Fuzzy Mathematical Model Research Articles

Optimization of Fuzzy Mathematical Model of Regular Octagon-Shaped Parking Space

In the vigorous development of the city population, there is a need to set up clear dimensions for the parking space. Car parking plays a significant part in the residential apartments and commercial buildings. Roadside parking spaces will create a huge traffic problem if the parking lots are not properly designed. Sometimes, it leads to the accident. Hence, keeping all these causes in mind, the flexible parking space is the necessary of the time. In the proposed research work, the parking space considered in the problem is of a regular octagon shape, and the mathematical model is developed under a fuzzy environment. LINGO Optimization Software is used to solve the mathematical model and MATLAB(Matrix Laboratory) is used to define the fuzzy variable. At the outset, the results will reveal the importance of making the length of the parking lot under fuzzy environment.

Optimization of Fuzzy Mathematical Model of Rectangular-Shaped Parking Space

Optimization of Fuzzy Mathematical Model of Rectangular-Shaped Parking Space

A Novel Visual System for Conducting Safety Evaluations of Operational Tunnel Linings

Based on the lining structure of an operational tunnel, the AHP and Fuzzy mathematical models were used to determine the weight of the evaluation index and solve the membership matrix. The weighted-average Fuzzy comprehensive function was used to combine the two, and the Fuzzy–AHP evaluation model was built and programmed. According to the self-developed Fuzzy–AHP evaluation-programmed model, a visualized structure safety evaluation system for operational tunnels was developed by using MATLAB. The system’s functional design, program development, and computational visualized interface were implemented, and key codes were provided. The system can be divided into four modules: data management, fuzzy computation, predictive analysis and key disease indexes to focus on. In addition, the system can easily edit and modify the evaluation function, which includes not only the Fuzzy evaluation but also other types of evaluation functions applicable to other practical engineering projects, improving the applicability of the system. After that, the system was applied to the structure safety evaluation of a mountain tunnel, which provided the evaluation results and key indexes to focus on in the tunnel. Finally, the rationality of the system design was verified by constructing the corresponding BP–RBF combined neural network. This study provides a reference for the establishment of an intelligent structure safety warning system for operational tunnels.

Mathematical optimization strategy for online scheduling of complex manufacturing systems based on thermal energy optimization and fuzzy mathematical model

With the rapid development of the manufacturing industry and the advancement of the intelligent process, the scheduling problem of complex manufacturing systems becomes more and more complicated, especially in the aspect of energy management and optimization. This study aims to propose an online scheduling mathematical optimization strategy based on thermal energy optimization and fuzzy mathematical model, so as to improve the scheduling efficiency and resource allocation rationality of complex manufacturing systems under different production conditions. A scheduling model considering thermal energy utilization rate, production priority and real-time demand is established by using fuzzy mathematics. The model deals with the uncertain factors by fuzzy logic and solves them by genetic algorithm to realize the dynamic adjustment and optimal scheduling of production resources. Through the experimental verification of a complex manufacturing system, the improvement of scheduling efficiency not only reduces the operating cost, but also improves the flexibility and response speed of the system. The fuzzy mathematical model based on thermal energy optimization provides an effective on-line scheduling strategy for complex manufacturing systems, which can realize efficient scheduling and energy management in dynamic environment.

Data-driven planning in socially responsible textile units amidst uncertainty

Social responsibility is a key factor for organizations to achieve sustainable success in the modern competitive market. This study proposes a hybrid VIKOR method to evaluate textile suppliers based on their social performance under uncertain and multi-objective conditions. The method can handle fuzzy, stochastic, and interval data simultaneously. The social criteria for the evaluation are derived from the literature review, the SA8000 standards, and the United Nations’ recommendations. Some of the criteria are also aligned with the World Bank’s Social Responsibility Diamond Model and the United Nations’ Sustainable Development Goals. Moreover, this study presents a fuzzy mathematical model for fabric purchasing that incorporates social criteria and the quality level into the optimization process. A goal programming method is developed based on the mathematical properties of the multi-objective model. A numerical study is conducted in the textile industry to demonstrate the efficiency and effectiveness of the proposed approaches. A comprehensive sensitivity analysis has been performed to investigate the behavior of the presented mathematical model under different conditions, and the results have been discussed concerning the insights for managers and stakeholders in the textile industry. The proposed model demonstrates that: 1) Customer demand and fabric orders have a direct relationship with increasing sales. 2) The fabric unit price has a direct impact on the quality value and requires cost control policies or pricing negotiations with suppliers. 3) Improving supplier and customer relations and formulating pricing consistent with social value are among the most important issues for the success of the textile and clothing industry. The best-fitting line successfully explains the variability of social performance and customer demand with an accuracy of 99.35 %.

