Fuzzy Optimization Research Articles

SOME CHARACTERIZATION RESULTS FOR NONSMOOTH INTUITIONISTIC FUZZY OPTIMIZATION VIA SYMMETRIC gH-DIFFERENTIABILITY

In recent years, there has been a growing interest in optimization problems with uncertainty. Intuitionistic fuzzy optimization is one of the approaches for investigating such real-world optimization problems that contain uncertain data and, therefore, that are not well defined. Nonetheless, there is not enough discussion on the optimality conditions for optimal solutions in intuitionistic fuzzy optimization problems (IFOPs) and methods for solving such uncertain extremum problems. Although the derivative notion is a very important property of optimization models, there are many real-world problems and processes with uncertainty that cannot be modeled as differentiable intuitionistic fuzzy functions (IFFs). In this work, therefore, a new notion of generalized derivative is defined. Namely, the definition of symmetric gH-derivative is introduced for nonsmooth IFOPs and some properties of this concept are analyzed. Further, the Karush–Kuhn–Tucker optimality conditions are established for an optimal solution in an intuitionistic fuzzy extremum problem with symmetric gH-differentiable IFFs and inequality constraints. Meanwhile, several examples are given to illuminate the obtained results.

Fuzzy multi-objective optimization model to design a sustainable closed-loop manufacturing system.

Republicans and Democrats practically everywhere have been demonstrating concerns about environmental conservation to achieve sustainable development goals (SDGs) since the turn of the century. To promote fuel (energy) savings and a reduction in the amount of carbon dioxide CO2 emissions in several enterprises, actions have been taken based on the concepts described. This study proposes an environmentally friendly manufacturing system designed to minimize environmental impacts. Specifically, it aims to develop a sustainable manufacturing process that accounts for energy consumption and CO2 emissions from direct and indirect energy sources. A multi-objective mathematical model has been formulated, incorporating financial and environmental constraints, to minimize overall costs, energy consumption, and CO2 emissions within the manufacturing framework. The input model parameters for real-world situations are generally unpredictable, so a fuzzy multi-objective model will be developed as a way to handle it. The validity of the proposed ecological industrial design will be tested using a scenario-based approach. Results demonstrate the high reliability, applicability, and effectiveness of the proposed network when analyzed using the developed techniques.

TQFLL: a novel unified analytics framework for translation quality framework for large language model and human translation of allusions in multilingual corpora

In large language models (LLMs), the translation quality has limitations in the translation when translated into different languages. This study compares Chinese allusions in human and machine translated corpora translated by OpenAI GPT-3.5, Volctrans, and human translated texts. The framework innovatively combines two automated evaluation metrics, BLEU and METEOR, with a translation quality assessment method derived from Fuzzy Mathematics and Optimality Theory. The findings of the study indicate that the GPT-3.5 translated version exhibits higher quality than the Volctrans version when evaluated by a machine. Similarly, human evaluations indicate that among the three versions, Volctrans is of the lowest quality, while the human version exceeds the GPT-3.5 version in terms of quality. Thus, the study further reveals that Volctrans version is deemed to have the lowest translation quality from both human and machine evaluation perspectives. Finally, this study not only introduces but also validates a novel framework for assessing machine translation quality.

A fuzzy logic and optimisation based approach for shipyard facility layout problem with consideration of risk, activity, and flow factors

One of the crucial factors of shipbuilding in terms of production efficiency is the arrangement of workstations. Since shipyard design involves the layout of many workstations, an initial setup is helpful for the shipyard designer. This paper proposes a new methodology for determining the relative locations of shipyard workstations. The novelties of this study are the use of the Simulated Annealing (SA) approach for determining shipyard workstation’s relative locations, the use of fuzzy logic and metaheuristic optimisation together in the shipyard facility layout planning (FLP) domain, and the incorporation of safety concept into the shipyard FLP. The procedure for determining proximity rating involves both qualitative (activity) and quantitative (flow and risk) factors and employs fuzzy logic. The problem of determining the relative locations of workstations is treated as an optimisation problem. The proposed methodology successfully generated three distinct shipyard layouts. These include U, L, and I-shaped arrangements for profiled panel production, as well as an almost star-shaped branched arrangement for sub-block production. Results show that this approach offers beneficial alternative starting layouts for a shipyard designer.

