Simple Membership Functions Research Articles

Implementing fuzzy SMRGT, ANN, and ANFIS for flow coefficient estimation in Antalya River Basin

The estimation of the flow coefficient is a vital hydrological procedure that holds considerable importance in flood prediction, water resource management, and flood mitigation. The precise estimation of the flow coefficient is imperative in mitigating flood-related damages, administering flood alert mechanisms, and regulating water discharge. It is hard to accurately determine the flow coefficient without a good understanding of the river basin’s hydrology, climate, topography, and soil characteristics. A range of methodologies have been documented in the most recent body of literaturefor flow coefficient modeling. The majority of these methods, however, depend on opaque techniques that lack generalizability. Therefore, this research employed three distinct methodologies—specifically, the Adaptive Neural Fuzzy Inference System (ANFIS), the Simple Membership Function, and the Fuzzy Rules Generation Technique (SMRGT) are all examples of fuzzy inference systems, and Artificial Neural Network (ANN), to achieve its objectives. The Aksu River Basin in Antalya, Turkey, was chosen as the study area. The models underwent multiple permutations of precipitation (P), temperature (T), relative humidity (Rh), wind speed (Ws), land use (LU), and soil properties (Sp) data that were tailored to the particular study region. The study analyzed the results using various performance metrics of the model such as mean absolute error (MAE), Nash–Sutcliffe efficiency coefficient (NSE), root mean square error (RMSE), and correlation coefficient (R2). The results indicate that the SMRGT method resulted in a remarkable degree of accuracy in forecasting the flow coefficient, as demonstrated with the minimal RMSE and MAE values and high correlation coefficient values. The study’s findings suggest that the SMRGT method was applied effectively in hydrological analysis to estimate the flow coefficient, contributing to more accurate flood prediction, water resource management, and flood mitigation strategies.

Application of a new fuzzy logic model known as "SMRGT" for estimating flow coefficient rate

Since we all have our own set of limitations when it comes to perceiving the world and reasoning profoundly, we are constantly met with uncertainty as a result of a lack of information (lexical impression, incompleteness), as well as specific measurement inaccuracies. It has been found that uncertainty, which shows up as ambiguity, is the root cause of complexity, which is everywhere in the real world. Most of the uncertainty in civil engineering systems comes from the fact that the constraints (parameters) are hard to understand and are described in a vague way. The ambiguity comes from a number of sources, including physical arbitrariness, statistical uncertainty due to using limited information to estimate these characteristics, and model uncertainty due to using overly simplified methods and idealized depictions of actual performances. Thus, it is better to combine fuzzy set theory and fuzzy logic. Fuzzy logic is well-suited to modelling the indeterminacy and ambiguity that results from multiple factors and a lack of data. In order to improve upon a previous predictive model, this paper uses a smart model built on a fuzzy logic system (FLS). Precipitation, temperature, humidity, slope, and land use data were all taken into account as input variables in the fuzzy model. Toprak's original explanation of the simple membership function and fuzzy rules generation technique (SMRGT) was based on the fuzzy-Mamdani methodology and used the flow coefficient as its output. The model's results were compared to available data. The following factors were considered in the comparison: 1) The maximum, minimum, mean, standard deviation, skewness, variation, and correlation coefficients are the seven statistical parameters. 2) Four types of error criteria: Mean Absolute Relative Error (MARE), Mean Square Error (MSE), Mean Absolute Error (MAE), and Root Mean Square Error (RMSE). 3) Scatter diagram.