Decision-Making Approach to Design a Sustainable Photovoltaic Closed-Loop Supply Chain Considering Market Share for Electric Vehicle Energy

This study aims to develop a model for the closed-loop supply chain of photovoltaic (PV) systems. The primary objective addresses strategic and tactical decision-making using a two-stage approach. To pinpoint suitable locations for solar power plants, the PROMETHEE II method is utilized, which is a component of multi-attribute decision making (MADM) approaches. Next, a multi-objective modeling of the closed-loop PV supply chain is conducted. This model aims to minimize total supply chain costs, reduce environmental impacts, mitigate adverse social effects, maximize the on-time delivery (OTD) of manufactured products, and maximize market share. Additionally, a robust fuzzy mathematical model is introduced to examine the model’s sustainability under various uncertainties. An evaluation of the effectiveness and utility of this model is conducted in Tehran city. Furthermore, a comprehensive analysis of various supply chain costs indicates that production centers have the highest costs, while separation centers have the lowest costs.

Fuzzy logic in the problems of determining the economic parameters of project implementation

The goal of this work is to forecast project execution terms and its main economic parameters using graph theory and fuzzy logic methods. The subject of research in the article is the method of calculating the main properties or parameters of the project, forecasting the terms of its implementation and the possibility of taking into account force majeure situations. The article discusses the task of finding the optimal plan for the project of creating an e-commerce site and calculating its main economic parameters. The work uses methods of the theory of network planning and management. Fuzzy logic methods are used to solve the fuzzy optimization problem. Graph theory methods, namely the CPM critical path method, are used to forecast project deadlines. The following results were obtained: the main economic parameters were calculated for two versions of the project to create an e-commerce site – sequential, when the team does not have many developers to implement it (or enough resources), and parallel execution of work, which allows you to optimize the execution time by involving additional workers. The cost of both projects was also calculated, which in the future can help managers draw conclusions regarding the implementation of one or another planning option for this type of project. For the first project, the project work plan will be completed in a time not exceeding 230 days, with a reliability of 30%. Or does not exceed 295 days with a reliability of 80% percent. For the second project, the project work plan will be completed in a time not exceeding 230 days, with a reliability of 30%. Or does not exceed 278 days with a reliability of 70% percent. Conclusions: the paper proposes a fuzzy mathematical model for finding the optimal plan and calculating the main economic parameters of the project of creating an e-commerce site with a fuzzy set of plans and a vaguely defined goal. The work also presents a method for solving this problem. The obtained results of the research are of great value for planning the project, for solving the question of the feasibility of its initiation, for forecasting the resources that will be needed for its implementation. These indicators are essential for improving processes and correct allocation of work, which can help strengthen competitiveness and increase project profits.

Research on the Composting Technology of Cattle and Sheep Manure Based on Intelligent and Efficient Composting Equipment and the Evaluation Standard of Decomposition Degree

