Trapezoidal Membership Functions Research Articles

A Mamdani fuzzy inference system with trapezoidal membership functions for investigating fishery production

Seas, marine ecosystems, and coastal regions are crucial components of our environment. Numerous scientific strategies have been adopted to boost fisheries and aquaculture productivity. This study proposes a fuzzy-logic-based model to produce fisheries in India, which ranks fourth worldwide for fisheries production. Five input variables, such as fish seed, export, post-harvesting, released fund, and temperature, are considered inputs, and the production of fisheries is taken as the output variable. A Mamdani-type fuzzy inference system with trapezoidal membership functions is prepared with 243 rules in the IF-THEN format. This mathematical model investigates the impacts of input parameters on the production of Indian fisheries. We fit the model with the real-world data and show that fish seed, export, released fund, and post-harvesting facilities positively impact fisheries production. However, a very high temperature is unsuitable for high production, even if all other parameters lie at their desired level.

New algorithm for two-machine fuzzy flow shop scheduling problem with trapezoidal fuzzy processing time

The flow-shop scheduling problem (FSSP) has received a considerable amount of attention due to its wide-ranging applications. However, the omission of uncertainty significantly diminishes the practicality of scheduling results, underscoring its the necessity to address uncertainty in the flow shop problem. In this paper, a fuzzy two-machine flow-shop problem is considered and an effective algorithm with a fuzzy ranking method is proposed to minimize the total waiting time. The processing times are represented using trapezoidal membership functions. Furthermore, a two-stage flow shop scheduling problem is used in the proposed algorithm and various categories of fuzzy mean techniques. The experimental results and statistical comparisons demonstrate that the proposed algorithm exhibits significant advantages in effectively solving the FFSSP (Fuzzy Flow-Shop Scheduling Problem).

Short-Term Electrical Energy Demand Forecasting Using Fuzzy Logic Technique

Minimization of electrical energy wastage and provision of its regular supply make electrical load forecasting an important aspect of the power infrastructure. An accurate load forecasting is crucial for the reduction of the cost of electrical energy generation and spinning reserve capacity. Therefore, in this study, fuzzy logic (FL) technique was employed for the projection of electrical energy demand on short-term basis. The FL model was trained using the six months hourly load and temperature data respectively obtained from 132/33 kV Ikeja West Transmission Station, Ayobo and Nigerian Meteorological Agency, Oshodi, Lagos State, Nigeria. Triangular and trapezoidal membership functions (MFs) were used in the training of the model with Mamdani fuzzy inference system. The time, load and temperature inputs were fuzzified into six, four and three MFs respectively while the fuzzification process used 25 fuzzy rule bases. The centroid method of defuzzification was used to change the results into readable values. The adequacy of the FL model was determined using five metrics including mean square error (MSE), mean absolute error (MAE), mean absolute percentage error (MAPE), chi square (χ2) and F- test. The obtained results revealed that the FL model developed excelled in all the five tests of adequacy considered with MSE, MAE, MAPE, χ2 and F-test values of 4.17, 6.74, 11.51%, 7.93 and 1.27 respectively and hence, performed satisfactorily. This work established that the fuzzy logic approach is appropriate for electrical load projection on short-term basis.

An optimization model for fuzzy nonlinear programming with Beale's conditions using trapezoidal membership functions

Non-linear Programming (NLP) is an optimization technique for determining the optimum solution to a broad range of research issues. Many times, the objective function is non-linear, owing to various economic behaviors such as demand, cost, and many others. Since the appearance of Kuhn and Tucker's fundamental theoretical work, a general NLP problem can be resolved using many methods to find the optimum solution. In this chapter, a fuzzy mathematical model based on Beale's condition is proposed to address NLP with inequality constraints in terms of fuzziness. Furthermore, the model demonstrates how quadratic programming problems can be solved using membership functions. The model also describes three stages: that is, mathematical formulation, computational procedures, and numerical illustration with comparative analysis. Likewise, the model illustrates the considered problem using two distinct approaches, namely membership functions (MF) and robust ranking index. Finally, the comparison analysis provides detailed results and discussion that justify the optimal outcome in order to address the vagueness of certain NLPPs.

