A vague-set-based fuzzy multi-objective decision making model is developed for evaluating bidding plans in a bid- ding purchase process. A group of decision-makers (DMs) first independently assess bidding plans accord...A vague-set-based fuzzy multi-objective decision making model is developed for evaluating bidding plans in a bid- ding purchase process. A group of decision-makers (DMs) first independently assess bidding plans according to their experience and preferences, and these assessments may be expressed as linguistic terms, which are then converted to fuzzy numbers. The resulting decision matrices are then transformed to objective membership grade matrices. The lower bound of satisfaction and upper bound of dissatisfaction are used to determine each bidding plan’s supporting, opposing, and neutral objective sets, which together determine the vague value of a bidding plan. Finally, a score function is employed to rank all bidding plans. A new score function based on vague sets is introduced in the model and a novel method is presented for calculating the lower bound of sat- isfaction and upper bound of dissatisfaction. In a vague-set-based fuzzy multi-objective decision making model, different valua- tions for upper and lower bounds of satisfaction usually lead to distinct ranking results. Therefore, it is crucial to effectively contain DMs’ arbitrariness and subjectivity when these values are determined.展开更多
Supplier selection is a multi-objective decision problem, which must be considered many objectives, some objectives are qualitative, and others are quantitative. Meanwhile, manufacturer has preference for different su...Supplier selection is a multi-objective decision problem, which must be considered many objectives, some objectives are qualitative, and others are quantitative. Meanwhile, manufacturer has preference for different suppliers. In this paper, a new multi-objective decision model with preference information of supplier is established. A practical example of supplier selection problem utilizing this model is studied. The result demonstrates the feasibility and effectiveness of the methods proposed in the paper.展开更多
Addressing the complex issue of emergency resource distribution center site selection in uncertain environments, this study was conducted to comprehensively consider factors such as uncertainty parameters and the urge...Addressing the complex issue of emergency resource distribution center site selection in uncertain environments, this study was conducted to comprehensively consider factors such as uncertainty parameters and the urgency of demand at disaster-affected sites. Firstly, urgency cost, economic cost, and transportation distance cost were identified as key objectives. The study applied fuzzy theory integration to construct a triangular fuzzy multi-objective site selection decision model. Next, the defuzzification theory transformed the fuzzy decision model into a precise one. Subsequently, an improved Chaotic Quantum Multi-Objective Harris Hawks Optimization (CQ-MOHHO) algorithm was proposed to solve the model. The CQ-MOHHO algorithm was shown to rapidly produce high-quality Pareto front solutions and identify optimal site selection schemes for emergency resource distribution centers through case studies. This outcome verified the feasibility and efficacy of the site selection decision model and the CQ-MOHHO algorithm. To further assess CQ-MOHHO’s performance, Zitzler-Deb-Thiele (ZDT) test functions, commonly used in multi-objective optimization, were employed. Comparisons with Multi-Objective Harris Hawks Optimization (MOHHO), Non-dominated Sorting Genetic Algorithm II (NSGA-II), and Multi-Objective Grey Wolf Optimizer (MOGWO) using Generational Distance (GD), Hypervolume (HV), and Inverted Generational Distance (IGD) metrics showed that CQ-MOHHO achieved superior global search ability, faster convergence, and higher solution quality. The CQ-MOHHO algorithm efficiently achieved a balance between multiple objectives, providing decision-makers with satisfactory solutions and a valuable reference for researching and applying emergency site selection problems.展开更多
In a world where supply chains are increasingly complex and unpredictable,finding the optimal way to move goods through transshipment networks is more important and challenging than ever.In addition to addressing the ...In a world where supply chains are increasingly complex and unpredictable,finding the optimal way to move goods through transshipment networks is more important and challenging than ever.In addition to addressing the complexity of transportation costs and demand,this study presents a novel method that offers flexible routing alternatives to manage these complexities.When real-world variables such as fluctuating costs,variable capacity,and unpredictable demand are considered,traditional transshipment models often prove inadequate.To overcome these challenges,we propose an innovative fully fuzzy-based framework using LR flat fuzzy numbers.This framework allows for more adaptable and flexible decision-making in multi-objective transshipment situations by effectively capturing uncertain parameters.To overcome these challenges,we develop an innovative,fully fuzzy-based framework using LR flat fuzzy numbers to effectively capture uncertainty in key parameters,offering more flexible and adaptive decision-making in multi-objective transshipment problems.The proposed model also presents alternative route options,giving decisionmakers a range of choices to satisfy multiple requirements,including reducing costs,improving service quality,and expediting delivery.Through extensive numerical experiments,we demonstrate that the model can achieve greater adaptability,efficiency,and flexibility than standard approaches.This multi-path structure provides additional flexibility to adapt to dynamic network conditions.Using ranking strategies,we compared our multi-objective transshipment model with existing methods.The results indicate that,while traditional methods such as goal and fuzzy programming generate results close to the anti-ideal value,thus reducing their efficiency,our model produces solutions close to the ideal value,thereby facilitating better decision making.By combining dynamic routing alternatives with a fully fuzzybased approach,this study offers an effective tool to improve decision-making and optimize complex networks under real-world conditions in practical settings.In this paper,we utilize LINGO 18 software to solve the provided numerical example,demonstrating the effectiveness of the proposed method.展开更多
Wireless Sensor Networks(WSNs)are one of the best technologies of the 21st century and have seen tremendous growth over the past decade.Much work has been put into its development in various aspects such as architectu...Wireless Sensor Networks(WSNs)are one of the best technologies of the 21st century and have seen tremendous growth over the past decade.Much work has been put into its development in various aspects such as architectural attention,routing protocols,location exploration,time exploration,etc.This research aims to optimize routing protocols and address the challenges arising from conflicting objectives in WSN environments,such as balancing energy consumption,ensuring routing reliability,distributing network load,and selecting the shortest path.Many optimization techniques have shown success in achieving one or two objectives but struggle to achieve the right balance between multiple conflicting objectives.To address this gap,this paper proposes an innovative approach that integrates Particle Swarm Optimization(PSO)with a fuzzy multi-objective framework.The proposed method uses fuzzy logic to effectively control multiple competing objectives to represent its major development beyond existing methods that only deal with one or two objectives.The search efficiency is improved by particle swarm optimization(PSO)which overcomes the large computational requirements that serve as a major drawback of existing methods.The PSO algorithm is adapted for WSNs to optimize routing paths based on fuzzy multi-objective fitness.The fuzzy logic framework uses predefined membership functions and rule-based reasoning to adjust routing decisions.These adjustments influence PSO’s velocity updates,ensuring continuous adaptation under varying network conditions.The proposed multi-objective PSO-fuzzy model is evaluated using NS-3 simulation.The results show that the proposed model is capable of improving the network lifetime by 15.2%–22.4%,increasing the stabilization time by 18.7%–25.5%,and increasing the residual energy by 8.9%–16.2% compared to the state-of-the-art techniques.The proposed model also achieves a 15%–24% reduction in load variance,demonstrating balanced routing and extended network lifetime.Furthermore,analysis using p-values obtained from multiple performance measures(p-values<0.05)showed that the proposed approach outperforms with a high level of confidence.The proposed multi-objective PSO-fuzzy model provides a robust and scalable solution to improve the performance of WSNs.It allows stable performance in networks with 100 to 300 nodes,under varying node densities,and across different base station placements.Computational complexity analysis has shown that the method fits well into large-scale WSNs and that the addition of fuzzy logic controls the power usage to make the system practical for real-world use.展开更多