A multi-objective fuzzy optimization model for multi-type aircraft flight scheduling problem

This study proposes a multi-objective optimization model for an Aircraft Flight Scheduling Problem (AFSP) for assigning a set of aircraft located at different airports to conduct all flight trips. The proposed model features each flight trip with its own special aircraft type and fuzzy flight time. Moreover, a flight trip with a small aircraft being covered by a larger one is fully accounted for in the model. The model can effectively reduce the number of aircraft and achieve the minimum total idle time for adjacent flight trips covered by an aircraft. A novel heuristic algorithm based on the Non-dominated Sorting Genetic Algorithm (NSGA-II) is further designed to yield meta-optimal solutions efficiently for such a Non-deterministic Polynomial (NP) problem. Finally, a real airline scheduling example in China is conducted using CPLEX and the proposed heuristic algorithm to evaluate the difference between the proposed and traditional models. The results show that the given scheduling problem effectively enhances the operational efficiency of the aircraft fleet. First published online 28 January 2025

The algorithm of fuzzy multi-criteria optimization of the preparation of minced meat of a given nutritional value

The algorithm of fuzzy multi-criteria optimization of the preparation of minced meat of a given nutritional value

Mathematical Models and Algorithms for Failed Equipment Planning Replacement

For the operability of deep well pump units under the conditions of oil and gas field equipment rental, it is necessary to plan the required resources. Failed equipment must be replaced with new one. If it is possible to repair the items, they are sent to repair service points. A review of literary sources on the subject of the study and the problem statement are provided. A large number of equipment application points and real operating conditions introduce great uncertainty into planning the failed equipment replacement. The value of the failure rate is a random variable. A mathematical model to manage the process of failed equipment replacing has been developed. Fuzzy logic methods have been used to take into account the uncertainty. Characteristics of fuzzy failure flow have been determined,based on the available information on failures. To perform computational operations, algorithms for working with fuzzy variables have been developed based on, in general case, asymmetric, and parabolic membership functions. The operations of addition, subtraction, multiplication, division, and exponentiation of fuzzy numbers are determined using interval arithmetic andα-cut method. The amount of equipment stock is determined by a fuzzy number. The use of a hybrid genetic algorithm provided an optimal solution to the optimization problem equipment replacement management. The calculation results are given. When solving the fuzzy optimization problem in comparative operations, the rank of the fuzzy number was calculated. The concept of centroid defuzzification of the fuzzy number is used to determine the rank value. The diagram of the fuzzy number membership function and the diagram of the optimization problem objective function: total costs were constructed. Compared with the optimization problem clear formulation, the total costs in the fuzzy formulation turned out to be higher, also the value of the safety stock was determined .

Application of optimal fuzzy and PI hybrid controllers for permanent magnet synchronous generator–based wind energy conversion systems

Permanent magnet synchronous generator (PMSG)–based wind turbines (WTs) are preferred over doubly fed induction generators (DFIGs) due to some appealing features. The control techniques used in this paper are fuzzy-based pitch angle controller, optimal torque-controlled maximum power point tracking, and optimal fuzzy and proportional integral (PI) hybrid controller under MATLAB-Simulink software. A grey wolf optimization technique is used to optimize the input scaling factor of the fuzzy logic controller (FLC) and gains of the PI controller. The results indicate that optimal FLC-PI performs better in DC-link voltage control than an optimal PI controller in terms of peak overshoot (0.82%), undershoot (2.51%), and settling time (0.18 s). However, the peak overshoot (1.87%), undershoot (10.6%), and settling time (0.22 s) are recorded for DC-link voltage response while utilizing the optimal PI controller. The generator’s efficiency reaches up to 97.35% for the optimal FLC-PI controller while 96.01% is obtained with the optimal PI controller at rated wind speed.

Solving fuzzy fractional programming problems by VNS algorithm using modified Kerre's inequality

Here, we propose a new variable neighbourhood search (VNS) algorithm for solving fractional fuzzy number linear programming problems (FFNLPPs). We make use of modified Kerre’s inequality for comparison of LR fuzzy numbers. In our proposed algorithm, we introduced a new local search defined based on descent directions, which are found by solving four crisp mathematical programming problems. In several methods, a fuzzy fractional optimization problem is converted to a crisp problem. Still, in our proposed method, using modified Kerre’s inequality, the fuzzy optimization problem is solved directly, without changing it to a crisp program. To show the effectiveness of our method, we compare our proposed algorithm with other available methods.