Noninvasive system for weight estimation in cactus crops: A YOLOv5-decision tree approach based on interval type-2 fuzzy sets

This study proposes a noninvasive system to estimate the weight of a prickly pear cactus (Opuntia ficus-indica), which combines a model based on deep learning to detect and estimate its area and a model based on supervised learning and developed under a type-2 interval fuzzy sets approach to estimate its weight. YOLOv5 was used for detection, which achieved results with an accuracy of 0.999, recall of 0.999, mAP_0.5 of 0.995, and mAP_0.5:0.95 of 0.990. Area estimation is performed based on the object's coordinates in the image. To perform the weight estimation task, a comparative analysis of models based on supervised learning was performed to identify the model that best described the response variable, selecting a decision tree model. The training and adjustment process included the uncertainty in a weight evaluation system using a granatary scale to enhance the weight estimation capability. Using a trapezoidal membership function, the type-2 interval fuzzy set approach was used to convert the collected data into fuzzy numbers. The model findings for the weight estimation task were also favorable, with a model-explained variance R2 of 0.98, a root mean square error (RMSE) of 10.02, and a mean absolute error (MEA) of 6.33 g. Finally, both models were incorporated into a graphical user interface to facilitate their use in the real weight estimation process. A real case application with the proposed system demonstrated its effectiveness in detecting and estimating weight dynamically with an error of 9 g. Therefore, its viability as an alternative system for weight estimation in cactus crops was demonstrated. Furthermore, a comparative analysis demonstrated the superiority of the proposed hybrid approach over similar approaches in the literature.

Investigation on the influence of a new trapezoidal-triangular membership function in IT2FLS with type-reductions for a manufacturing application

The performance of Interval type-2 fuzzy logic system (IT2FLS) can be affected by many factors including the type of reduction methodology followed and the kind of membership function applied. Further, a particular membership function is influenced by its construction, the type of optimisation and adaptiveness applied, and the learning scheme adopted. The available literature lags in providing detailed information about such factors affecting the performance of IT2FLS. In this work, an attempt has been made to comprehensively study the factors affecting the performance of IT2FLS by introducing a new trapezoidal-triangular membership function (TTMF). A real-time application of drilling operation has been considered as an example for predicting temperature of the job, which is considered as one of the key state variables to evaluate. A detailed comparison based on membership functions (MFs) such as triangular membership function (TrMF), trapezoidal membership function (TMF), the newly introduced trapezoidal-triangular membership function (TTMF), semi-elliptic membership function (SEMF), and Gaussian membership function (GMF) has been performed and presented. Further, the average error rate obtained with two “type-reduction” methods such as “Wu-Mendel” uncertainty bounds and Center of sets type reduction (COS TR) has also been discussed. This study provides information for selecting a particular MF and “type reduction” scheme for the implementation of IT2FLS. Also, concludes that MF having fewer parameters such as GMF and SEMF possess significant advantages in terms of computation complexity compared to others.

Filtering of Complex Signals Based on a Two-Level Fuzzy-Logic Model

Purpose of research. Development of a method and algorithm of complex analog radio signals filtering and binarization, such as the signal of Automatic dependent surveillance-broadcast (ADS-B), which allows to increase the sensitivity of the receiver of the AZN-B signal and increase the number of correctly detected received messages.Methods. To solve this problem, the basics of the theory of signal filtering and the theory of fuzzy sets were applied in the work. The proposed method is based on combining signal filtering by known filters and a two-level fuzzy model. The first and second levels of the fuzzy model contain three operations: automatic formation of membership functions, compositional output and defuzzification. Input variables of both levels are given by trapezoidal membership functions. At the first level, they are formed automatically depending on the characteristics of the complex signal. The output function at the first level is given by a singleton function, and defuzzification is carried out using a simplified center of gravity model.Results. The proposed algorithm was implemented in the developed device based on a programmable logic integrated circuit (FPGA). In addition to filtering, the developed device implements all signal processing functions, such as: receiving input data, decoding, checking the correctness of decoded data, storing them, transmitting ADS-B messages for further processing. A distinctive feature of the device is its small size and low power consumption, which allows use it in small spacecraft and unmanned aerial vehicles.Conclusion. A method of filtering complex signals based on a fuzzy logic model is considered, which can be used to filter complex signals, such as ADS-B messages in small spacecraft modules. The proposed implementation of the filtering method makes it possible to increase the sensitivity of the AZN-B signal receiver by 20% and correctly decode the received signal. The method was implemented by an FPGA-based device, which made it possible to reduce the size and power consumption compared to analogues.