Transportation systems are rapidly transforming in response to urbanization,sustainability challenges,and advances in digital technologies.This review synthesizes the intersection of artificial intelligence(AI),fuzzy ...Transportation systems are rapidly transforming in response to urbanization,sustainability challenges,and advances in digital technologies.This review synthesizes the intersection of artificial intelligence(AI),fuzzy logic,and multi-criteria decision-making(MCDM)in transportation research.A comprehensive literature search was conducted in the Scopus database,utilizing carefully selected AI,fuzzy,and MCDM keywords.Studies were rigorously screened according to explicit inclusion and exclusion criteria,resulting in 73 eligible publications spanning 2006-2025.The review protocol included transparent data extraction on methodological approaches,application domains,and geographic distribution.Key findings highlight the prevalence of hybrid fuzzyAHPand TOPSIS methods,the widespread integration of machine learning for prediction and optimization,and a predominant focus on logistics and infrastructure planning within the transportation sector.Geographic analysis underscores a marked concentration of research activity in Asia,while other regions remain underrepresented,signaling the need for broader international collaboration.The review also addresses persistent challenges such asmethodological complexity,data limitations,and model interpretability.Future research directions are proposed,including the integration of reinforcement learning,real-time analytics,and big data-driven adaptive solutions.This study offers a comprehensive synthesis and critical perspective,serving as a valuable reference for researchers,practitioners,and policymakers seeking to enhance the efficiency,resilience,and sustainability of transportation systems through intelligent decision-making frameworks.展开更多
This study introduces a novel distance measure(DM)for(p,q,r)-spherical fuzzy sets((p,q,to improve decision-making in complex and uncertain environments.Many existing distance measures eitherr)-SFSs)fail to satisfy ess...This study introduces a novel distance measure(DM)for(p,q,r)-spherical fuzzy sets((p,q,to improve decision-making in complex and uncertain environments.Many existing distance measures eitherr)-SFSs)fail to satisfy essential axiomatic properties or produce unintuitive outcomes.To address these limitations,we propose a new three-dimensional divergence-based DM that ensures mathematical consistency,enhances the discrimination of information,and adheres to the axiomatic framework of distance theory.Building on this foundation,we construct a multi-criteria decision-making(MCDM)model that utilizes the proposed DM to evaluate and rank alternatives effectively.The applicability and robustness of the model are validated through a practical case study,demonstrating that it leads to more rational,consistent,and reliable decision outcomes compared to existing approaches.展开更多
In this manuscript,the notion of a hesitant fuzzy soft fixed point is introduced.Using this notion and the concept of Suzuki-type(μ,ν)-weak contraction for hesitant fuzzy soft set valued-mapping,some fixed point res...In this manuscript,the notion of a hesitant fuzzy soft fixed point is introduced.Using this notion and the concept of Suzuki-type(μ,ν)-weak contraction for hesitant fuzzy soft set valued-mapping,some fixed point results are established in the framework of metric spaces.Based on the presented work,some examples reflecting decision-making problems related to real life are also solved.The suggested method’s flexibility and efficacy compared to conventional techniques are demonstrated in decision-making situations involving uncertainty,such as choosing the best options in multi-criteria settings.We noted that the presented work combines and generalizes two major concepts,the idea of soft sets and hesitant fuzzy set-valued mapping from the existing literature.展开更多
The existing algorithms for solving multi-objective optimization problems fall into three main categories:Decomposition-based,dominance-based,and indicator-based.Traditional multi-objective optimization problemsmainly...The existing algorithms for solving multi-objective optimization problems fall into three main categories:Decomposition-based,dominance-based,and indicator-based.Traditional multi-objective optimization problemsmainly focus on objectives,treating decision variables as a total variable to solve the problem without consideringthe critical role of decision variables in objective optimization.As seen,a variety of decision variable groupingalgorithms have been proposed.However,these algorithms are relatively broad for the changes of most decisionvariables in the evolution process and are time-consuming in the process of finding the Pareto frontier.To solvethese problems,a multi-objective optimization algorithm for grouping decision variables based on extreme pointPareto frontier(MOEA-DV/EPF)is proposed.This algorithm adopts a preprocessing rule to solve the Paretooptimal solution set of extreme points generated by simultaneous evolution in various target directions,obtainsthe basic Pareto front surface to determine the convergence effect,and analyzes the convergence and distributioneffects of decision variables.In the later stages of algorithm optimization,different mutation strategies are adoptedaccording to the nature of the decision variables to speed up the rate of evolution to obtain excellent individuals,thusenhancing the performance of the algorithm.Evaluation validation of the test functions shows that this algorithmcan solve the multi-objective optimization problem more efficiently.展开更多
The large-scale multi-objective optimization algorithm(LSMOA),based on the grouping of decision variables,is an advanced method for handling high-dimensional decision variables.However,in practical problems,the intera...The large-scale multi-objective optimization algorithm(LSMOA),based on the grouping of decision variables,is an advanced method for handling high-dimensional decision variables.However,in practical problems,the interaction among decision variables is intricate,leading to large group sizes and suboptimal optimization effects;hence a large-scale multi-objective optimization algorithm based on weighted overlapping grouping of decision variables(MOEAWOD)is proposed in this paper.Initially,the decision variables are perturbed and categorized into convergence and diversity variables;subsequently,the convergence variables are subdivided into groups based on the interactions among different decision variables.If the size of a group surpasses the set threshold,that group undergoes a process of weighting and overlapping grouping.Specifically,the interaction strength is evaluated based on the interaction frequency and number of objectives among various decision variables.The decision variable with the highest interaction in the group is identified and disregarded,and the remaining variables are then reclassified into subgroups.Finally,the decision variable with the strongest interaction is added to each subgroup.MOEAWOD minimizes the interactivity between different groups and maximizes the interactivity of decision variables within groups,which contributed to the optimized direction of convergence and diversity exploration with different groups.MOEAWOD was subjected to testing on 18 benchmark large-scale optimization problems,and the experimental results demonstrate the effectiveness of our methods.Compared with the other algorithms,our method is still at an advantage.展开更多