Optimization of elements transfer in low carbon steel welds during submerged arc welding

This study suggests that the optimal flux can be designed and selected for the Mn/S ratio in the weld and high penetration. Fuzzy logic optimization technique has been used for the selection of flux. The Mn/S ratio is important in the welds as the mechanical properties such as impact strength, toughness and tensile strength also depends upon the ratio of Mn/S in the welds. This ratio also affects the weld bead geometry like weld width, penetration and reinforcement. The fluxes were designed using RSM and were made by agglomeration technique. The optimized flux contains CaF2, FeMn and NiO each as 8, 2 and 2%

Erratum to “Enhancing production inventory management for imperfect items using fuzzy optimization strategies and Differential Evolution (DE) algorithms” [Franklin Open Volume 5, December 2023, 10005

Erratum to “Enhancing production inventory management for imperfect items using fuzzy optimization strategies and Differential Evolution (DE) algorithms” [Franklin Open Volume 5, December 2023, 10005

Feasibility-guaranteed machine learning unit commitment: Fuzzy Optimization approaches

The unit commitment (UC) problem is solved several times daily in a limited amount of time and is commonly formulated using mixed-integer linear programs (MILP). However, solution time for MILP formulation increases exponentially with the number of binary variables required. To address this, machine learning (ML) models have been attempted with limited success as they cannot be trained for all scenarios, whereby they may contain false predictions leading to infeasibility, hindering their practical applicability. To overcome these issues, we first propose a hybrid deep learning model comprising a convolutional neural network (CNN) and bidirectional long-short-term memory (BiLSTM) to predict the UC decisions. Second, we incorporate these predictions as non-binding fuzzy constraints, enhancing the traditional UC model and creating an ML-fuzzy UC model. Two implementations of non-binding fuzzy constraints are studied. The first develops each ML decision variable as a separate fuzzy set, while the second creates one fuzzy set per hour, considering all decisions within. Introducing ML-UC decisions as non-binding fuzzy constraints ensures the ML-fuzzy UC model has a feasible solution if the basic MILP-UC problem does, while leveraging ML predictions. Moreover, the proposed model benefits from a reduced solution space, leading to substantial reductions in computing time. Results on IEEE 118-bus and Polish 2383-bus systems demonstrate 92 % and 89 % computation time reductions for both systems, respectively and achieve 100 % feasibility for both seen and unseen datasets when the basic MILP-UC problem has a feasible solution.

Assessment of water electrolysis projects for green hydrogen production with a novel hybrid Q-learning algorithm and molecular fuzzy-based modelling

Determining the most important criteria for increasing the efficiency of water electrolysis investments provides businesses with a competitive advantage. Although there are many studies in the literature on this importance, there are very few studies determining the most important of these performance indicators. To satisfy this gap, the purpose of this study is to make assessment of water electrolysis projects for green hydrogen production via a novel model. First, the balanced expert evaluation matrices are obtained by q-learning algorithm. Secondly, the criteria for water electrolysis investments are prioritized using molecular fuzzy Bayesian network (BANEW). Thirdly, green hydrogen strategies for water electrolysis investments are ranked with molecular fuzzy multi-objective particle swarm optimization (MOPSO). The most important contribution of this study to the literature is the determination of the criteria that should be applied primarily for the performance increase of water electrolysis investments by creating a new model. The use of molecular fuzzy numbers is a very important contribution of the model to the literature. In this process, the use of three-dimensional geometric figures allows the reduction of uncertainties in decision-making processes. The findings indicate that lifespan of electrolysers and production capacity are the most essential criteria. Additionally, proton exchange membrane electrolysers and alkaline water electrolysis are found as the most critical green hydrogen strategies. Extending the life of electrolysers is crucial to increase sustainability in hydrogen production and reduce long-term costs. In this context, research incentives should be provided for the development of materials and technologies to increase the durability of electrolysers. Similarly, establishing quality standards to extend the life of electrolysers also contributes to achieving this goal.