Proposal of a facilitating methodology for fuzzy FMEA implementation with application in process risk analysis in the aeronautical sector

PurposeThis study aims to propose a facilitating methodology for the application of Fuzzy FMEA (Failure Mode and Effect Analysis), comparing the traditional approach with fuzzy variations, supported by a case application in the aeronautical sector.Design/methodology/approachBased on experts' opinions in risk analysis within the aeronautical sector, rules governing the relationship between severity, occurrence, detection and risk factor were defined. This served as input for developing a fuzzyfied FMEA tool using the Matlab Fuzzy Logic Toolbox. The tool was applied to the sealing process in a company within the aeronautical sector, using triangular and trapezoidal membership functions, and the results were compared with the traditional FMEA approach.FindingsThe results of the comparative application of traditional FMEA and fuzzyfied FMEA using triangular and trapezoidal functions have yielded valuable insights into risk analysis. The findings indicated that fuzzyfied FMEA maintained coherence with the traditional analysis in identifying higher-risk effects, aligning with the prioritization of critical failure modes. Additionally, fuzzyfied FMEA allowed for a more refined prioritization by accounting for variations in each variable through fuzzy rules, thereby improving the accuracy of risk analysis and providing a more realistic representation of potential hazards. The application of the developed fuzzyfied FMEA approach showed promise in enhancing risk assessment in the aeronautical sector by considering uncertainties and offering a more detailed and context-specific analysis compared to conventional FMEA.Practical implicationsThis study emphasizes the potential of fuzzyfied FMEA in enhancing risk assessment by accurately identifying critical failure modes and providing a more realistic representation of potential hazards. The application case reveals that the proposed tool can be integrated with expert knowledge to improve decision-making processes and risk mitigation strategies within the aeronautical industry. Due to its straightforward approach, this facilitating methodology could also prove beneficial in other industrial sectors.Originality/valueThis paper presents the development and application of a facilitating methodology for implementing Fuzzy FMEA, comparing it with the traditional approach and incorporating variations using triangular and trapezoidal functions. This proposed methodology uses the Toolbox Fuzzy Logic of Matlab to create a fuzzyfied FMEA tool, enabling a more nuanced and context-specific risk analysis by considering uncertainties.

Expert opinion based optimziation of CNC machining parameters for Al-CNT composites using fuzzy TOPSIS method

Machinability of Al-CNT composites at optimum conditions of machining parameters saves a lot of time, improves quality of machined components at minimum possible cost of machining. In conventional methods, controlled experimentation is performed. In order to obtain best machining parameters, optimization methods are applied but they are inadequate in many situations. Hence, an attempt was made in this work to collect subjective data for response parameters such as, quality, cost, and time, from selected experts in this field for various combinations of input process parameters of CNC milling machine for the case of Al-CNT composites with high-speed steel as tool material. 27 sets of experiments were devised for various combinations of machining parameters systematically by taking cutting speed (in rpm), feed, step over ratio, and depth of cut each at 3 levels. Two experts were invited for collection of data for the response parameters and three experts were involved for giving weightages for the response parameters. Fuzzy trapezoidal membership functions were made use of, for representing fuzzy set and fuzzy Technique and TOPSIS method was applied for finding the best solution. Results revealed that best solution was obtained for a spindle speed of 3000 rpm, feed of 150 mm rev−1, step-over ratio of 0.5, and depth of cut of 0.2 mm.