A new fuzzification method for multi-objective decision-making and selective sorting is proposed on the basis of the fuzzy consistent relation, and the specific algorithm is presented. The method is applied to the eva...A new fuzzification method for multi-objective decision-making and selective sorting is proposed on the basis of the fuzzy consistent relation, and the specific algorithm is presented. The method is applied to the evaluation of highway planning of Zhanjiang city. To decrease the subjectivity in the process of decision-making, the LOWA operator is introduced, and a discussion on how to select appropriate weights involved in multi-objective sorting is made. It is concluded that it is feasible to apply the fuzzy consistent relation to multi-objective decision-making analysis, and the improved fuzzication method is workable.展开更多
The presence of numerous uncertainties in hybrid decision information systems(HDISs)renders attribute reduction a formidable task.Currently available attribute reduction algorithms,including those based on Pawlak attr...The presence of numerous uncertainties in hybrid decision information systems(HDISs)renders attribute reduction a formidable task.Currently available attribute reduction algorithms,including those based on Pawlak attribute importance,Skowron discernibility matrix,and information entropy,struggle to effectively manages multiple uncertainties simultaneously in HDISs like the precise measurement of disparities between nominal attribute values,and attributes with fuzzy boundaries and abnormal values.In order to address the aforementioned issues,this paper delves into the study of attribute reduction withinHDISs.First of all,a novel metric based on the decision attribute is introduced to solve the problem of accurately measuring the differences between nominal attribute values.The newly introduced distance metric has been christened the supervised distance that can effectively quantify the differences between the nominal attribute values.Then,based on the newly developed metric,a novel fuzzy relationship is defined from the perspective of“feedback on parity of attribute values to attribute sets”.This new fuzzy relationship serves as a valuable tool in addressing the challenges posed by abnormal attribute values.Furthermore,leveraging the newly introduced fuzzy relationship,the fuzzy conditional information entropy is defined as a solution to the challenges posed by fuzzy attributes.It effectively quantifies the uncertainty associated with fuzzy attribute values,thereby providing a robust framework for handling fuzzy information in hybrid information systems.Finally,an algorithm for attribute reduction utilizing the fuzzy conditional information entropy is presented.The experimental results on 12 datasets show that the average reduction rate of our algorithm reaches 84.04%,and the classification accuracy is improved by 3.91%compared to the original dataset,and by an average of 11.25%compared to the other 9 state-of-the-art reduction algorithms.The comprehensive analysis of these research results clearly indicates that our algorithm is highly effective in managing the intricate uncertainties inherent in hybrid data.展开更多
Aiming at the triangular fuzzy(TF)multi-attribute decision making(MADM)problem with a preference for the distribution density of attribute(DDA),a decision making method with TF number two-dimensional density(TFTD)oper...Aiming at the triangular fuzzy(TF)multi-attribute decision making(MADM)problem with a preference for the distribution density of attribute(DDA),a decision making method with TF number two-dimensional density(TFTD)operator is proposed based on the density operator theory for the decision maker(DM).Firstly,a simple TF vector clustering method is proposed,which considers the feature of TF number and the geometric distance of vectors.Secondly,the least deviation sum of squares method is used in the program model to obtain the density weight vector.Then,two TFTD operators are defined,and the MADM method based on the TFTD operator is proposed.Finally,a numerical example is given to illustrate the superiority of this method,which can not only solve the TF MADM problem with a preference for the DDA but also help the DM make an overall comparison.展开更多
With the increasing integration of emerging source-load types such as distributed photovoltaics,electric vehicles,and energy storage into distribution networks,the operational characteristics of these networks have ev...With the increasing integration of emerging source-load types such as distributed photovoltaics,electric vehicles,and energy storage into distribution networks,the operational characteristics of these networks have evolved from traditional single-load centers to complex multi-source,multi-load systems.This transition not only increases the difficulty of effectively classifying distribution networks due to their heightened complexity but also renders traditional energy management approaches-primarily focused on economic objectives-insufficient to meet the growing demands for flexible scheduling and dynamic response.To address these challenges,this paper proposes an adaptive multi-objective energy management strategy that accounts for the distinct operational requirements of distribution networks with a high penetration of new-type source-loads.The goal is to establish a comprehensive energy management framework that optimally balances energy efficiency,carbon reduction,and economic performance in modern distribution networks.To enhance classification accuracy,the strategy constructs amulti-dimensional scenario classification model that integrates environmental and climatic factors by analyzing the operational characteristics of new-type distribution networks and incorporating expert knowledge.An improved split-coupling K-means preclustering algorithm is employed to classify distribution networks effectively.Based on the classification results,fuzzy logic control is then utilized to dynamically optimize the weighting of each objective,allowing for an adaptive adjustment of priorities to achieve a flexible and responsivemulti-objective energy management strategy.The effectiveness of the proposed approach is validated through practical case studies.Simulation results indicate that the proposed method improves classification accuracy by 18.18%compared to traditional classification methods and enhances energy savings and carbon reduction by 4.34%and 20.94%,respectively,compared to the fixed-weight strategy.展开更多
This paper investigates a distributed heterogeneous hybrid blocking flow-shop scheduling problem(DHHBFSP)designed to minimize the total tardiness and total energy consumption simultaneously,and proposes an improved pr...This paper investigates a distributed heterogeneous hybrid blocking flow-shop scheduling problem(DHHBFSP)designed to minimize the total tardiness and total energy consumption simultaneously,and proposes an improved proximal policy optimization(IPPO)method to make real-time decisions for the DHHBFSP.A multi-objective Markov decision process is modeled for the DHHBFSP,where the reward function is represented by a vector with dynamic weights instead of the common objectiverelated scalar value.A factory agent(FA)is formulated for each factory to select unscheduled jobs and is trained by the proposed IPPO to improve the decision quality.Multiple FAs work asynchronously to allocate jobs that arrive randomly at the shop.A two-stage training strategy is introduced in the IPPO,which learns from both single-and dual-policy data for better data utilization.The proposed IPPO is tested on randomly generated instances and compared with variants of the basic proximal policy optimization(PPO),dispatch rules,multi-objective metaheuristics,and multi-agent reinforcement learning methods.Extensive experimental results suggest that the proposed strategies offer significant improvements to the basic PPO,and the proposed IPPO outperforms the state-of-the-art scheduling methods in both convergence and solution quality.展开更多