A Fuzzy Inference-Based TCSC Control Technique to Improve Dynamic Power System Responses

With the expansion of transmission systems, the devices that contribute to the overall power system performance must be adequate to the increasing modeling complexity and requirements. In this sense, the Flexible AC transmission system (FACTS) devices are often employed to improve stability and power quality, while the Thyristor-Controlled Series Compensator (TCSC) is a common example, able to change the equivalent transmission line impedance, improving power flow. This work discusses two established techniques for the control of TCSC devices based on the lead-lag model, whose parameters are defined through metaheuristic techniques, such as Genetic Algorithm and Particle Swarm Optimization. The results found in these publications are implemented in the Matlab/Simulink environment and confronted with the proposed Fuzzy logic application, written with linguistic inference, simplified rules, and simple membership functions. The two published models and the proposed Fuzzy logic performed satisfactorily with very similar results in all scenarios simulated considering a Single Machine Infinite Bus (SMIB) equivalent system model. The big advantage of the use of Fuzzy logic is its modeling simplicity, unlike the heuristic techniques that require much more modeling time and, sometimes, a large number of iterations to achieve acceptable parameters.

Flow Coefficient Determination in Catchment Based on Analysis of Temperature and Wind Speed Data Using the Fuzzy SMRGT Method

In engineering hydrology, calculating the flow coefficient is a crucial step. The flow coefficient calculation is necessary for directing the rational profiteering of water resources, improving the overall efficiency of water resource utilization, and minimizing the effect of catastrophic events. By precisely determining the flow coefficient, which is the most influential factor in flood flow, the current issues will be mitigated substantially. Various techniques are available in the existing literature for modelling flow coefficient. Most of them, however, rely on black-box approaches that are not generalizable. Therefore, this paper applied an intelligent model based on a fuzzy logic system called the Simple Membership Function and Fuzzy Rules Generation Technique (SMRGT). The new technique considers the physical cause-effect relationship and is intended to aid individuals who struggle to choose the number, form, and logic of membership functions and fuzzy rules in any fuzzy set. The study area’s temperature and wind speed data were incorporated into the SMRGT model’s input variables. The output was the flow coefficient. The prediction made by the model was validated against observational data. The comparison relies on numerous statistics and errors. The results indicated that the SMRGT model predicts the flow coefficient extraordinarily well and is an excellent method for generating membership functions and fuzzy rules.

A Comparative Study of Using Adaptive Neural Fuzzy Inference System (ANFIS), Gaussian Process Regression (GPR), and SMRGT Models in Flow Coefficient Estimation

Estimating the flow coefficient is a crucial hydrologic process that plays a significant role in flood forecasting, water resource planning, and flood control. Accurate prediction of the flow coefficient is essential to prevent flood-related losses, manage flood warning systems, and control water flow. This study aimed to predict the flow coefficient for a period of 19 years (2000-2019) in the Aksu River Sub-Basin in Turkey, using historical climatic data, including precipitation, temperature, and humidity, provided by The Turkish State of Meteorological Service (TSMS). The study utilized three different approaches, namely, the Adaptive Neural Fuzzy Inference System (ANFIS), Simple Membership function and fuzzy Rules Generation Technique (SMRGT), and Gaussian Process Regression (GPR), to predict the flow coefficient. The models were evaluated using several statistical tests, such as Root Mean Square Error (RMSE), Coefficient of Determination (R2), Mean Absolute Error (MAE), and Mean Square Error (MSE), to determine their accuracy. Based on the evaluation criteria, it is concluded that the Simple Membership Functions and Fuzzy Rules Generation Technique (SMRGT) model has superior flow coefficient estimation performance than the other models.

A comparative study on daily evapotranspiration estimation by using various artificial intelligence techniques and traditional regression calculations.

