Trapezoidal Fuzzy Membership Function Research Articles

An Experimental Private Small Hydropower Plant Investments Selection Classification System

Investment selection problems and models are crucial for humans, communities, and states. Private small hydroelectric power/ hydropower plant investments (PSHPPIs) selection problem is a unique one in those problems and models. Many available scientific methods can be implemented on this research topic. One methods group is type-2 Mamdani’s type fuzzy inference systems (FISs). This study presents an experimental one-node general type-2 4-zslices Mamdani’s type FIS model for PSHPPIs selection. There are 3 input variables (total estimated electricity generation: M1, total estimated cost: M2, change in the average runoff: M3), 1 output variable (O1: selected/unselected, selection classification of PSHPPIs), and 49 rules. M1 is designed in 5 triangular and trapezoidal general type-2 4-zslices fuzzy membership functions (MFs), M2 in 5 triangular and trapezoidal general type-2 4-zslices fuzzy MFs, M3 in 5 Gaussian type-2 4-zslices fuzzy MFs, and O1 in 2 Gaussian type-2 4-zslices fuzzy MFs. All modeling details are finalized by a human-expert decision process. JuzzyOnline V2.0, a browser-based platform of Juzzy (a Java-based library: Juzzy toolkit), is used for all FIS modeling and calculation activities. Five PSHPPI options assumed to be in their very early investment stages in Turkiye are evaluated in an experimental application. It is clear that an improved, tuned, and fine-tuned version of this model will help private investors to take more convenient/satisfying actions/decisions in a very short evaluation period in their PSHPPIs decision processes. An automatic investment selection classification system can be built in an appropriate development period after experiencing many methods and models. This study is one of the open-science humanoid robot, robot and platform development activities entitled Global Power Robots and Platforms: GPRP/GPRAP (Global Power Plants Developers: GP2D/G2PD/GPPD, Global Power Plants Engineers: GP2E/G2PE/ GPPE, Global Power Plants Owners: GP2O/G2PO/GPOO, Global Power Prediction Systems: GP2S/G2PS/GPPS), Global Profile Analyses Systems, and Global Social Network Analyses Systems.

Research on fuzzy weighted gain scheduling water level control system of U-tube steam generator

U-tube steam generator (UTSG) is one of the key components of the pressurized water reactor (PWR) in nuclear power plant (NPP). The Traditional UTSG water level control system (WLCS) copes with a wide range of load variations by changing the gain of the water level controller. The water level controller is designed based on a specific power level. At other power levels simply changing the gain of the controller will not perform well. Therefore, it is necessary to study a full power range UTSG WLCS. In this paper, based on the transfer function, the traditional controller is designed, including water level controllers and flow rate controllers under five power levels. However, the traditional controller is designed based on fixed working points, and the performance is poor when applied to other power levels. In order to solve this problem, the fuzzy weighted (FW) controller is designed by using the triangle fuzzy membership function and trapezoidal fuzzy membership function respectively. The simulation results show that the FW controller using the triangle fuzzy membership function is recommended.

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.

Risk-Averse Multiobjective Optimization for Integrated Electricity and Heating System: An Augment Epsilon-Constraint Approach

Uncertainties including demand and environmental factors would increase the operational risk of the energy supply networks. It significantly affects the technical and financial aspects of the integrated electricity and heating system (IEHS). This article presents a risk-averse multiobjective optimization strategy for short-term decision-making. The objective is to optimize the total cost and the technical dissatisfaction in a way that the economy of system operation and energy supply quality for the risk-averse scheme is guaranteed simultaneously. Based on the trapezoidal fuzzy membership function, the fuzzy constraint is constructed to quantify the technical dissatisfaction of the nodal voltage and supply temperature. Then, a multiobjective min–max–min problem is formulated to hedge the IEHS against risk imposed by the uncertain variables. Since the formulated two objectives compete with each other, a risk-averse multiobjective solution procedure based on the augmented epsilon-constraint algorithm is developed to recast the multiobjective problem into its equivalent single objective problem. And the accurate Pareto fronts under different risk levels are obtained with several iterations. Numerical case studies are conducted to evaluate the effectiveness and applicability of the proposed method. It provides benefits in the aspect of balancing the economy and energy supply quality under network constraints and uncertainties.