The evaluation of the electricity market is crucial for fostering market construction and development.An accurate assessment of the electricity market reveals developmental trends,identifies operational issues,and con...The evaluation of the electricity market is crucial for fostering market construction and development.An accurate assessment of the electricity market reveals developmental trends,identifies operational issues,and contributes to stable and healthy market growth.This study investigated the characteristics of electricity markets in different provinces and synthesized a comprehensive set of evaluation indicators to assess market effectiveness.The evaluation framework,comprising nine indicators organized into two tiers,was constructed based on three aspects:market design,market efficiency,and developmental coordination.Furthermore,a novel fuzzy multi-criteria decision-making evaluation model for electricity market performance was developed based on the Fuzzy-BWM and fuzzy COPRAS methodologies.This model aimed to ensure both accuracy and comprehensiveness in market operation assessment.Subsequently,empirical analyses were conducted on four typical provincial-level electricity markets in China.The results indicate that Guangdong’s electricity market performed best because of its effective balance of stakeholder interests and adherence to contractual integrity principles.Zhejiang and Shandong ranked second and third,respectively,whereas Sichuan exhibited the poorest market performance.Sichuan’s electricity market must be improved in terms of market design,such that market players can obtain a fairly competitive environment.The sensitivity analysis of the constructed indicators verified the effectiveness of the evaluation model proposed in this study.Finally,policy recommendations were proposed to facilitate the sustainable development of China’s electricity markets with the objective of transforming them into efficient and secure markets adaptable to the evolution of novel power systems.展开更多
A decision support system, including a multi-objective optimization framework and a multi-attribute decision making approach is proposed for satellite equipment layout. Firstly, given three objectives (to minimize the...A decision support system, including a multi-objective optimization framework and a multi-attribute decision making approach is proposed for satellite equipment layout. Firstly, given three objectives (to minimize the C.G. offset, the cross moments of inertia and the space debris impact risk), we develop a threedimensional layout optimization model. Unlike most of the previous works just focusing on mass characteristics of the system, a space debris impact risk index is developed. Secondly, we develop an efficient optimization framework for the integration of computer-aided design (CAD) software as well as the optimization algorithm to obtain the Pareto front of the layout optimization problem. Thirdly, after obtaining the candidate solutions, we present a multi-attribute decision making approach, which integrates the smart Pareto filter and the correlation coefficient and standard deviation (CCSD) method to select the best tradeoff solutions on the optimal Pareto fronts. Finally, the framework and the decision making approach are applied to a case study of a satellite platform.展开更多
The problem of multiple attribute decision making under fuzzy linguistic environments, in which decision makers can only provide their preferences （attribute values）in the form of trapezoid fuzzy linguistic variable...The problem of multiple attribute decision making under fuzzy linguistic environments, in which decision makers can only provide their preferences （attribute values）in the form of trapezoid fuzzy linguistic variables（TFLV）, is studied. The formula of the degree of possibility between two TFLVs is defined, and some of its characteristics are studied. Based on the degree of possibility of fuzzy linguistic variables, an approach to ranking the decision alternatives in multiple attribute decision making with TFLV is developed. The trapezoid fuzzy linguistic weighted averaging （TFLWA） operator method is utilized to aggregate the decision information, and then all the alternatives are ranked by comparing the degree of possibility of TFLV. The method can carry out linguistic computation processes easily without loss of linguistic information, and thus makes the decision results reasonable and effective. Finally, the implementation process of the proposed method is illustrated and analyzed by a practical example.展开更多
[Objective]The aim was to overcome the shortage of being difficult to build land evaluation model when the impact factors had continuous value in the traditional land evaluation process,as well as to improve the intel...[Objective]The aim was to overcome the shortage of being difficult to build land evaluation model when the impact factors had continuous value in the traditional land evaluation process,as well as to improve the intelligibility of the land evaluation knowledge.[Method] The land evaluation method combining classification rule extracted by C4.5 algorithm with fuzzy decision was proposed in this study.[Result] The result of Second General Soil Survey of Guangdong Province had demonstrated that the method was convenient to extract classification rules,and by using only 100 rules,quantity correct rate 86.67% and area correct rate 84.80% of land evaluation could be obtained.[Conclusions] The use of C4.5 algorithm to obtain the rules,combined with fuzzy decision algorithm to build classifiers had got satisfactory results,which provided a practical algorithm for the land evaluation.展开更多
Intuitionistic trapezoidal fuzzy numbers and their operational laws are defined. Based on these operational laws, some aggregation operators, including intuitionistic trapezoidal fuzzy weighted arithmetic averaging op...Intuitionistic trapezoidal fuzzy numbers and their operational laws are defined. Based on these operational laws, some aggregation operators, including intuitionistic trapezoidal fuzzy weighted arithmetic averaging operator and weighted geometric averaging operator are proposed. Expected values, score function, and accuracy function of intuitionitsic trapezoidal fuzzy numbers are defined. Based on these, a kind of intuitionistic trapezoidal fuzzy multi-criteria decision making method is proposed. By using these aggregation operators, criteria values are aggregated and integrated intuitionistic trapezoidal fuzzy numbers of alternatives are attained. By comparing score function and accuracy function values of integrated fuzzy numbers, a ranking of the whole alternative set can be attained. An example is given to show the feasibility and availability of the method.展开更多
基金Project (No. K81077) supported by the Department of Automation, Xiamen University, China
文摘A vague-set-based fuzzy multi-objective decision making model is developed for evaluating bidding plans in a bid- ding purchase process. A group of decision-makers (DMs) first independently assess bidding plans according to their experience and preferences, and these assessments may be expressed as linguistic terms, which are then converted to fuzzy numbers. The resulting decision matrices are then transformed to objective membership grade matrices. The lower bound of satisfaction and upper bound of dissatisfaction are used to determine each bidding plan’s supporting, opposing, and neutral objective sets, which together determine the vague value of a bidding plan. Finally, a score function is employed to rank all bidding plans. A new score function based on vague sets is introduced in the model and a novel method is presented for calculating the lower bound of sat- isfaction and upper bound of dissatisfaction. In a vague-set-based fuzzy multi-objective decision making model, different valua- tions for upper and lower bounds of satisfaction usually lead to distinct ranking results. Therefore, it is crucial to effectively contain DMs’ arbitrariness and subjectivity when these values are determined.