Fuzzy multi-objective optimization for sustainable agricultural water management of irrigation networks

Sustainable water resource management in arid and water deficit regions requires optimal use of water resources due to competition among different water sectors. The purpose of this study is to model uncertainties in economic and hydro-climatic variables and parameters to optimize agricultural water management in irrigation system networks to have sustainable water use. The study focuses on mitigating water shortages in Iran's Varamin irrigation network through improved agricultural patterns and efficient water consumption. The impact of employing reclaimed wastewater containing nitrates instead of nitrogen fertilizers is also evaluated. A Fuzzy Multi-Objective Particle Swarm Optimization (F-MOPSO) is applied to maximize the net benefit, restore groundwater, and minimize nitrate leaching into the aquifer. The results demonstrate that replacing groundwater with reclaimed wastewater boosted net benefits by 21% while improving groundwater restoration by 82%. These results indicate that the developed fuzzy model can handle uncertainties in irrigation system networks with a sustainable water use perspective. This research can assist decision-makers within the water, agriculture, and the environment in finding sustainable water solutions and improving the current water consumption practices, considering environmental aspects of nitrogen leaching in other regions and highlighting the potential of the developed fuzzy model.

Moisture Distribution and Ice Front Identification in Freezing Soil Using an Optimized Circular Capacitance Sensor.

As the interface between frozen and unfrozen soil, the ice front is not only a spatial location concept, but also a potentially dangerous interface where the mechanical properties of soil could change abruptly. Accurately identifying its spatial position is essential for the safe and efficient execution of large-scale frozen soil engineering projects. Electrical capacitance tomography (ECT) is a promising method for the visualization of frozen soil due to its non-invasive nature, low cast, and rapid response. This paper presents the design and optimization of a mobile circular capacitance sensor (MCCS). The MCCS was used to measure frozen soil samples along the depth direction to obtain moisture distribution and three-dimensional images of the ice front. Finally, the experimental results were compared with the simulation results from COMSOL Multiphysics to analyze the deviations. It was found that the fuzzy optimization design based on multi-criteria orthogonal experiments makes the MCCS meet various performance requirements. The average permittivity distribution was proposed to reflect moisture distribution along the depth direction and showed good correlation. Three-dimensional reconstructed images could provide the precise position of the ice front. The simulation results indicate that the MCCS has a low deviation margin in identifying the position of the ice front.

Fuzzy TOPSIS optimization of MHD trihybrid nanofluid in heat pipes

Heat pipes have the potential to benefit from nanofluid flow between coaxial cylinders. Heat is effectively transferred from one place to another by means of heat pipes. Heat pipes can be used for electronics cooling, spacecraft thermal management, and heat recovery systems by adding nanofluids, which enhances the heat pipe's thermal conductivity and heat transfer capability. This work aims to discover an approximate solution for the flow of a trihybrid nanofluid (THNF) consisting of graphene, copper, and silver between two coaxial cylinders in magneto-hydrodynamics, taking into account the broad variety of applications. The nanomaterial is tested in a system with a fixed inner cylinder and a rotating outer cylinder. It contains graphene, copper, silver, and kerosene oil as the base fluid. For examining the flow characteristics, magnetic field is applied along radial direction of the cylinder, while inner cylinder is fixed, and outer cylinder is rotating. Moreover, temperature of the outer cylinder is higher than the lower cylinder. The objective of this study is to develop a mathematical model of the problem and solve the governing equation numerically using the MATLAB built-in routine called bvp4c. Additionally, we identify the most effective physical parameter to optimize the heat transfer rate using Fuzzy Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS). Using a variety of factors, we calculate fluid velocity, skin friction, temperature, and Nusselt number graphically. According to the study, higher Brinkman numbers (Br) and magnetic parameter (M) characteristics lead to higher temperatures. Furthermore, Fuzzy TOPSIS shows that alternative A11 (ϕ=(0.9,1.0,1.0),M=(0.5,0.7,0.9),Br=(0.9,1.0,1.0)) has the maximum heat transfer rate, while another A8 (ϕ=(0,0,0.1),M=(0,0,0.1),Br=(0,0,0.1)) has the lowest.