Proposal Yager Ranking Function to Solve the Fuzzy Transportation Model via Trapezoidal Fuzzy Number

Transportation theory is the name given to the study of optimal transportation (OT) and resource allocation in mathematics and economics. In any discipline of science and technology, engineering, medicine, and management, uncertainty plays a critical role. Fuzzy Mathematics (FM) and fuzzy logic (FL) are used in Artificial Intelligence (AI) to process natural language and are frequently employed in decision making (DM). In this paper, using three ranking function to treat the fuzzy transportation model, two of them are Yager and Maleki ranking functions and the other is proposal and suggest depend up on of Yager ranking function based on trapezoidal fuzzy membership function when the total demand, cost of transportation, and the total amount of product (supply) are fuzzy, then the fuzzy model shrinkage to traditional or crisp model. Finally solving these models to the real data that we got it from The General Company for Food Products Abo ghreeb / Iraq.

A Mathematical Model for Nonlinear Optimization Which Attempts Membership Functions to Address the Uncertainties

The problem of optimizing an objective function that exists within the constraints of equality and inequality is addressed by nonlinear programming (NLP). A linear program exists if all of the functions are linear; otherwise, the problem is referred to as a nonlinear program. The development of highly efficient and robust linear programming (LP) algorithms and software, the advent of high-speed computers, and practitioners’ wider understanding and portability of mathematical modeling and analysis have all contributed to LP’s importance in solving problems in a variety of fields. However, due to the nature of the nonlinearity of the objective functions and any of the constraints, several practical situations cannot be completely explained or predicted as a linear program. Efforts to overcome such nonlinear problems quickly and efficiently have made rapid progress in recent decades. The past century has seen rapid progress in the field of nonlinear modeling of real-world problems. Because of the uncertainty that exists in all aspects of nature and human life, these models must be viewed through a system known as a fuzzy system. In this article, a new fuzzy model is proposed to address the vagueness presented in the nonlinear programming problems (NLPPs). The proposed model is described; its mathematical formulation and detailed computational procedure are shown with numerical illustrations by employing trapezoidal fuzzy membership functions (TFMFs). Here, the computational procedure has an important role in acquiring the optimum result by utilizing the necessary and sufficient conditions of the Lagrangian multipliers method in terms of fuzziness. Additionally, the proposed model is based on the previous research in the literature, and the obtained optimal result is justified with TFMFs. A model performance evaluation was completed with different set of inputs, followed by a comparison analysis, results and discussion. Lastly, the performance evaluation states that the efficiency level of the proposed model is of high impact. The code to solve the model is implemented in LINGO, and it comes with a collection of built-in solvers for various problems.

Generating Type 2 Trapezoidal Fuzzy Membership Function Using Genetic Tuning

Fuzzy inference system (FIS) is a process of fuzzy logic reasoning to produce the output based on fuzzified inputs. The system starts with identifying input from data, applying the fuzziness to input using membership functions (MF), generating fuzzy rules for the fuzzy sets and obtaining the output. There are several types of input MFs which can be introduced in FIS, commonly chosen based on the type of real data, sensitivity of certain rule implied and computational limits. This paper focuses on the construction of interval type 2 (IT2) trapezoidal shape MF from fuzzy C Means (FCM) that is used for fuzzification process of mamdani FIS. In the process, upper MF (UMF) and lower MF (LMF) of the MF need to be identified to get the range of the footprint of uncertainty (FOU). This paper proposes Genetic tuning process, which is a part of genetic algorithm (GA), to adjust parameters in order to improve the behavior of existing system, especially to enhance the accuracy of the system model. This novel process is a hybrid approach which produces Genetic Fuzzy System (GFS) that helps to enhance fuzzy classification problems and performance. The approach provides a new method for the construction and tuning process of the IT2 MF, based on the FCM outcomes. The result is compared to Gaussian shape IT2 MF and trapezoid IT2 MF generated by the classic GA method. It is shown that the proposed approach is able to outperform the mentioned benchmarked approaches. The work implies a wider range of IT2 MF types, constructed based on FCM outcomes, and an optimum generation of the FOU so that it can be implemented in practical applications such as prediction, analytics and rule-based solutions.