The Inner Mongolia Autonomous Region is a crucial area in China with a significant advantage in animal husbandry, particularly in cattle and sheep farming. However, the disposal of the large quantities of manure produced during farming has severely impacted the industry’s healthy development. Proper treatment of the manure can convert it into organic fertilizer beneficial to farmland; otherwise, it will cause substantial environmental pollution. This study focuses on existing composting equipment and addresses the issues of cattle and sheep manure mixture ratios and compost maturity evaluation. Through experiments on the mixture of cattle and sheep manure, the optimal ratio for converting cattle and sheep manure into organic fertilizer was determined. Additionally, a fuzzy mathematical evaluation model was employed, along with experimental data, to establish a comprehensive evaluation system for aerobic compost maturity based on multiple indicators, revealing the variation patterns of maturity levels under different mixture ratios. The test results revealed that the composting equipment effectively controls the composting process, shortens the composting cycle, ensures the complete decomposition of organic matter, and meets national standards for livestock and poultry manure treatment. Regarding temperature and humidity, oxygen concentration, seed germination rate, pH value, electrical conductivity (EC), nitrogen, phosphorus, potassium content, and carbon-to-nitrogen ratio, the mixed compost of cattle and sheep manure in various ratios met the relevant standards for agricultural application. Various ratios of organic fertilizers containing cattle and sheep manure significantly promoted the growth of maize, wheat, and mung bean crops. Specifically, the compost decomposition cycle was shortest when sheep and cattle dung were mixed at a ratio of 2:1, while it was longest for all cattle dung. Finally, a fuzzy mathematical comprehensive evaluation model was established by selecting four indicators: water content, carbon-to-nitrogen ratio, apparent score, and germination index. The study demonstrates that the equipment and method offer significant advantages in efficiently treating cattle and sheep manure and producing organic fertilizer, thereby providing strong support for the sustainable development of animal husbandry.

Measuring quality of life in Europe: A new fuzzy multicriteria approach

Quality of life indicators include measures of both objective and subjective well-being to broaden the traditional income-focused view towards a multidimensional view of welfare. In this paper, we develop a single reliable composite index employing fuzzy mathematical modelling that considers the effect of uncertainty and imprecision related to the specific nature of the phenomenon being measured. Additionally, we suggest a procedure for incorporating this new way of assigning priorities through multicriteria techniques. To this end, we propose a new multicriteria approach that introduces the recent notion of picture fuzzy sets to deal with uncertainty and imprecision in the assessment of objective and subjective dimensions of quality-of-life performance. To verify the effectiveness of the whole approach and the credibility of the results, we show its application for monitoring the quality of life in the European Union. Our results show that fuzzy numbers can be a useful tool when combined with multicriteria techniques in the prioritization phase of the criteria and that they increase the quality and reliability of the overall aggregate indicator. Furthermore, through statistical measures we found that in a picture environment the results are consistent regardless of the multi-criteria approach used to provide a final classification.

Fuzzy Mathematical Model of Photosynthesis in Jalapeño Pepper

Photosynthesis is one of the essential processes for life on the planet. Photosynthesis cannot be measured directly because this complex process involves different variables; therefore, if some variables of interest are integrated and measured, photosynthesis can be inferred through a mathematical model. This article presents a fuzzy mathematical model to estimate photosynthesis. This approach uses as input variables: Soil moisture, ambient temperature, incident radiation, relative humidity, and leaf temperature. The fuzzy system was trained through data obtained from experiments with jalapeño pepper plants and then validated against the LI−COR Li−6800 equipment. The correlation coefficient (R2) obtained was 0.95, which is a higher value than some published in the literature. Based on the Takagi−Sugeno method, the proposed model was designed and implemented on the MATLAB platform using ANFIS (adaptive neuro−fuzzy inference system) to determine the parameters, thus achieving a high−precision model. In addition, the fuzzy model can predict photosynthesis at different temperature changes, soil moisture levels, and light levels. The results of this study indicate the possibility of modeling photosynthesis using the fuzzy logic technique, whose performance is much higher than other methods published in recent articles.

A multi-objective fuzzy mathematical model for circular economy with leasing as a strategy