Control of the temperature regime of the process of bacterial oxidation on the basis of fuzzy logic

The work is devoted to modeling the temperature control system for the process of bacterial oxidation of refractory gold-bearing sulfide ores. The simulation was performed using the Fuzzy Logic Toolbox editor in the MATLAB software package. The substantiation of the set of input and output variables, the type of membership functions was carried out, the base of rules for the inference engine was formed. The main stages of modeling are described and the results are analyzed. The use of trapezoidal membership functions is substantiated.

Adaptation and application of the fuzzy synthetic evaluation (FSE) method for characterizing the trophic state of tropical semiarid reservoirs.

Eutrophication is a recurrent problem in water bodies, especially in tropical semiarid reservoirs. The trophic state index (TSI) is an important tool for the environmental management of aquatic systems. However, determining the TSI involves uncertainties that can affect decision-making. This study aimed to adapt and apply the fuzzy synthetic evaluation (FSE) to characterize the TSI considering the uncertainties of the reference eutrophication classification system. The Castanhão reservoir, the largest in the State of Ceará, Brazil, was taken as a case study. The results showed that (i) the uncertainty of the trophic classification system can be characterized by the triangular and trapezoidal membership functions; (ii) the result matrix associates the global trophic level with a degree of certainty, providing greater confidence to the decision maker; (iii) the eutrophication index (EI) is not an adequate tool for hierarchizing the trophic degree; and (iv) the membership level of the global trophic state generated by the FSE method is a suitable alternative to the EI. It is concluded that the proposed FSE model can be a useful tool for improving water resources management, especially in drylands.

Isosceles Triangular and Isosceles Trapezoidal Membership Functions Using Centroid Method

Summary Since isosceles triangular and trapezoidal membership functions [4] are easy to manage, they were applied to various fuzzy approximate reasoning [10], [13], [14]. The centroids of isosceles triangular and trapezoidal membership functions are mentioned in this article [16], [9] and formalized in [11] and [12]. Some propositions of the composition mapping (f + · g, or f +* g using Mizar formalism, where f, g are a ne mappings), are proved following [3], [15]. Then different notations for the same isosceles triangular and trapezoidal membership function are formalized. We proved the agreement of the same function expressed with different parameters and formalized those centroids with parameters. In addition, various properties of membership functions on intervals where the endpoints of the domain are fixed and on general intervals are formalized in Mizar [1], [2]. Our formal development contains also some numerical results which can be potentially useful to encode either fuzzy numbers [7], or even fuzzy implications [5], [6] and extends the possibility of building hybrid rough-fuzzy approach in the future [8].

Optimal adaptive neuro-fuzzy inference system with biogeography-based optimization for numbers of COVID-19 vaccination prediction

This study attempts to develop the adaptive neuro-fuzzy inference system (ANFIS) with biogeography-based optimization (BBO) (ANFIS-BBO) for a case study of the actual number of COVID-19 vaccinations in a medical center, considering the variables of the date and time of vaccination, the brand of vaccine, and the number of open appointments on the government network platform in Taiwan. The COVID-19 has brought about a great burden on the health and economy of the world since the end of 2019. Many scholars have proposed a prediction model for the number of confirmed cases and deaths. However, there is still a lack of research in the prediction model for mass vaccination. In this study, ANFIS-BBO is developed to predict the number of COVID-19 vaccination, and three other forecasting models, support vector machines (SVM), least-square support vector machines (LSSVM) and general regression neural network (GRNN) are employed for forecasting the same data sets. Empirical results show that the ANFIS-BBO with trapezoidal membership function model can achieve better performance than other methods and provide robust predictions for the actual number of COVID-19 mass vaccination.

Ultra‐efficient fully programmable membership function generator based on independent double‐gate FinFET technology