A multi-stage multi-criteria hierarchical decision-making approach for sustainable supplier selection

Sustainable supplier selection is known as a crucial objective in supply chains due to its impact on profitability, adorability, flexibility, and agility of the system. This study proposes a new multi-stage hierarchical fuzzy index-based approach with which decision-makers are empowered to select the most sustainable supplier based on sustainability triple bottom line criteria. Besides, a new fuzzy extension for the best-worst method is proposed considering trapezoidal fuzzy membership functions that can cover uncertainty under imprecise environments. This study makes a contribution to the literature of sustainable supply chains in the sense that it facilitates the computational complexity of previous decision-making approaches by collecting the most relevant criteria and a straightforward fuzzy process. Besides, the graded mean integration representation method has been adopted for prioritizing the supplier based on their performance of sustainable development, which enhances the accuracy of selection compared with previous ranking methods. The proposed study can be utilized as a benchmark for sustainability evaluations between suppliers. A real-world case study is resolved to illustrate the superiority and broad application of the proposed model.

Forecast of Tropical Cyclone Occurrences based on Fuzzy Logic Algorithm

Most studies of the tropical cyclone (TC) forecasting are focused on the track and the wind radius forecasting, even though a tropical cyclone formation alerts also developed. This paper takes a different approach and explores and forecast the TC occurrences. This study presents the development of fuzzy logic (FL) models for predicting the occurrence of TC from five primary TC genesis parameters. These parameters are low-level relative vorticity (θ), horizontal wind of upper troposphere (u), sea surface temperature (SST), equivalent potential temperature (θe), and specific humidity (q). The FL model was developed by employing the trapezoidal and triangular fuzzy membership functions for the input and output variables. The fuzzy rules were inferred from the TC genesis parameters data, with a daily calculation period from 1989 to 2018. The amount of TC genesis parameters when the cyclone occurred of the lowest, middle, and upper tercile reconstruction was used as a threshold to build FL model. The model satisfactorily simulated the occurrence of TC with comparable error measures. The result exhibits the accuracy at 0.75 (range: 0 to 1, perfect score: 1). The evidence shows that the result provides insights into the adequacy of FL methods for forecasting the TC occurrences.

Normalisation of imprecise temporal expressions extracted from text

Information extraction systems and techniques have been largely used to deal with the increasing amount of unstructured data available nowadays. Time is among the different kinds of information that may be extracted from such unstructured data sources, including text documents. However, the inability to correctly identify and extract temporal information from text makes it difficult to understand how the extracted events are organised in a chronological order. Furthermore, in many situations, the meaning of temporal expressions (timexes) is imprecise, such as in “less than 2 years” and “several weeks”, and cannot be accurately normalised, leading to interpretation errors. Although there are some approaches that enable representing imprecise timexes, they are not designed to be applied to specific scenarios and difficult to generalise. This paper presents a novel methodology to analyse and normalise imprecise temporal expressions by representing temporal imprecision in the form of membership functions, based on human interpretation of time in two different languages (Portuguese and English). Each resulting model is a generalisation of probability distributions in the form of trapezoidal and hexagonal fuzzy membership functions. We use an adapted F1-score to guide the choice of the best models for each kind of imprecise timex and a weighted F1-score (hbox {textit{F}1}_{3mathrm{D}}) as a complementary metric in order to identify relevant differences when comparing two normalisation models. We apply the proposed methodology for three distinct classes of imprecise timexes, and the resulting models give distinct insights in the way each kind of temporal expression is interpreted.

A Fuzzy Decision-Making Trial and Evaluation Laboratory approach to analyse risk factors related to environmental health and safety aspects in the healthcare industry

In healthcare firms, environmental health and safety (EHS) remains as a vital factor as healthcare products pose very intricate problems related to environment safety. The different similar and dissimilar risk factors that prevail in the system have complicated known and unknown causal relationships that are difficult to understand and interpret. Hence, improving the EHS remains as a challenge in healthcare industry. A research study is carried out utilizing the data (in conjunction with expert’s opinion) and conditions of a healthcare firm in India to categorize and obtain the prominent risk factors based on identifying the most adverse causal relationship among them. A Fuzzy Decision-Making Trial and Evaluation Laboratory (fuzzy DEMATEL)-based approach is designed and employed to assess and rank different EHS risk factors. The trapezoidal fuzzy membership function of the model facilitates better learning of interrelationships in spite of the prevailing vagueness in the causal relationships between the risk factors. The outcomes (the decisive risk factors) out of the experimentation using the proposed methodology strongly coincide with the actual causes of the EHS factors during the last one decade. As the proposed approach is found to be very effective in fixing the causal relationships and ranking among the risk factors, this may be successfully employed in similar healthcare firms/industries for finding out their respective decisive risk factors.