文摘Supplier selection is a multi-objective decision problem, which must be considered many objectives, some objectives are qualitative, and others are quantitative. Meanwhile, manufacturer has preference for different suppliers. In this paper, a new multi-objective decision model with preference information of supplier is established. A practical example of supplier selection problem utilizing this model is studied. The result demonstrates the feasibility and effectiveness of the methods proposed in the paper.
文摘Addressing the complex issue of emergency resource distribution center site selection in uncertain environments, this study was conducted to comprehensively consider factors such as uncertainty parameters and the urgency of demand at disaster-affected sites. Firstly, urgency cost, economic cost, and transportation distance cost were identified as key objectives. The study applied fuzzy theory integration to construct a triangular fuzzy multi-objective site selection decision model. Next, the defuzzification theory transformed the fuzzy decision model into a precise one. Subsequently, an improved Chaotic Quantum Multi-Objective Harris Hawks Optimization (CQ-MOHHO) algorithm was proposed to solve the model. The CQ-MOHHO algorithm was shown to rapidly produce high-quality Pareto front solutions and identify optimal site selection schemes for emergency resource distribution centers through case studies. This outcome verified the feasibility and efficacy of the site selection decision model and the CQ-MOHHO algorithm. To further assess CQ-MOHHO’s performance, Zitzler-Deb-Thiele (ZDT) test functions, commonly used in multi-objective optimization, were employed. Comparisons with Multi-Objective Harris Hawks Optimization (MOHHO), Non-dominated Sorting Genetic Algorithm II (NSGA-II), and Multi-Objective Grey Wolf Optimizer (MOGWO) using Generational Distance (GD), Hypervolume (HV), and Inverted Generational Distance (IGD) metrics showed that CQ-MOHHO achieved superior global search ability, faster convergence, and higher solution quality. The CQ-MOHHO algorithm efficiently achieved a balance between multiple objectives, providing decision-makers with satisfactory solutions and a valuable reference for researching and applying emergency site selection problems.
基金the financial support of the European Union under the REFRESH-Research Excellence for Region Sustainability and High-tech Industries project number CZ.10.03.01/00/22_003/0000048 via the Operational Programme Just Transition and has been done in connection with project Students Grant Competition SP2025/062"specific research on progressive and sustainable production technologies"and SP2025/063"specific research on innovative and progressive manufacturing technologies"financed by the Ministry of Education,Youth and Sports and Faculty of Mechanical Engineering VSB-TUOThe authors would like to extend their sincere appreciation to Researchers Supporting Project number(RSP2025R472)King Saud University,Riyadh,Saudi Arabia.
文摘In a world where supply chains are increasingly complex and unpredictable,finding the optimal way to move goods through transshipment networks is more important and challenging than ever.In addition to addressing the complexity of transportation costs and demand,this study presents a novel method that offers flexible routing alternatives to manage these complexities.When real-world variables such as fluctuating costs,variable capacity,and unpredictable demand are considered,traditional transshipment models often prove inadequate.To overcome these challenges,we propose an innovative fully fuzzy-based framework using LR flat fuzzy numbers.This framework allows for more adaptable and flexible decision-making in multi-objective transshipment situations by effectively capturing uncertain parameters.To overcome these challenges,we develop an innovative,fully fuzzy-based framework using LR flat fuzzy numbers to effectively capture uncertainty in key parameters,offering more flexible and adaptive decision-making in multi-objective transshipment problems.The proposed model also presents alternative route options,giving decisionmakers a range of choices to satisfy multiple requirements,including reducing costs,improving service quality,and expediting delivery.Through extensive numerical experiments,we demonstrate that the model can achieve greater adaptability,efficiency,and flexibility than standard approaches.This multi-path structure provides additional flexibility to adapt to dynamic network conditions.Using ranking strategies,we compared our multi-objective transshipment model with existing methods.The results indicate that,while traditional methods such as goal and fuzzy programming generate results close to the anti-ideal value,thus reducing their efficiency,our model produces solutions close to the ideal value,thereby facilitating better decision making.By combining dynamic routing alternatives with a fully fuzzybased approach,this study offers an effective tool to improve decision-making and optimize complex networks under real-world conditions in practical settings.In this paper,we utilize LINGO 18 software to solve the provided numerical example,demonstrating the effectiveness of the proposed method.
基金funded by Deanship of Graduate studies and Scientific Research at Jouf University under grant No.(DGSSR-2023-2-02038).