Evapotranspiration is an important parameter to be considered in hydrology. In the design of water structures, accurate estimation of the amount of evapotranspiration allows for safer designs. Thus, maximum efficiency can be obtained from the structure. In order to accurately estimate evapotranspiration, the parameters affecting evapotranspiration should be well known. There are many factors that affect evapotranspiration. Some of these can be listed as temperature, humidity in the atmosphere, wind speed, pressure and water depth. In this study, models were created for the estimation of the daily evapotranspiration amount by using the simple membership functions and fuzzy rules generation technique (fuzzy-SMRGT), multivariate regression (MR), artificial neural networks (ANNs), adaptive neuro-fuzzy inference system (ANFIS) and support vector regression (SMOReg) methods. Model results were compared with each other and traditional regression calculations. The ET amount was calculated empirically using the Penman-Monteith (PM) method which was taken as a reference equation. In the created models, daily air temperature (T), wind speed (WS), solar radiation (SR), relative humidity (H) and evapotranspiration (ET) data were obtained from the station near Lake Lewisville (Texas, USA). The coefficient of determination (R2), root mean square error (RMSE) and average percentage error (APE) were used to compare the model results. According to the performance criteria, the best model was obtained by Q-MR (quadratic-MR), ANFIS and ANN methods. The R2, RMSE, APE values of the best models were 0,991, 0,213, 18,881% for Q-MR; 0,996; 0,103; 4,340% for ANFIS and 0,998; 0,075; 3,361% for ANN, respectively. The Q-MR, ANFIS and ANN models had slightly better performance than the MLR, P-MR and SMOReg models.

Turning inserts the selection approach based on fuzzy comprehensive evaluation

Tool selection is a multi-criteria decision-making problem in the presence of various selection criteria and a set of alternatives, but previous works are limited to evaluating the tools within the workshop tool library. To intelligently select proper inserts across suppliers under the Internet environment, an insert data format based on ISO 513 was established, and a framework was then designed to obtain a set of alternatives from different suppliers based on fuzzy intervals. Then, knowledge was described with convenient language and the simple membership function to build an intelligent system, which would infer the matching degree of insert characteristics to the machining conditions. Furthermore, analytic hierarchy process was applied to sort the alternatives. Finally, the case study shows that compared with previous works and machinists, this work not only obtains a set of alternatives from all suppliers who uploaded their product data with the designed format but comprehensively evaluates the insert (take finishing low-carbon steel as an example, both cemented carbide and cermet are recommended, the nose radius reduces 25%, the environmental index increases 25%, while the rake reduces 11.25%, when compared with machinists who tend to select the larger rake angle foe finishing). A platform was also developed based on Visual Studio 2015 and SQL Server 2012 to improve selection efficiency for inexperienced CNC operators, purchasers, and vendors.

Prediction of CO<SUB align="right">2 emission in transportation sector by computational intelligence techniques

Carbon footprint is considered the main cause of global warming. There are various studies on environmental sustainability carried out global scale. In this study, prediction models were developed for CO2 emissions in transportation sector. Artificial neural networks (ANN), simple membership functions and fuzzy rule generation technique (SMRGT), support vector machine (SVM) and adaptive neuro fuzzy inference system (ANFIS) methods, which are artificial intelligence techniques (AI), and also multiple linear regression (MLR), which is a statistical method, were used for the analysis. As a result of the comparison the best performance was seen in ANN model.

An Adaptive Smoothness Parameter Strategy for Variational Optical Flow Model

The smoothness parameter is used to balance the weight of the data term and the smoothness term in variational optical flow model, which plays very significant role for the optical flow estimation, but existing methods fail to obtain the optimal smoothness parameters (OSP). In order to solve this problem, an adaptive smoothness parameter strategy is proposed. First, an amalgamated simple linear iterative cluster (SLIC) and local membership function (LMF) algorithm is used to segment the entire image into several superpixel regions. Then, image quality parameters (IQP) are calculated, respectively, for each superpixel region. Finally, a neural network model is applied to compute the smoothness parameter by these image quality parameters of each superpixel region. Experiments were done in three public datasets (Middlebury, MPI_Sintel, and KITTI) and our self-constructed outdoor dataset with the proposed method and other existing classical methods; the results show that our OSP method achieves higher accuracy than other smoothness parameter selection methods in all these four datasets. Combined with the dual fractional order variational optical flow model (DFOVOFM), the proposed model shows better performance than other models in scenes with illumination inhomogeneity and abnormity. The OSP method fills the blank of the research of adaptive smoothness parameter, pushing the development of the variational optical flow models.