Assessment of Abandoned Coal Mines as Urban Reservoirs

The closure of many coal mines has resulted in many being used as massive underground mine water storage systems in urban areas. We used a comprehensive fuzzy method to assess the suitability of abandoned coal mines as underground reservoirs. Five first-level and four second-level indices were chosen based on the hydrogeological conditions. The degree of membership of each index was determined and quantitatively graded into suitability grades of I–V using a trapezoidal fuzzy number membership function. The weight of each index was determined in accordance with information entropy. Abandoned mines in Xuzhou city were examined as a case study. The degree of suitability of the water in 14 abandoned mines was assessed. Six of the abandoned mines earned a suitability grade of I and II and should be given priority. The evaluation of abandoned mines as underground reservoirs provides a new means to potentially secure an emergency water supply in urban settings.

A bi-objective multi-echelon supply chain model with Pareto optimal points evaluation for perishable products under uncertainty

Selecting the most suitable optimal point among the Pareto optimal points could help the experts to make an appropriate decision in an uncertain and complex situation. In this paper, an evaluating and ranking approach is proposed based on hesitant fuzzy set environment to assess the obtained Pareto optimal points from the proposed bi-objective multi-echelon supply chain model with locating distribution centers. In this respect, the proposed model has elaborated for perishable products based on fuzzy customers' demand. To address the issue, the possibilistic chance constraint programming approach has manipulated based on the trapezoidal fuzzy membership function. Moreover, the proposed hesitant fuzzy ranking approach is constructed based on group decision analysis and the last aggregation approach. Thereby, the last aggregation approach by aggregating the experts' opinions in last step could prevent the data loss. However, a case study about the perishable dairy products is considered to indicate the applicability of the proposed bi-objective multi-echelon supply chain model with locating distribution centers. Finally, a comparative analysis is provided between the obtained results and the current practice to show the feasibility and efficiency of the proposed model.

Self-learning interval type-2 fuzzy neural network controllers for trajectory control of a Delta parallel robot

Abstract This paper presents a self-learning interval type-2 fuzzy neural network (SLIT2FNN) control scheme for trajectory tracking problem of a Delta robot. This intelligent control scheme is computationally efficient and can be easily applied to existing equipment. The controller has a parallel structure, which combines an interval type-2 fuzzy neural network (IT2FNN) controller and a traditional proportional-derivative (PD) controller. We use the PD controller to compensate the transient performance, and use the IT2FNN to learn the dynamic characteristics of the system. A novel arrangement of trapezoidal interval type-2 fuzzy membership functions (IT2MF) is proposed, the arrangement enables the adaptation laws to have an analytical form. A learning algorithm based on sliding mode control (SMC) theory is proposed for the parameter training of the IT2FNN system. The control algorithm learns from the feedback error online and tunes the parameters of the IT2FNN, and will become the main source of the control signal after several learning iterations. Unlike model-based control, this control method has no requirement of prior information and constraint conditions from the robot plant. Lyapunov stability method is employed to prove asymptotic stability of the proposed approach. The structure of the SLIT2FNN and the operations in each layer are introduced in detail. The performance and robustness of the proposed controller is demonstrated on the Delta robot trajectory tracking problems in the presence of structured and unstructured uncertainties. Simulation results illustrate that the proposed SLIT2FNN control approach produces higher trajectory tracking accuracy and more robust to uncertainties as compared to its counterparts.

Data-Based Control for Humanoid Robots Using Support Vector Regression, Fuzzy Logic, and Cubature Kalman Filter

Time-varying external disturbances cause instability of humanoid robots or even tip robots over. In this work, a trapezoidal fuzzy least squares support vector regression- (TF-LSSVR-) based control system is proposed to learn the external disturbances and increase the zero-moment-point (ZMP) stability margin of humanoid robots. First, the humanoid states and the corresponding control torques of the joints for training the controller are collected by implementing simulation experiments. Secondly, a TF-LSSVR with a time-related trapezoidal fuzzy membership function (TFMF) is proposed to train the controller using the simulated data. Thirdly, the parameters of the proposed TF-LSSVR are updated using a cubature Kalman filter (CKF). Simulation results are provided. The proposed method is shown to be effective in learning and adapting occasional external disturbances and ensuring the stability margin of the robot.

