, the use of computed tomography to study the degree of their damage is proposed. A fuzzy regression model has been developed to consider linguistic variable that describes the status of a sample (broken or censored). With fuzzy dependent variables of the of regression model, the coefficients of the equation also turn out to be fuzzy. For the fuzzy dependent variable of the time before failures of censored samples, the degree of damage is additionally evaluated based on the rating of experts by the analysis of tomography images. The model made it possible to estimate the interval of expected life for a given stress amplitude using an uncertainty accounting method that differs from the classical statistical description. An example of constructing a fuzzy fatigue curve for polymer composite materials is considered.

Quantum Fuzzy Regression Model for Uncertain Environment

In the era of big data, traditional regression models cannot deal with uncertain big data efficiently and accurately. In order to make up for this deficiency, this paper proposes a quantum fuzzy regression model, which uses fuzzy theory to describe the uncertainty in big data sets and uses quantum computing to exponentially improve the efficiency of data set preprocessing and parameter estimation. In this paper, data envelopment analysis (DEA) is used to calculate the degree of importance of each data point. Meanwhile, Harrow, Hassidim and Lloyd (HHL) algorithm and quantum swap circuits are used to improve the efficiency of high-dimensional data matrix calculation. The application of the quantum fuzzy regression model to small-scale financial data proves that its accuracy is greatly improved compared with the quantum regression model. Moreover, due to the introduction of quantum computing, the speed of dealing with high-dimensional data matrix has an exponential improvement compared with the fuzzy regression model. The quantum fuzzy regression model proposed in this paper combines the advantages of fuzzy theory and quantum computing which can efficiently calculate high-dimensional data matrix and complete parameter estimation using quantum computing while retaining the uncertainty in big data. Thus, it is a new model for efficient and accurate big data processing in uncertain environments.

NEURO-FUZZY MODELING AS SUPPORT FOR DECISION-MAKING IN THE PRODUCTION OF IRRIGATED CORIANDER UNDER MULCH IN THE SEMI-ARID REGION

Reducing water consumption by crops in semi-arid regions is an important factor for the sustainability of agriculture in these locations. In this sense, this study aims to evaluate the neuro-fuzzy inference method as a support for decision-making in irrigated coriander cultivation. The experiment was performed in two cultivation cycles in Pentecoste-CE, Brazil. The experiment was conducted in randomized blocks arranged in a split-plot design with five primary treatments, consisting of irrigation depths (50, 75, 100, 125, and 150% of the localized evapotranspiration, ETcloc), and five secondary treatments, consisting of different levels of bagana mulch (0, 25, 50, 75, and 100%, equivalent to 16 t ha−1). Neuro-fuzzy models with two input variables and eight output biometric variables were developed to evaluate growth (plant height, number of roots, and root length) and yield variables (productivity and shoot and root fresh and dry mass). In the first cycle, the best results occurred close to 55% ETcloc and between 40 and 50% of mulch; in the second cycle, water consumption returned results between 50 and 80% ETcloc. The fuzzy and multiple regression models showed MAE, MSE, and RMSE errors of 9, 22, and 10% lower, respectively. The neuro-fuzzy model might be a viable option for decision-making in irrigated crops, being able to optimize the use of natural resources and available water in semi-arid regions. The use of 55% of irrigation depth and a range of 40 to 50% of mulch can be a strategy for a higher water use efficiency.

On modeling regression in full interval-valued fuzzy environment

We apply the general extension-principle-based approach to make predictions based on a regression model in a full interval-valued fuzzy environment. We use triangular interval-valued fuzzy numbers that model the uncertainty of the observed inputs and outputs to derive the predicted outputs in full accordance with Zadeh's extension principle. On one side, we enhance the Monte Carlo based algorithm introduced in the literature for simulating the output predictions of a fuzzy regression model by reducing the universe of random selections still keeping the accuracy of the empirical results; and on the other side, we solve quadratic models to derive the left endpoints of the α-cut intervals of the exact results. We use one real-life problem from hydrology engineering with data recalled from the literature to carry out numerical experiments and illustrate our proposed methodology.

Estimating fuzzy nonparametric regression model based on some smoothing methods with practical application

في هذا البحث تم تطبيق طرائق التقدير اللامعلمية الضبابية المستندة على بعض أساليب التمهيد على بيانات حقيقية خاصة بسوق العراق للأوراق المالية، إذ تم دراسة حركة التداول لشركة بغداد للمشروبات الغازية لعام (2016)(للفترة من 2016/1/1 ولغاية 2016/12/31) وتم الحصول على عينة بـ(148) مشاهدة من اجل بناء أنموذج للعلاقة مابين أسعار الأسهم (الأدنى والأعلى والمتوسط) وحجم التداول . ومن خلال مقارنة نتائج معيار (G.O.F) ولأساليب التمهيد الثلاثة وعند دوال النواة المعتمدة والمقترحة من قبل الباحثين تم ملاحظة بأن أقل قيمة لهذا المعيار كانت لأسلوب الجوار الأقرب(K-NN) وعند دوال النواة (Gaussian).