River Flow Estimation Using Artificial Intelligence and Fuzzy Techniques

Accurate determination of river flows and variations is used for the efficient use of water resources, the planning of construction of water structures, and preventing flood disasters. However, accurate flow prediction is related to a good understanding of the hydrological and meteorological characteristics of the river basin. In this study, flow in the river was estimated using Multi Linear Regression (MLR), Artificial Neural Network (ANN), M5 Decision Tree (M5T), Adaptive Neuro-Fuzzy Inference System (ANFIS), Mamdani-Fuzzy Logic (M-FL) and Simple Membership Functions and Fuzzy Rules Generation Technique (SMRGT) models. The Stilwater River in the Sterling region of the USA was selected as the study area and the data obtained from this region were used. Daily rainfall, river flow, and water temperature data were used as input data in all models. In the paper, the performance of the methods is evaluated based on the statistical approach. The results obtained from the generated models were compared with the recorded values. The correlation coefficient (R), Mean Square Error (MSE), and Mean Absolute Error (MAE) statistics are computed separately for each model. According to the comparison criteria, as a final result, it is considered that Mamdani-Fuzzy Logic (M-FL) and Simple Membership Functions and Fuzzy Rules Generation Technique (SMRGT) model have better performance in river flow estimation than the other models.

A comparative study of estimating solar radiation using machine learning approaches: DL, SMGRT, and ANFIS

ABSTRACT Solar energy has a key role in producing clean and emissions-free power compare to conventional methods. However, sustainable development also requires a reliable and predictable energy source. It also needs methods to measure and predict predictable supply. The main aim of the study is to improve reliable and precise solar radiation prediction models on monthly mean daily basis using various machine learning techniques. Simple Membership Function and Fuzzy Rule Generating Technique (SMGRT), which does not require error and trial for model adjustment, is the first-choice model in this study. Experience and observations about the model will greatly reduce the volume of processing for the fuzzy SMGRT model. On the other hand, Deep Learning (DL) and Adaptive Neuro-Fuzzy Inference System (ANFIS) have become increasingly popular in understanding nonlinear data structures and solving complex problems. Therefore, DL and ANFIS were also applied to estimate solar radiation. The data set used in the study were created using sunshine duration (s), extra-terrestrial solar radiation (H0 ), relative humidity (RH), cloudiness (C), air temperature (T) and soil temperature (ST) parameters. Estimation performance of models was evaluated by using several statistical indicators which are Mean Bias Error (MBE), Mean Square Error (MSE), Root Mean Square Error (RMSE), and Correlation Coefficient (R2). When the performances of the models were compared, it was seen that all three models obtained remarkable results. In addition, it was shown that the models performed well based on the metrics in the testing phase. The SMGRT model has slightly better performance than DL and ANFIS for different input combinations. SMGRT Model 1 (with inputs H0, s, and T) shows the best statistical performance (MBE = 0.156, MSE = 1.878, RMSE = 1.371, and R2 = 0.960) not only in SMGRT models but also in others.

Combining fuzzy RES with GA for predicting wear performance of circular diamond saw in hard rock cutting process

Predicting the wear performance of circular diamond saw in the process of sawing hard dimensional stone is an important step in reducing production costs in the stone sawing industry. In the present research work, the effective parameters on circular diamond saw wear are defined, and then the weight of each parameter is determined through adopting a fuzzy rock engineering system (Fuzzy RES) based on defining an accurate Gaussian pattern in fuzzy logic with analogous weighting. After this step, genetic algorithm (GA) is used to determine the levels of the four major variables and the amounts of the saw wear (output parameter) in the classification operation based on the fixed, dissimilar, and logarithmic spanning methods. Finally, a mathematical relationship is suggested for evaluation of the accuracy of the proposed models. The main contribution of our method is the novelty of combination of these methods in fuzzy RES. Before this work, all Fuzzy RESs only use simple membership functions and uniform spanning. Using GA for spanning and normal distribution as membership function based upon our latest work is the first work in fuzzy RES. To verify the selected proposed model, rock mechanics tests are conducted on nine hard stone samples, and the diamond saw wear is measured and compared with the proposed model. According to the results obtained, the proposed model exhibits acceptable capabilities in predicting the circular diamond saw wear.