Fuzzy comprehensive evaluation model for construction risk analysis in urban subway

On the basis of expert questionnaire and the relevant specification, multi-factors influencing weight matrix was constructed by Analytic Hierarchy Process (AHP) improved in transfer matrix algorithm, and influential factors were fuzzy classified to construct the fuzzy evaluation matrix by using trapezoidal fuzzy membership function. Fuzzy evaluation analysis was carried out through multistage fuzzy comprehensive evaluation method, and verified in combination with engineering construction condition of shallow buried tunnel with large span of Zhongshan Park Station in Qingdao Metro, and four kinds of risk control schemes were established and compared on the analysis of tunnel construction risk. Results show that the model was feasible and the improved construction scheme was very effective to reduce the construction risk.

A novel adaptive modified harmony search algorithm to solve multi-objective environmental/economic dispatch

This paper proposes a novel adaptive modification approach based on harmony search algorithm (HS) to solve the multi- objective environmental economic dispatch problem. The proposed algorithm makes use of adaptive formulations to update the adjusting parameters of HS including the pitch adjusting and bandwidth parameters and the harmony memory consideration rate during the optimization process. Meanwhile, a useful modification is proposed to improve the variety of the harmony population effectively. In order to handle both the cost and emission objective functions, the ideas of trapezoidal fuzzy membership function and weighting factor are employed. The satisfying performance of the proposed method is examined through the IEEE standard test system.

A method for determining customer requirement weights based on TFMF and TLR

‘Customer requirements’ (CRs) management plays an important role in enterprise systems (ESs) by processing customer-focused information. Quality function deployment (QFD) is one of the main CRs analysis methods. Because CR weights are crucial for the input of QFD, we developed a method for determining CR weights based on trapezoidal fuzzy membership function (TFMF) and 2-tuple linguistic representation (TLR). To improve the accuracy of CR weights, we propose to apply TFMF to describe CR weights so that they can be appropriately represented. Because the fuzzy logic is not capable of aggregating information without loss, TLR model is adopted as well. We first describe the basic concepts of TFMF and TLR and then introduce an approach to compute CR weights. Finally, an example is provided to explain and verify the proposed method.

Modeling of Transient Groundwater Flow Using Fuzzy Approach

This paper considers the modeling transient groundwater flow under imprecisely known parameters using fuzzy approach. A new approach has been developed to study the effects of parameters uncertainty on the dependent variable, herein is the head. The proposed approach is developed based on fuzzy set theory combined with interval analysis. The kind of uncertainty modeled here is the imprecision associated with model parameters as a result of machine or human imprecision or lack of information. In this technique each parameter is described by a membership function. The fuzzy inputs into the model are in the form of intervals so as the outputs. The resulting head interval represents the change in the output due to interval inputs of model parameters. The proposed technique is illustrated using a two dimensional flow problem solved with finite difference schemes using triangular and trapezoidal fuzzy membership functions. Three input parameters are considered as a fuzzy number (transmissivity, storage coefficient, and recharge). This model was applicable for transient flow through isotropic, heterogeneous soil. The groundwater flow problem analysis requires interval input values for the parameters, the output may be presented in terms of mean value, upper and lower bounds of the hydraulic head. The width of the resulting head interval can be used as a measure of uncertainty due to inputs imprecision. The model compared with other models (fuzzy with finite difference, stochastic, and Kriging), analytical solution for examples, and then applied to the field data (Bahr Al-Najaf, a case study in Iraq), the proposed technique shows good results. When more than one parameter are considered as a fuzzy number, the condition became more complicated and the uncertainty will increase, that was really shown by the proposed model. The model outputs can be used as the inputs for the subsequent risk analysis, decision making-processes and evaluation.

A Novel TwoStage Impulse Noise Removal Technique based on Neural Networks and Fuzzy Decision

enhancement is plays a vital role in various applications. There are many techniques to remove the noise from the image and produce the clear visual of the image. Moreover, there are several filters and image smoothing techniques available in the literature. All these available techniques have certain limitations. Recently, neural networks are found to be a very efficient tool for image enhancement. A novel two-stage noise removal technique for image enhancement and noise removal is proposed in this paper. In noise removal stage, an adaptive two-level feed forward Neural Network (NN) with a Modified Levenberg-Marquardt training algorithm was used to eliminate the impulse noise. In the image enhancement stage, the fuzzy decision rules inspired by the Human Visual System (HVS) are used to categorize the image pixels into human perception sensitive class and nonsensitive class, and to enhance the quality of the image. The Hyper trapezoidal fuzzy membership function is used in the proposed technique. In order to improve the sensitive regions with higher visual quality, a Neural Network (NN) is proposed. The experiment is conducted with standard image. It is observed from the experimental result that the proposed two stage technique shows significant performance when compared to existing methods.