PurposeThis paper aims at developing a multi-objective mathematical model of circular economy that integrates key concept of leasing as a strategy in addition to reuse, refurbishing, primary recycling, secondary recycling and disposal.Design/methodology/approachThis paper proposes multi-objective fuzzy mixed integer linear programming mathematical model considering multi-product, multi-echelon and multi-capacitated concepts of the circular economy. The three objectives of the proposed model, namely, economic, environmental and social are solved simultaneously using constraint approach to obtain balanced trade-off between the objective functions. The model is validated by solving a case study from the literature. The proposed model is made pragmatic for industrial application by considering multi-external suppliers multi-customer zones, multi-disassembly centers, multi-collection centers and multi-refurbishing centers and accounting for purchasing, processing, transportation, set-up costs and capacity constraints at the same time.FindingsThe results show that the leasing of the products improves the economic function in addition to the known environmental improvements. The proposed model also shows that the circular economy can generate the jobs for the unskilled people at different locations.Research limitations/implicationsThe proposed model can be further improved by considering the non-linearity due to economy of scale at various centers and in transportation. The model can be further extended to make it multi-period model.Practical implicationsThe proposed model of circular economy can be used by the organizations as a policy tool to decide the optimum number of collection centers, disassembly centers, refurbishing centers, recycling centers and disposal centers and their optimum locations and allocations. The organizations can also trade-off among economic, environmental and social benefits of their proposed decisions in circular economy.Originality/valueThe originality of the proposed mathematical model is consideration of leasing as a strategy to have better control over the supply chain for circularity; considering the training of unskilled people for backward supply chain jobs and accounting for primary recycling and secondary recycling separately for economical computation.

College English Teaching Classroom Based on Fuzzy Mathematical Model

The use of English in daily communication is becoming more and more important. The degree of mastery of English is largely related to the quality of college English teaching. College English Teaching (CET) has always been the focus of college classroom teaching. The quality of CET directly affects the ability of college students to master English. The evaluation of College English Classroom Teaching (CECT) can reflect the quality of CECT, but the traditional CECT evaluation mainly adopts the average method to analyze, which leads to insufficient understanding of the teaching effect by teachers and low English learning efficiency of students. CET has a fuzzy boundary, and the fuzzy mathematical model can be used to analyze the evaluation indexes that affect the effect of CET and the relative weights of each index, so as to conduct a comprehensive evaluation of CET. A comparative analysis is made between the CET classroom based on fuzzy mathematical model and the traditional mean CET classroom. The experimental results show that the teaching efficiency of practical CET under the two CET evaluation methods is 63% and 75.7%, respectively, while the efficiency of professional CET is about 65.7% and 82.7%, respectively. It can be shown that analyzing CET through Fuzzy Comprehensive Evaluation (FCE) can improve the teaching efficiency of college English classrooms and promote the mastery of English.

A fuzzy mathematical model to solve multi-objective trapezoidal fuzzy fractional programming problems

A fuzzy mathematical model to solve multi-objective trapezoidal fuzzy fractional programming problems

Developing a tactical decision-making framework for a sustainable egg supply chain considering switchable parallel machines

ABSTRACT The increasing world population has increased food supply needs in recent years. Despite the numerous studies in the field of food supply chains, there are few articles on optimizing a sustainable egg supply chain. A fuzzy multi-objective mathematical model is presented to optimize a sustainable egg supply chain in a tactical decision structure. Switchable green packaging and labeling machines in parallel production lines, suppliers with different reliability rates and the provision of raw materials with different qualities have been studied in this article. Despite the significant reduction of the total costs while using switchable machines, the majority of the costs are still related to raw materials so that an increase of 2 to 4 times in the amount of input materials can change the values of objective functions by 23% to 60%. By using the unused capacity of the packaging and labeling machines, the total costs can be reduced significantly.

Optimisasi Portofolio Saham Syariah dengan Pendekatan Fuzzy Goal Programming

This study discusses about solving the problem of stock portfolio optimization. The portfolio optimization problem can be modeled as a multiobjective model with two objective functions, they are maximizing return and minimizing risk. This study uses the mean-variance Markowitz model to model the portfolio. The fuzzy goal programming approach is used to solve stock portfolio problems by converting a multi-objective model into a fuzzy mathematical programming model which is solved using a nonlinear programming method. The results of implementing the model on stocks listed on the Jakarta Islamic Index show that the best investment proportion forms an optimal portfolio according to the level of aspirations. Several different optimal portfolios can be formed using the fuzzy goal programming approach. The difference in the results of these portfolios depends on the level of aspiration of investors.