文摘Wireless Sensor Networks(WSNs)are one of the best technologies of the 21st century and have seen tremendous growth over the past decade.Much work has been put into its development in various aspects such as architectural attention,routing protocols,location exploration,time exploration,etc.This research aims to optimize routing protocols and address the challenges arising from conflicting objectives in WSN environments,such as balancing energy consumption,ensuring routing reliability,distributing network load,and selecting the shortest path.Many optimization techniques have shown success in achieving one or two objectives but struggle to achieve the right balance between multiple conflicting objectives.To address this gap,this paper proposes an innovative approach that integrates Particle Swarm Optimization(PSO)with a fuzzy multi-objective framework.The proposed method uses fuzzy logic to effectively control multiple competing objectives to represent its major development beyond existing methods that only deal with one or two objectives.The search efficiency is improved by particle swarm optimization(PSO)which overcomes the large computational requirements that serve as a major drawback of existing methods.The PSO algorithm is adapted for WSNs to optimize routing paths based on fuzzy multi-objective fitness.The fuzzy logic framework uses predefined membership functions and rule-based reasoning to adjust routing decisions.These adjustments influence PSO’s velocity updates,ensuring continuous adaptation under varying network conditions.The proposed multi-objective PSO-fuzzy model is evaluated using NS-3 simulation.The results show that the proposed model is capable of improving the network lifetime by 15.2%–22.4%,increasing the stabilization time by 18.7%–25.5%,and increasing the residual energy by 8.9%–16.2% compared to the state-of-the-art techniques.The proposed model also achieves a 15%–24% reduction in load variance,demonstrating balanced routing and extended network lifetime.Furthermore,analysis using p-values obtained from multiple performance measures(p-values<0.05)showed that the proposed approach outperforms with a high level of confidence.The proposed multi-objective PSO-fuzzy model provides a robust and scalable solution to improve the performance of WSNs.It allows stable performance in networks with 100 to 300 nodes,under varying node densities,and across different base station placements.Computational complexity analysis has shown that the method fits well into large-scale WSNs and that the addition of fuzzy logic controls the power usage to make the system practical for real-world use.
文摘Transportation systems are rapidly transforming in response to urbanization,sustainability challenges,and advances in digital technologies.This review synthesizes the intersection of artificial intelligence(AI),fuzzy logic,and multi-criteria decision-making(MCDM)in transportation research.A comprehensive literature search was conducted in the Scopus database,utilizing carefully selected AI,fuzzy,and MCDM keywords.Studies were rigorously screened according to explicit inclusion and exclusion criteria,resulting in 73 eligible publications spanning 2006-2025.The review protocol included transparent data extraction on methodological approaches,application domains,and geographic distribution.Key findings highlight the prevalence of hybrid fuzzyAHPand TOPSIS methods,the widespread integration of machine learning for prediction and optimization,and a predominant focus on logistics and infrastructure planning within the transportation sector.Geographic analysis underscores a marked concentration of research activity in Asia,while other regions remain underrepresented,signaling the need for broader international collaboration.The review also addresses persistent challenges such asmethodological complexity,data limitations,and model interpretability.Future research directions are proposed,including the integration of reinforcement learning,real-time analytics,and big data-driven adaptive solutions.This study offers a comprehensive synthesis and critical perspective,serving as a valuable reference for researchers,practitioners,and policymakers seeking to enhance the efficiency,resilience,and sustainability of transportation systems through intelligent decision-making frameworks.
文摘This study introduces a novel distance measure(DM)for(p,q,r)-spherical fuzzy sets((p,q,to improve decision-making in complex and uncertain environments.Many existing distance measures eitherr)-SFSs)fail to satisfy essential axiomatic properties or produce unintuitive outcomes.To address these limitations,we propose a new three-dimensional divergence-based DM that ensures mathematical consistency,enhances the discrimination of information,and adheres to the axiomatic framework of distance theory.Building on this foundation,we construct a multi-criteria decision-making(MCDM)model that utilizes the proposed DM to evaluate and rank alternatives effectively.The applicability and robustness of the model are validated through a practical case study,demonstrating that it leads to more rational,consistent,and reliable decision outcomes compared to existing approaches.
基金funded by National Science,Research and Innovation Fund(NSRF)King Mongkut's University of Technology North Bangkok with Contract No.KMUTNB-FF-68-B-46.
文摘In this manuscript,the notion of a hesitant fuzzy soft fixed point is introduced.Using this notion and the concept of Suzuki-type(μ,ν)-weak contraction for hesitant fuzzy soft set valued-mapping,some fixed point results are established in the framework of metric spaces.Based on the presented work,some examples reflecting decision-making problems related to real life are also solved.The suggested method’s flexibility and efficacy compared to conventional techniques are demonstrated in decision-making situations involving uncertainty,such as choosing the best options in multi-criteria settings.We noted that the presented work combines and generalizes two major concepts,the idea of soft sets and hesitant fuzzy set-valued mapping from the existing literature.
基金the Liaoning Province Nature Fundation Project(2022-MS-291)the National Programme for Foreign Expert Projects(G2022006008L)+2 种基金the Basic Research Projects of Liaoning Provincial Department of Education(LJKMZ20220781,LJKMZ20220783,LJKQZ20222457)King Saud University funded this study through theResearcher Support Program Number(RSPD2023R704)King Saud University,Riyadh,Saudi Arabia.
文摘The existing algorithms for solving multi-objective optimization problems fall into three main categories:Decomposition-based,dominance-based,and indicator-based.Traditional multi-objective optimization problemsmainly focus on objectives,treating decision variables as a total variable to solve the problem without consideringthe critical role of decision variables in objective optimization.As seen,a variety of decision variable groupingalgorithms have been proposed.However,these algorithms are relatively broad for the changes of most decisionvariables in the evolution process and are time-consuming in the process of finding the Pareto frontier.To solvethese problems,a multi-objective optimization algorithm for grouping decision variables based on extreme pointPareto frontier(MOEA-DV/EPF)is proposed.This algorithm adopts a preprocessing rule to solve the Paretooptimal solution set of extreme points generated by simultaneous evolution in various target directions,obtainsthe basic Pareto front surface to determine the convergence effect,and analyzes the convergence and distributioneffects of decision variables.In the later stages of algorithm optimization,different mutation strategies are adoptedaccording to the nature of the decision variables to speed up the rate of evolution to obtain excellent individuals,thusenhancing the performance of the algorithm.Evaluation validation of the test functions shows that this algorithmcan solve the multi-objective optimization problem more efficiently.
基金supported in part by the Central Government Guides Local Science and TechnologyDevelopment Funds(Grant No.YDZJSX2021A038)in part by theNational Natural Science Foundation of China under(Grant No.61806138)in part by the China University Industry-University-Research Collaborative Innovation Fund(Future Network Innovation Research and Application Project)(Grant 2021FNA04014).