Optimal planning for hybrid renewable energy systems under limited information based on uncertainty quantification

Developing hybrid renewable energy systems (HRES) is crucial for ensuring affordable, sustainable, and reliable energy access in remote rural and island regions. Rich and detailed data play a pivotal role in the optimal design of HRES. However, remote areas often face data limitations due to inadequate metering infrastructure, which further increases uncertainties in HRES design. This paper proposes a planning optimization method that quantifies multiple uncertainties, requiring only limited information for the optimal HRES design. First, uncertainties in HRES planning are classified into different types based on intrinsic randomness, data availability, and impact level. Then, by integrating uncertainty quantification with credibility theory, knowledge-based scenario generation models are developed to leverage limited available information to generate extreme and typical operating conditions for a tailored HRES design. Finally, a fuzzy credibility-constrained stochastic-robust optimization model is proposed to optimize the design of HRES. A practical case facing significant data scarcity and gaps is used to validate the effectiveness of the proposed method. The proposed approach reduces the loss of load probability for HRES to 0.02 % and lowers the levelized cost of energy to $0.16/kWh—33 % lower than that of the deterministic method and 79 % lower than that of the traditional stochastic method.

Research on intelligent optimal allocation control strategy for stability and braking of heavy tyre blowout vehicle

The traditional control strategy mainly compensates and corrects the driving state of heavy vehicles with a tyre blowout, and rarely considers the need for emergency braking. It is also difficult to effectively coordinate the problems of lateral yaw, slip and tailspin, and longitudinal braking performance degradation. For this, an intelligent optimization allocation control strategy combining stability control and braking control is innovatively designed in this article. The joint simulation model for heavy tyre blowout vehicles is built based on the Dugoff tyre blowout model and the TruckSim vehicle model. A linear quadratic form regulator stable control based on the particle swarm optimization algorithm optimization is used to dynamic equilibrium of the additional yaw moment generated by the vehicle tyre blowout. A logic threshold braking control based on adaptive adjustment is adopted to achieve an ideal braking effect for the vehicle. In order to simultaneously consider the stability and braking performance of vehicles with blowout tyre, a braking force distribution strategy and a fuzzy optimization allocation algorithm are proposed to achieve coordination of lateral and longitudinal control strategies. The results indicate that intelligent optimized allocation control can effectively correct the deviation trajectory of a heavy tyre blowout vehicle, enabling it to achieve rapid braking while maintaining stability.

Predicting Portfolios Using Fuzzy Logic and Optimization Techniques: A Case Study of BSE-IT Listed Companies

Stock price trends were considered in this study, the companies in the BSE-IT index, with a view to optimizing portfolio allocation based on risk tolerance. The GARCH model has been applied here to allow an investigation into the volatility of the stock returns and to set up different clusters using K-Means clustering that group together companies owning the same attributes related to volatility for strategic classification. Data collection and processing occur between April 1, 2014, and March 31, 2024, for reasons of reliability and relevance. Descriptive statistics report on the variance of stock performance across companies; different risk-return profiles are thus exposed. The GARCH model measures each stock's long-term variance, along with sensitivity to past shocks, and overall volatility persistence, making this an excellent inventory for risk assessment. K-Means clustering groups companies based on similar volatility patterns, thereby informing portfolio construction. Findings present how clustering with econometric modeling may assist in the production of optimal portfolios that depend on specified risk capacities, thus efficiently managing and implementing an IT investment strategy.

Low-Carbon Water–Rail–Road Multimodal Routing Problem with Hard Time Windows for Time-Sensitive Goods Under Uncertainty: A Chance-Constrained Programming Approach

In this study, a low-carbon freight routing problem for time-sensitive goods is investigated in the context of water–rail–road multimodal transportation. To enhance the on-time transportation of time-sensitive goods, hard time windows are employed to regulate both pickup and delivery services at the start and end of their transportation. The uncertainty of both the demand for time-sensitive goods and the capacity of the transportation network are modeled using L-R triangular fuzzy numbers in the routing process to make the advanced routing more feasible in the actual transportation. Based on the carbon tax policy, a fuzzy linear optimization model is established to address the proposed problem, and an equivalent chance-constrained programming formulation is then obtained to make the solution to the problem attainable. A numerical experiment is carried out to verify the feasibility of incorporating the carbon tax policy, uncertainty, and water–rail–road multimodal transportation to optimize the low-carbon freight routing problem for time-sensitive goods. Furthermore, a multi-objective optimization is used to reveal that lowering the transportation costs, reducing the carbon emissions, and avoiding the risk are in conflict with each in the routing. We also analyze the sensitivity of the optimization results concerning the confidence level of the chance constraints and the uncertainty degree of the uncertain demand and capacity. Based on the numerical experiment, we draw several conclusions to help the shipper, receiver, and multimodal transportation operator to organize efficient water–rail–road multimodal transportation for time-sensitive goods.