An Alternative Method for Finding the Critical Path of the Network in Fuzzy Time Cost Trade off Problem

Background : The critical path approach is used to determine the network's longest path, according to historical records. This study examines a different approach to determining the construction network's longest path. Method: Here, the network is viewed as a directed acyclic graph, and the critical path of the network is found using the longest path algorithm of the network. To find the best answer for a building project, the longest path that was found was integrated into a linear programming issue. The triangle fuzzy variable defines all of the project's inputs. The 992 square foot building area is incorporated, and three project manager’s quotes are used as a triangular fuzzy variable. Findings : This work has the options of getting quotation from the project managers, convert them as the fuzzy variables such as triangular fuzzy variable, Trapezoidal fuzzy variable and pentagonal fuzzy variable. After the network is converted into a linear programming problem using the fully fuzzy mathematical model, the best possible solution is found. Novelty and applications : Alternative method for critical path of the network has been incorporated. It has been found that the proposed method reduces the time to find the critical path of the larger networks. Keywords: Directed Acyclic Graph, Longest Path Algorithm, Triangular Fuzzy Variable, Fuzzy Linear Programming Problem, Fully Fuzzy Mathematical Model

Designing a Fuzzy Mathematical Model for a Two-Echelon Allocation-Routing Problem by Applying Route Conditions: A New Interactive Fuzzy Approach

In vehicle routing problems (VRP), the optimal allocation of transportation by considering factors such as route hardness, driver experience and vehicle worn-out has a significant effect on costs reduction and approaching real-world conditions. In this paper, a novel fuzzy mixed integer non-linear mathematical model to address the two-echelon allocation-routing problem under uncertainty is proposed by applying route and fleet conditions. The cost of allocating drivers to diverse vehicles is computed at the first echelon of the problem, considering factors such as vehicle type, vehicle wear-out, and driver experience. Additionally, different routes are defused with varying levels of hardness. The goal of the second echelon of the model is to improve reliability by defining the reliability of routes within each section. To solve the model, the Torabi and Hessini (TH), the Selimi and Ozkarahan (SO) methods, and a newly proposed approach (PIA) were utilized to transform the multi-objective model into a single-objective one. Numerical tests and performance indicators were used to validate the effectiveness of both the multi-objective mathematical model and the proposed solution method. The validation computation results indicate that the proposed solution approach outperforms both the TH and SO approaches.

Using new fuzzy regression aptness and healthcare equity indices in cancer hospitals network design: a fuzzy multi-objective mathematical model

Using new fuzzy regression aptness and healthcare equity indices in cancer hospitals network design: a fuzzy multi-objective mathematical model

A novel two-phase approach for a sustainable p-hub median problem with multiple service levels and carbon cap-and trade policy under uncertainty

ABSTRACT To reduce the carbon emissions for society's sustainable development and satisfy customers' personalized delivery service, this paper addresses the cap-and-trade policy and multiple service levels into a p-hub median problem. In the hub network designing, single-assignment patterns between hubs and demand nodes, the choice of transportation mode for each O-D pair and the uncertainties of carbon emission and price are taken into account. Based on a fuzzy chance-constrained programming approach, a fuzzy mathematical model under an expected cost-minimization context with some fuzzy constraints is first presented. Then a two-phase approach is proposed to solve the proposed model. Finally, in view of the comparative analysis with small- and large-scale Turkish instances, serval managerial insights are finally obtained for government and logistics companies in the reduction of carbon emission and the hub network's total designing cost for the sustainable development.

Prediction and decision making in corona virus using fuzzy mathematical model

During the period of 2019–20, forecasting was of utmost priority for health care planning and to combat COVID-19 pandemic. Almost everyone’s life has been greatly impacted by COVID-19. Understanding how the disease spreads is crucial to know how the disease behaves dynamically. The aim of the research is to construct an SEI Q1Q2 R model for COVID-19 with fuzzy parameters. The fuzzy parameters are the transmission rate, the infection rate, the recovery rate and the death rate. We compute the basic reproduction number, using next-generation matrix method, which will be used further to study the model’s prediction. The COVID-free and endemic equilibrium points attain local and global stability when R0 < 1. A sensitivity analysis of the reproduction number against its internal parameter has been done. The results of this model showed that intervention measures. The numerical simulation along with graphical representations at COVID-free and endemic points are shown. The SEIQ1Q2R model is a successful model to analyse the spreading and controlling the epidemics like COVID-19.