Membership Function-Weighted Non-Linear Fitting Method for Optical-Sensing Modeling and Reconstruction.

Imprecise measurements present universally due to variability in the measurement error. We devised a very simple membership function to evaluate fuzzily the quality of optical sensing with a small dataset, where a normal distribution cannot be assumed. The proposed membership function was further used as a weighting function for non-linear curve fitting under expected mathematical model constraints, namely the membership function-weighted Levenberg–Marquardt (MFW-LM) algorithm. The robustness and effectiveness of the MFW-LM algorithm were demonstrated by an optical-sensing simulation and two practical applications. (1) In laser-absorption spectroscopy, molecular spectral line modeling was greatly improved by the method. The measurement uncertainty of temperature and pressure were reduced dramatically, by 53.3% and 43.5%, respectively, compared with the original method. (2) In imaging, a laser beam-profile reconstruction from heavy distorted observations was improved by the method. As the dynamic range of the infrared camera increased from 256 to 415, the detailed resolution of the laser-beam profiles increased by an amazing 360%, achieving high dynamic-range imaging to capture optical signal details. Therefore, the MFW-LM algorithm provides a robust and effective tool for fitting a proper physical model and precision parameters from low-quality data.

Image Edge Orientation Estimation via Fuzzy Logic

This paper proposes a novel image edge orientation estimation using fuzzy logic approach. The idea behind orientation estimation is to design edge directed image interpolation for image super resolution enhancement. The calculation of image edge pixel orientation is based on different types of gradients measured across different angles from particular edge pixel. Orientation of edge pixel is classified in to nine angles to ensure the quality of orientation estimation. The advantage of proposed fuzzy based method is that, orientation calculation is done in human language with the help of simple fuzzy rules. Use of simple membership function and rules helps to design an efficient orientation estimation frame work. The experimental results show that fuzzy based orientation estimation outperforms even if the image is affected by noise.

Fuzzy Linear Regression for the Time Series Data which is Fuzzified with SMRGT Method

Our work on regression and classification provides a new contribution to the analysis of time series used in many areas for years. Owing to the fact that convergence could not obtained with the methods used in autocorrelation fixing process faced with time series regression application, success is not met or fall into obligation of changing the models’ degree. Changing the models’ degree may not be desirable in every situation. In our study, recommended for these situations, time series data was fuzzified by using the simple membership function and fuzzy rule generation technique (SMRGT) and to estimate future an equation has created by applying fuzzy least square regression (FLSR) method which is a simple linear regression method to this data. Although SMRGT has success in determining the flow discharge in open channels and can be used confidently for flow discharge modeling in open canals, as well as in pipe flow with some modifications, there is no clue about that this technique is successful in fuzzy linear regression modeling. Therefore, in order to address the luck of such a modeling, a new hybrid model has been described within this study. In conclusion, to demonstrate our methods’ efficiency, classical linear regression for time series data and linear regression for fuzzy time series data were applied to two different data sets, and these two approaches performances were compared by using different measures.

A Fuzzy Tuned Adaptive PI Controller Based UPFC to Improve Power Oscillations Damping in Multi Machine Power System

In this paper, a fuzzy tuned adaptive PI controller (FTAPIC) was proposed for the series inverter of a unified power flow controller (UPFC), which controls the real power flow in a transmission line, to improve power system oscillations damping. In the proposed control method the parameters of a PI controller namely proportional gain (Kp) and integral gain (Ki) were adjusted on-line by a fuzzy logic controller (FLC). The proposed FTAPIC controller was designed using a very simple control knowledge base and simple membership functions (MFs). To compare performances of the proposed FTAPIC and the standard PI controller, transient response studies were conducted using MATLAB/Simulink® software, over a wide range of operating conditions. The simulation results have shown that the UPFC equipped with a FTAPIC provide better performance compared to UPFC equipped with standard PI controller.