SummaryThis paper demonstrates an ultra‐efficient, fully programmable membership function generator (MFG) utilizing independent double‐gate (IDG) FinFET technology. The proposed MFG can produce s‐shaped, z‐shaped, triangular, and trapezoidal membership functions. By employing only six transistors, the designed MFG provides full controllability over the height, position, width, and slope of the generated waveforms. Without using any additional transistor and changing the dimensions, the proposed MFG can calibrate the slope of the output based on the back‐gate bias voltage of the IDG‐FinFETs. According to our extensive simulations, the proposed MFG shows promising improvements in transistor count (70%), power‐delay‐product (PDP) (80%), and maximum absolute error (61%) as compared with its state‐of‐the‐art counterparts. To benchmark the functionality of the proposed MFG in practical applications, our generated membership function is exploited as the neuron's activation function in a multilayer perceptron (MLP) neural network. The simulation results indicate that the training process of the simulated MLP with the proposed MFG closely tracks the results obtained from the ideal MLP with the sigmoid activation function. A figure of merit (FoM) is defined considering the hardware efficiency and accuracy of the neural networks to evaluate the entire performance of the proposed MFG. The FoM simulations demonstrate that the proposed MFG presents an excellent trade‐off between hardware performance and accuracy in neural network applications. Our results emphasize that the proposed MFG is a potential candidate for designing high‐performance on‐chip neural networks.

Fuzzy analytic hierarchy process for pentagonal fuzzy numbers and its application in sustainable supplier selection

Different fuzzy analytic hierarchy process (FAHP) methods are typically developed for conventional fuzzy numbers (FNs), mainly triangular and trapezoidal FNs. The ascending and descending parts of triangular and trapezoidal membership functions (MFs) are straight lines. Therefore, if the value of a member increases by the same values, its membership degrees in ascending (descending) part increase (decrease) equally. These MFs do not necessarily reflect the experts' preferences. Consider two different cases; in the first one, the product quality of supplier A compared to supplier B increases from 2 to 3 times, and in the second case, this quality increases from 8 to 9 times. Triangular and trapezoidal membership degrees in both cases increase equally. However, the quality advantage of supplier A increases by 50% in the first case, while it increases by 12.5% in the second case. Therefore, the experts’ preferences may increase differently for these cases that cannot be reflected accurately by triangular and trapezoidal MFs. To overcome this flaw, we develop four FAHP methods for pentagonal FNs (PFNs). We also use an indirect method to defuzzify the fuzzy local weights. Indirect defuzzification is a simple method equivalent to the center of gravity (COG) method and needs low computations. Numerical examples are used to illustrate the proposed methods. A real example of ranking suppliers in a sustainable framework based on pentagonal fuzzy preferences is also presented. To extract crisp local weights from pentagonal fuzzy comparison matrices, we use the pentagonal FAHP methods presented in this study.

WSO‐T2FSM: War strategy optimization‐based type‐2 fuzzy‐based starling murmuration for addressing the routing problem in mobile ad hoc network

SummaryNowadays, research based on mobile ad hoc network's (MANET) performance improvement has drawn a particular concentration from scientists worldwide. The shortest path selection among destination and source nodes determines the network's throughput in MANET. In addition, power management and energy consumption are also the major difficulties that MANET suffers. The conventional routing protocols are intended for static bonding, but that protocol does not satisfy the stability in ad hoc networks by means of regularly changing connectivity. This shows the routing problem in MANETs. Therefore, to overcome the routing issues and maintain energy efficiently, the Type‐2 fuzzy‐based Starling Murmuration Optimizer (SMO)‐War Strategy Optimization (WSO) (T2FSMO‐WSO) routing protocol is proposed in this paper. MANET takes into account four input parameters: route length, active link ratio to global traffic, network lifetime, and control packet ratio. The SMO algorithm is employed to choose the relay node with low energy consumption. The trapezoidal membership functions are used to describe the fuzzy sets for these parameters. The content‐based routing among source and destination nodes is determined using the WSO algorithm. The simulation outcomes reveal that the proposed method discovers highly stable paths with minimum distance and minimized the consumption of energy.

Premature Ventricular Contraction Recognition using a Fuzzy Maximum Approaching Degree

This work presents a new methodology for ventricular premature contraction arrhythmias recognition using a set of geometrical attributes recently proposed and a fuzzy maximum approaching degree. Pattern models based on triangular and trapezoidal membership functions are proposed and a committee comprising these functions is composed using some statistical data, beyond a mechanism for manual selection of attributes and automatic weighting for each attribute. The obtained results show the efficiency and validity of the proposed approach, with 99.07%, 98.36% and 99.79% of accuracy, sensibility and specificity, respectively, as good as the ones obtained by the state-of-art methods.