文摘The large-scale multi-objective optimization algorithm(LSMOA),based on the grouping of decision variables,is an advanced method for handling high-dimensional decision variables.However,in practical problems,the interaction among decision variables is intricate,leading to large group sizes and suboptimal optimization effects;hence a large-scale multi-objective optimization algorithm based on weighted overlapping grouping of decision variables(MOEAWOD)is proposed in this paper.Initially,the decision variables are perturbed and categorized into convergence and diversity variables;subsequently,the convergence variables are subdivided into groups based on the interactions among different decision variables.If the size of a group surpasses the set threshold,that group undergoes a process of weighting and overlapping grouping.Specifically,the interaction strength is evaluated based on the interaction frequency and number of objectives among various decision variables.The decision variable with the highest interaction in the group is identified and disregarded,and the remaining variables are then reclassified into subgroups.Finally,the decision variable with the strongest interaction is added to each subgroup.MOEAWOD minimizes the interactivity between different groups and maximizes the interactivity of decision variables within groups,which contributed to the optimized direction of convergence and diversity exploration with different groups.MOEAWOD was subjected to testing on 18 benchmark large-scale optimization problems,and the experimental results demonstrate the effectiveness of our methods.Compared with the other algorithms,our method is still at an advantage.
基金SupportedbytheNationalNaturalScienceFoundationofChina (No .60 1 340 1 0 )
文摘A new fuzzification method for multi-objective decision-making and selective sorting is proposed on the basis of the fuzzy consistent relation, and the specific algorithm is presented. The method is applied to the evaluation of highway planning of Zhanjiang city. To decrease the subjectivity in the process of decision-making, the LOWA operator is introduced, and a discussion on how to select appropriate weights involved in multi-objective sorting is made. It is concluded that it is feasible to apply the fuzzy consistent relation to multi-objective decision-making analysis, and the improved fuzzication method is workable.
基金Anhui Province Natural Science Research Project of Colleges and Universities(2023AH040321)Excellent Scientific Research and Innovation Team of Anhui Colleges(2022AH010098).
文摘The presence of numerous uncertainties in hybrid decision information systems(HDISs)renders attribute reduction a formidable task.Currently available attribute reduction algorithms,including those based on Pawlak attribute importance,Skowron discernibility matrix,and information entropy,struggle to effectively manages multiple uncertainties simultaneously in HDISs like the precise measurement of disparities between nominal attribute values,and attributes with fuzzy boundaries and abnormal values.In order to address the aforementioned issues,this paper delves into the study of attribute reduction withinHDISs.First of all,a novel metric based on the decision attribute is introduced to solve the problem of accurately measuring the differences between nominal attribute values.The newly introduced distance metric has been christened the supervised distance that can effectively quantify the differences between the nominal attribute values.Then,based on the newly developed metric,a novel fuzzy relationship is defined from the perspective of“feedback on parity of attribute values to attribute sets”.This new fuzzy relationship serves as a valuable tool in addressing the challenges posed by abnormal attribute values.Furthermore,leveraging the newly introduced fuzzy relationship,the fuzzy conditional information entropy is defined as a solution to the challenges posed by fuzzy attributes.It effectively quantifies the uncertainty associated with fuzzy attribute values,thereby providing a robust framework for handling fuzzy information in hybrid information systems.Finally,an algorithm for attribute reduction utilizing the fuzzy conditional information entropy is presented.The experimental results on 12 datasets show that the average reduction rate of our algorithm reaches 84.04%,and the classification accuracy is improved by 3.91%compared to the original dataset,and by an average of 11.25%compared to the other 9 state-of-the-art reduction algorithms.The comprehensive analysis of these research results clearly indicates that our algorithm is highly effective in managing the intricate uncertainties inherent in hybrid data.
基金supported by the Natural Science Foundation of Hunan Province(2023JJ50047,2023JJ40306)the Research Foundation of Education Bureau of Hunan Province(23A0494,20B260)the Key R&D Projects of Hunan Province(2019SK2331)。
文摘Aiming at the triangular fuzzy(TF)multi-attribute decision making(MADM)problem with a preference for the distribution density of attribute(DDA),a decision making method with TF number two-dimensional density(TFTD)operator is proposed based on the density operator theory for the decision maker(DM).Firstly,a simple TF vector clustering method is proposed,which considers the feature of TF number and the geometric distance of vectors.Secondly,the least deviation sum of squares method is used in the program model to obtain the density weight vector.Then,two TFTD operators are defined,and the MADM method based on the TFTD operator is proposed.Finally,a numerical example is given to illustrate the superiority of this method,which can not only solve the TF MADM problem with a preference for the DDA but also help the DM make an overall comparison.
基金supported by the Science and Technology Project of the Headquarters of the State Grid Corporation(project code:5400-202323233A-1-1-ZN).
文摘With the increasing integration of emerging source-load types such as distributed photovoltaics,electric vehicles,and energy storage into distribution networks,the operational characteristics of these networks have evolved from traditional single-load centers to complex multi-source,multi-load systems.This transition not only increases the difficulty of effectively classifying distribution networks due to their heightened complexity but also renders traditional energy management approaches-primarily focused on economic objectives-insufficient to meet the growing demands for flexible scheduling and dynamic response.To address these challenges,this paper proposes an adaptive multi-objective energy management strategy that accounts for the distinct operational requirements of distribution networks with a high penetration of new-type source-loads.The goal is to establish a comprehensive energy management framework that optimally balances energy efficiency,carbon reduction,and economic performance in modern distribution networks.To enhance classification accuracy,the strategy constructs amulti-dimensional scenario classification model that integrates environmental and climatic factors by analyzing the operational characteristics of new-type distribution networks and incorporating expert knowledge.An improved split-coupling K-means preclustering algorithm is employed to classify distribution networks effectively.Based on the classification results,fuzzy logic control is then utilized to dynamically optimize the weighting of each objective,allowing for an adaptive adjustment of priorities to achieve a flexible and responsivemulti-objective energy management strategy.The effectiveness of the proposed approach is validated through practical case studies.Simulation results indicate that the proposed method improves classification accuracy by 18.18%compared to traditional classification methods and enhances energy savings and carbon reduction by 4.34%and 20.94%,respectively,compared to the fixed-weight strategy.