Qualitative Model of the Input Impedance of Rectangular Microstrip Antenna

In this paper, a fuzzy-based approach is proposed so as to predict the input impedance of the rectangular microstrip antenna. In the proposed approach, at first, behavior of single microstrip antenna is represented as simple and unchanged membership functions, and the feed probe effect on the input impedance is then extracted as simple curves so that the input impedance of microstrip antenna in despite of other existing models is efficiently predicted.

Linear matrix inequalities‐based membership‐function‐dependent stability analysis for non‐parallel distributed compensation fuzzy‐model‐based control systems

This study investigates the stability of fuzzy-model-based (FMB) control system, which is formed by a Takagi–Sugeno (T–S) fuzzy model representing a non-linear plant and a fuzzy controller connected in a closed loop. The proposed fuzzy controller considers a higher design flexibility that the premise membership functions and the number of fuzzy rules are allowed to be not the same as those of the T–S fuzzy model. By employing simple membership functions and a smaller number of fuzzy rules, the complexity of the fuzzy controller can be reduced to facilitate its implementation. Based on the Lyapunov stability theory, a membership-function-dependent (MFD) stability analysis is proposed to develop stability conditions in the form of linear matrix inequalities (LMIs) to determine the system stability and facilitate the control synthesis. The information of the membership functions is brought to the MFD LMI-based stability conditions, which are dedicated to the FMB control system under consideration. It is thus the proposed MFD stability analysis result is more relaxed compared with the existing membership-function-independent stability analysis results. A simulation example is given to illustrate the effectiveness of the proposed approach.

Fuzzy Decision Support System for Coronary Artery Disease Diagnosis Based on Rough Set Theory

The objective of this research is to develop an evidence based fuzzy decision support system for the diagnosis of coronary artery disease. The development of decision support system is implemented based on three processing stages: rule generation, rule selection and rule fuzzification. Rough Set Theory (RST) is used to generate the classification rules from training data set. The training data are obtained from University California Irvine (UCI) data repository. Rule selection is conducted by transforming the rules into a decision table based on unseen data set. Furthermore, RST attributes reduction is proposed and applied to select the most important rules. The selected rules are transformed into fuzzy rules based on discretization cuts of numerical input attributes and simple triangular and trapezoidal membership functions. Fuzzy rules weighing is also proposed and applied based on rules support on the training data. The system is validated using UCI heart disease data sets collected from the U.S., Switzerland and Hungary and data set from Ipoh Specialist Hospital Malaysia. The system is verified by three cardiologists. The results show that the system is able to give the approximate possibility of coronary artery blocking.

Design of stable fuzzy controller for non-linear systems subject to imperfect premise matching based on grid-point approach

This study investigates the systems stability of fuzzy-model-based (FMB) control systems. Based on the T-S fuzzy model representing the non-linear system, a fuzzy controller using grid-point (GP) technique is proposed to close the feedback loop. A GP is defined as the sub-operating domain of the non-linear system. For each GP, a corresponding GP fuzzy controller is employed to control the system. As the non-linearity in each GP is lower compared to that of the full operating domain, it is in favour of yielding relaxed stability analysis result using the GP control technique of which the nature of the membership functions and operating domain are taken into account. Furthermore, unlike most of the fuzzy control approaches, the proposed one can be applied to FMB control systems subject to imperfect premise matching that the fuzzy model and fuzzy controller do not share the same premise membership functions. As a result, some simple membership functions can be employed for the fuzzy controllers to lower the implementation cost. Based on the Lyapunov stability theory, stability conditions in terms of linear matrix inequalities are derived to guarantee the system stability and facilitate the controller synthesis. Simulation examples are given to demonstrate the merits of the proposed FMB control scheme using the proposed GP technique.