Design Development of Detection System and Ro-Ro Ship Notification based on Fuzzy Inference System

Ship stability is very important for the safety of ship motion. There are many factors that affect the stability of a ship. One of the causes of accidents on ships is the problem of ship stability, including the ship cannot be controlled, and loses balance due to improper placement of cargo loads. This study combines gyroscopes, accelerometers, compasses, and GPS sensors, so that more accurate ship tilt information is obtained through an Android smartphone application. This study uses the fuzzy inference system (FIS) method with a trapezoidal membership function where there are 2 inputs and 1 output. Ship tilt input uses 3 linguistic variables very tilted, tilted, and stable. The slope duration input uses 5 very fast, fast, fairly fast, slow, and very slow linguistic variables. Ship status output is divided into 3 linguistic variables safe, alert, and dangerous. Testing and implementation with an input slope of 4.8 and a slope duration of 10 seconds using the Sugeno fuzzy method, the ship's crips value of 0.65 with an alert status was obtained. Calculation of the accuracy of the gyroscope sensor error using the MAPE method, the result is an error percentage of 6.55% (very good). The system accuracy error of 39 trials (36 correct and 3 incorrect) is 92.30% (very good). This research is expected to make it easier for the captain to monitor the stability of the ship and can provide notification of the status of the ship to the captain of the ship if there is a condition of the ship that needs to be watched out for. In addition, the notification will also be received by Port officers on land.

A model for green-resilient supplier selection: fuzzy best-worst multi-criteria decision-making method and its applications.

Supplier selection is regarded as the primary goal of supply chain management (SCM) because it affects its performance, productivity, pleasure, flexibility, and system speed in lockdown. A new method is proposed based on a multi-stage fuzzy sustainable supplier index (FSSI). Experts can use the triple bottom line (TBL) criteria to select the best supplier. In addition, the worst method is proposed based on trapezoidal membership and fuzzy membership functions, which can cover uncertainties and ambiguous environments. Because it collects the related criteria and sub-criteria and uses a direct fuzzy methodology, this research has impacted the SCM literature because it helps solve previous expert methods' computational difficulties. In addition, an ordered mean integration representation method has been implemented to prioritize the selection of the best supplier (SS) based on the sustainability performance of the best supplier, which improves the selection accuracy compared to the previous ranking method. This study can be used as a benchmark to determine which supplier is the best in sustainability. To provide the superiority and broad applicability of the proposed model, a practical case study was completed. On the other hand, the COVID-19 pandemic harms productivity, company performance, and selecting the best suppliers based on sustainability performance. The lockdown situation caused by the COVID-19 pandemic hurts company performance and management.

Comparison of ANN and ANFIS Models for AF Diagnosis Using RR Irregularities

Classification of normal sinus rhythm (NSR), paroxysmal atrial fibrillation (PAF), and persistent atrial fibrillation (AF) is crucial in order to diagnose and effectively plan treatment for patients. Current classification models were primarily developed by electrocardiogram (ECG) signal databases, which may be unsuitable for local patients. Therefore, this research collected ECG signals from 60 local Thai patients (age 52.53 ± 23.92) to create a classification model. The coefficient of variance (CV), the median absolute deviation (MAD), and the root mean square of the successive differences (RMSSD) are ordinary feature variables of RR irregularities used by existing models. The square of average variation (SAV) is a newly proposed feature that extracts from the irregularity of RR intervals. All variables were found to be statistically different using ANOVA tests and Tukey’s method with a p-value less than 0.05. The methods of artificial neural network (ANN) and adaptive neuro-fuzzy inference system (ANFIS) were also tested and compared to find the best classification model. Finally, SAV showed the best performance using the ANFIS model with trapezoidal membership function, having the highest system accuracy (ACC) at 89.33%, sensitivity (SE), specificity (SP), and positive predictivity (PPR) for NSR at 100.00%, 94.00%, and 89.29%, PAF at 88.00%, 90.57%, and 81.48%, and AF at 80.00%, 96.00%, and 90.91%, respectively.