基金partially supported by the National Key Research and Development Program of the Ministry of Science and Technology of China(2022YFE0114200)the National Natural Science Foundation of China(U20A6004).
文摘This paper investigates a distributed heterogeneous hybrid blocking flow-shop scheduling problem(DHHBFSP)designed to minimize the total tardiness and total energy consumption simultaneously,and proposes an improved proximal policy optimization(IPPO)method to make real-time decisions for the DHHBFSP.A multi-objective Markov decision process is modeled for the DHHBFSP,where the reward function is represented by a vector with dynamic weights instead of the common objectiverelated scalar value.A factory agent(FA)is formulated for each factory to select unscheduled jobs and is trained by the proposed IPPO to improve the decision quality.Multiple FAs work asynchronously to allocate jobs that arrive randomly at the shop.A two-stage training strategy is introduced in the IPPO,which learns from both single-and dual-policy data for better data utilization.The proposed IPPO is tested on randomly generated instances and compared with variants of the basic proximal policy optimization(PPO),dispatch rules,multi-objective metaheuristics,and multi-agent reinforcement learning methods.Extensive experimental results suggest that the proposed strategies offer significant improvements to the basic PPO,and the proposed IPPO outperforms the state-of-the-art scheduling methods in both convergence and solution quality.
文摘The evaluation of the electricity market is crucial for fostering market construction and development.An accurate assessment of the electricity market reveals developmental trends,identifies operational issues,and contributes to stable and healthy market growth.This study investigated the characteristics of electricity markets in different provinces and synthesized a comprehensive set of evaluation indicators to assess market effectiveness.The evaluation framework,comprising nine indicators organized into two tiers,was constructed based on three aspects:market design,market efficiency,and developmental coordination.Furthermore,a novel fuzzy multi-criteria decision-making evaluation model for electricity market performance was developed based on the Fuzzy-BWM and fuzzy COPRAS methodologies.This model aimed to ensure both accuracy and comprehensiveness in market operation assessment.Subsequently,empirical analyses were conducted on four typical provincial-level electricity markets in China.The results indicate that Guangdong’s electricity market performed best because of its effective balance of stakeholder interests and adherence to contractual integrity principles.Zhejiang and Shandong ranked second and third,respectively,whereas Sichuan exhibited the poorest market performance.Sichuan’s electricity market must be improved in terms of market design,such that market players can obtain a fairly competitive environment.The sensitivity analysis of the constructed indicators verified the effectiveness of the evaluation model proposed in this study.Finally,policy recommendations were proposed to facilitate the sustainable development of China’s electricity markets with the objective of transforming them into efficient and secure markets adaptable to the evolution of novel power systems.
基金supported by the National Natural Science Foundation of China(51405499)
文摘A decision support system, including a multi-objective optimization framework and a multi-attribute decision making approach is proposed for satellite equipment layout. Firstly, given three objectives (to minimize the C.G. offset, the cross moments of inertia and the space debris impact risk), we develop a threedimensional layout optimization model. Unlike most of the previous works just focusing on mass characteristics of the system, a space debris impact risk index is developed. Secondly, we develop an efficient optimization framework for the integration of computer-aided design (CAD) software as well as the optimization algorithm to obtain the Pareto front of the layout optimization problem. Thirdly, after obtaining the candidate solutions, we present a multi-attribute decision making approach, which integrates the smart Pareto filter and the correlation coefficient and standard deviation (CCSD) method to select the best tradeoff solutions on the optimal Pareto fronts. Finally, the framework and the decision making approach are applied to a case study of a satellite platform.
基金2008 Soft Science Program of Jiangsu Science and Technology Department (No.BR2008098)
文摘The problem of multiple attribute decision making under fuzzy linguistic environments, in which decision makers can only provide their preferences （attribute values）in the form of trapezoid fuzzy linguistic variables（TFLV）, is studied. The formula of the degree of possibility between two TFLVs is defined, and some of its characteristics are studied. Based on the degree of possibility of fuzzy linguistic variables, an approach to ranking the decision alternatives in multiple attribute decision making with TFLV is developed. The trapezoid fuzzy linguistic weighted averaging （TFLWA） operator method is utilized to aggregate the decision information, and then all the alternatives are ranked by comparing the degree of possibility of TFLV. The method can carry out linguistic computation processes easily without loss of linguistic information, and thus makes the decision results reasonable and effective. Finally, the implementation process of the proposed method is illustrated and analyzed by a practical example.
基金Supported by Science and Technology Plan Project of Guangdong Province (2009B010900026,2009CD058,2009CD078,2009CD079,2009CD080)Special Funds for Support Program of Development of Modern Information Service Industry of Guangdong Province(06120840B0370124 )Fund Project of South China Agricultural University (2007K017)~~
文摘[Objective]The aim was to overcome the shortage of being difficult to build land evaluation model when the impact factors had continuous value in the traditional land evaluation process,as well as to improve the intelligibility of the land evaluation knowledge.[Method] The land evaluation method combining classification rule extracted by C4.5 algorithm with fuzzy decision was proposed in this study.[Result] The result of Second General Soil Survey of Guangdong Province had demonstrated that the method was convenient to extract classification rules,and by using only 100 rules,quantity correct rate 86.67% and area correct rate 84.80% of land evaluation could be obtained.[Conclusions] The use of C4.5 algorithm to obtain the rules,combined with fuzzy decision algorithm to build classifiers had got satisfactory results,which provided a practical algorithm for the land evaluation.
基金supported by the National Natural Science Foundation of China (70771115).
文摘Intuitionistic trapezoidal fuzzy numbers and their operational laws are defined. Based on these operational laws, some aggregation operators, including intuitionistic trapezoidal fuzzy weighted arithmetic averaging operator and weighted geometric averaging operator are proposed. Expected values, score function, and accuracy function of intuitionitsic trapezoidal fuzzy numbers are defined. Based on these, a kind of intuitionistic trapezoidal fuzzy multi-criteria decision making method is proposed. By using these aggregation operators, criteria values are aggregated and integrated intuitionistic trapezoidal fuzzy numbers of alternatives are attained. By comparing score function and accuracy function values of integrated fuzzy numbers, a ranking of the whole alternative set can be attained. An example is given to show the feasibility and availability of the method.