FEWMA and Fuzzy Regression Model Control Chart one a-cut With Application

Abstract:
 In many real-world applications, the data to be used in a control charting method are not crisp since they are approximated due to environmental uncertainties, In these situations, fuzzy numbers and linguistic variables are used to grab such uncertainties. That is why the use of a fuzzy control chart, in which fuzzy data are used, is justified. As an exponentially weighted moving average (EWMA) scheme is usually used to detect small shifts, in this paper a fuzzy EWMA (F-EWMA) control chart is proposed to detect small shifts in the process mean when fuzzy data are available. As well as The fuzzy regression control chart which is a functional technique to evaluate the process in which the average has a trend and the data represents a linguistic or approximate value.
 In this paper, the application of fuzzy logic in statistical quality control have been done by plotting fuzzy EWMA chart and Fuzzy linear regression model control chart depending on a suggested algorithm prepared for this purpose, as well as the theoretical structure of the “a-level fuzzy midrange for a-cut fuzzy -regression control chart” is proposed for triangular membership functions and applying that to the chemical analysis data of a water component, Total Dissolved Solid ( TDS) in water from the KANY Factory to detect small shifts in the process means, the data contains three groups (TDS-a, TDS-b, TDS-c), for 24 days each day containing 5 hour data, as shown in Table (1)
 The comparison showed that the fuzzy linear regression model Control chart is a good technique and more suitable, accuracy, sensitivity than the traditional linear regression model Control chart.

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.

An application of fuzzy logistic regression for predicting CVSS severity category of industrial control systems

Cybersecurity is rapidly gaining significance due to growing use of computers in daily life and business sectors. Likewise, industrial sector has also become more vulnerable to cyber threats exclusively with the onset of Industry 4.0, which is a digital transformation evolved with industrial control systems (ICS). Nowadays industrial organizations aim to build capacity towards protection of ICS to be cybersafe. To assess the effects of vulnerabilities in ICS, organizations utilize Common Vulnerability Scoring System (CVSS), which calculates severity categories/scores. In this study, we implemented a prediction model for CVSS vulnerability categorization of ICS. Although there exist many applicable methods to use in data analysis paradigm such as statistical regression, cluster and classification analysis, the categorical form of CVSS data based on verbal statements and the failure to satisfy basic statistical assumptions for classical models motivated us to focus on implementation of fuzzy logistic regression (FLR) model, which is one possible alternative method. We chose the FLR method to explore that it is applicable to ICS vulnerability data. Furthermore, the model was improved by employing metaheuristic algorithms to optimize the spread of fuzzy numbers representing input variables. This study is expected to contribute to practical application of vulnerability categorization of ICS.

Hemodynamic Analysis for Olfactory Perceptual Degradation Assessment Using Generalized Type-2 Fuzzy Regression

Olfactory perceptual degradation (OPD) refers to the inability of people to recognize the variation in concentration levels of olfactory stimuli. This article attempts to assess the degree of OPD of subjects from their hemodynamic response to olfactory stimuli. This is done in two phases. In the first (training) phase, a regression model is developed to assess the degree of concentration levels of an olfactory stimulus by a subject from her hemodynamic response to the stimulus. In the second (test) phase, the model is employed to predict the possible concentration level experienced by the subject in [0, 100] scale. The difference between the model-predicted response and the oral response (the center value of the qualitative grades) of the subject about her perceived concentration level is regarded as the quantitative measure of the degree of subject’s olfactory degradation. The novelty of the present research lies in the design of a general type-2 fuzzy regression model, which is capable of handling uncertainty due to the presence of intrasession and intersession variations in the brain responses to olfactory stimuli. The attractive feature of the article lies in adaptive tuning of secondary membership functions to reduce model prediction error in an evolutionary optimization setting. The effect of such adaptation in secondary measures is utilized to adjust the corresponding primary memberships in order to reduce the uncertainty involved in the regression process. The proposed regression model has good prediction accuracy and high time efficiency as evident from average percentage success rate (PSR) and runtime complexity analysis, respectively. The Friedman test undertaken also confirms the superior performance of the proposed technique with other competitive techniques at 95% confidence level.

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

Meticulous Land Cover Classification of High-Resolution Images Based on Interval Type-2 Fuzzy Neural Network with Gaussian Regression Model

This paper proposes a land cover classification method that combines a Gaussian regression model (GRM) with an interval type-2 fuzzy neural network (IT2FNN) model as a classification decision model. Problems such as the increase in the complexity of ground cover, the increase in the heterogeneity of homogeneous regions, and the increase in the difficulty of classification due to the increase in similarity in different regions are overcome. Firstly, the local spatial information between adjacent pixels was introduced into the Gaussian model in image gray space to construct the GRM. Then, the GRM was used as the base model to construct the interval binary fuzzy membership function model and characterize the uncertainty of the classification caused by meticulous land cover data. Thirdly, the upper and lower boundaries of the membership degree of the training samples in all categories and the principle membership degree as input were used to build the IT2FNN model. Finally, in the membership space, the neighborhood relationship was processed again to further overcome the classification difficulties caused by the increased complexity of spatial information to achieve a classification decision. The classical method and proposed method were used to conduct qualitative and quantitative experiments on synthetic and real images of coastal areas, suburban areas, urban areas, and agricultural areas. Compared with the method considering only one spatial neighborhood relationship and the classical classification method without a classification decision model, for images with relatively simple spatial information, the accuracy of the interval type-2 fuzzy neural network Gaussian regression model (IT2FNN_GRM) was improved by 1.3% and 8%, respectively. For images with complex spatial information, the accuracy of the proposed method increased by 5.0% and 16%, respectively. The experimental results prove that the IT2FNN_GRM method effectively suppressed the influence of regional noise in land cover classification, with a fast running speed, high generalization ability, and high classification accuracy.