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Dynamic Surface-Based Adaptive Fuzzy Fixed-Time Fault-Tolerant Control for Nonstrict Feedback Nonlinear Systems With Non-affine Faults 基于动态曲面的非严格反馈非线性系统自适应模糊固定时间容错控制
IF 4.3 3区 计算机科学 Q2 AUTOMATION & CONTROL SYSTEMS Pub Date : 2024-04-20 DOI: 10.1007/s40815-024-01720-4
Yueyang Wang, Zhumu Fu, Fazhan Tao, Nan Wang, Zhengyu Guo

In the paper, a dynamic surface-based adaptive fuzzy fixed-time fault-tolerant control scheme is developed for nonstrict feedback nonlinear systems with non-affine faults. Firstly, the computational complexity is reduced by adopting dynamic surface control technique, and unknown nonlinear functions are approximated with the help of fuzzy logic systems. Secondly, non-affine faults involving system states and controller output are taken into account and treated by transforming it into nonlinear in the unknown parameters. Then, under the framework of fixed-time stability, a novel adaptive fuzzy fault-tolerant control strategy is designed so that the closed-loop system is semi-globally practically fixed-time stable. Finally, a numerical simulation and a model simulation are given to demonstrate the effectiveness of the proposed control scheme.

本文针对非严格反馈非线性系统的非线性故障,提出了一种基于动态曲面的自适应模糊定时容错控制方案。首先,通过采用动态曲面控制技术降低了计算复杂度,并借助模糊逻辑系统逼近了未知非线性函数。其次,考虑到涉及系统状态和控制器输出的非线性故障,并将其转化为未知参数的非线性来处理。然后,在固定时间稳定性框架下,设计了一种新的自适应模糊容错控制策略,使闭环系统具有半全局实际固定时间稳定性。最后,通过数值模拟和模型仿真证明了所提控制方案的有效性。
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引用次数: 0
Artificial Intelligence-Based Expert Prioritizing and Hybrid Quantum Picture Fuzzy Rough Sets for Investment Decisions of Virtual Energy Market in the Metaverse 基于人工智能的专家优先排序和混合量子图像模糊粗糙集用于元宇宙中虚拟能源市场的投资决策
IF 4.3 3区 计算机科学 Q2 AUTOMATION & CONTROL SYSTEMS Pub Date : 2024-04-20 DOI: 10.1007/s40815-024-01716-0
Peide Liu, Serhat Yüksel, Hasan Dinçer, Gabriela Oana Olaru

Improvements are necessary for the performance improvements of the digital twin technology developed for the virtual energy market on the Metaverse platform. However, more important factors need to be improved first to avoid excessive increases in costs. Thus, a priority analysis needs to be carried out to determine the variables that most affect the performance of technology investments. Accordingly, the purpose of this study is to evaluate the investments of digital twin technologies for virtual energy market in the Metaverse. A novel artificial intelligence-based fuzzy decision-making model is constructed to reach this objective. Firstly, the expert choices are prioritized with artificial intelligence-based decision-making method. Secondly, the investment priorities are analyzed for digital twin technologies with quantum picture fuzzy rough sets (QPFRS)-based Multi Stepwise Weight Assessment Ratio Analysis (M-SWARA). Finally, the alternatives for virtual energy market in the metaverse are ranked by VIKOR (VIsekriterijumska optimizacija i KOmpromisno Resenje). There are limited studies in the literature that computes the weights of the experts while generating a decision-making model. Therefore, the main contribution of this study is integrating the artificial intelligence approach and fuzzy multi-criteria decision-making methodology. Within this scope, an artificial intelligence-based application is performed when creating the decision matrix. Owing to this issue, the importance weights of experts are determined according to the qualifications of these people. This situation contributes to the results obtained being more realistic. The findings demonstrate that operational performance is the most important indicator for the improvements of the digital twin technology investments for virtual energy markets in metaverse platform because it has the greatest weight (0.267). Furthermore, integrated data production is another critical factor for the performance increase of these projects with the weight of 0.257. It is also concluded that optimization of energy consumption with smart grids has the best ranking performance among the alternatives.

为了提高在 Metaverse 平台上为虚拟能源市场开发的数字孪生技术的性能,有必要对其进行改进。不过,需要首先改进更重要的因素,以避免成本过度增加。因此,需要进行优先级分析,以确定对技术投资性能影响最大的变量。因此,本研究的目的是对 Metaverse 虚拟能源市场的数字孪生技术投资进行评估。为实现这一目标,我们构建了一个基于人工智能的新型模糊决策模型。首先,采用基于人工智能的决策方法对专家选择进行优先排序。其次,利用基于量子图模糊粗糙集(QPFRS)的多步骤权重评估比率分析法(M-SWARA)分析数字孪生技术的投资优先级。最后,利用 VIKOR(Vonsekriterijumska optimizacija i KOmpromisno Resenje)对元宇宙中虚拟能源市场的替代方案进行了排序。文献中关于在生成决策模型时计算专家权重的研究非常有限。因此,本研究的主要贡献在于整合了人工智能方法和模糊多标准决策方法。在此范围内,在创建决策矩阵时执行了基于人工智能的应用。由于这个问题,专家的重要性权重是根据这些人的资历确定的。这种情况有助于获得更加真实的结果。研究结果表明,运营绩效是改进元数据平台虚拟能源市场数字孪生技术投资的最重要指标,因为它的权重最大(0.267)。此外,综合数据生产是提高这些项目绩效的另一个关键因素,权重为 0.257。结论还表明,在各种备选方案中,利用智能电网优化能源消耗的排名表现最佳。
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引用次数: 0
Towards an Efficient Approach for Mamdani Interval Type-3 Fuzzy Inference Systems 实现马姆达尼区间-3 型模糊推理系统的高效方法
IF 4.3 3区 计算机科学 Q2 AUTOMATION & CONTROL SYSTEMS Pub Date : 2024-04-20 DOI: 10.1007/s40815-024-01722-2
Emanuel Ontiveros, Patricia Melin, Oscar Castillo

This paper is part of the increasing interest regarding the application of interval type-3 fuzzy logic in real-world problems, where a better handling of uncertainty can be useful in achieving enhanced results. The main contribution of this paper is the proposal of new methods, such as Interval Type-3 Reduction and a practical way for modeling Interval Type-3 Membership Functions, based on the Footprint of Uncertainty (FOU) and Core of Uncertainty (COU) concepts, which reduce the gap between the theory and the practical implementation of Mamdani Interval Type-3 Fuzzy Systems. The main aim of the paper is not proving the superiority of Interval Type-3 Fuzzy Systems but providing a framework and a comprehensive illustration of the theory concepts to help future research work in developing optimization methodologies and new applications for this kind of systems, as well as finding their potential applicability, which can result from their ability in handling more complex uncertainty. Simulation results with two illustrative application examples show the potential of the presented approach in achieving an efficient implementation of Interval type-3 fuzzy systems.

在现实世界的问题中,更好地处理不确定性有助于取得更好的结果,而本文正是在这种情况下应用区间-3 型模糊逻辑日益受到关注的一部分。本文的主要贡献在于基于不确定性足迹(FOU)和不确定性核心(COU)概念,提出了一些新方法,如 3 型区间还原法和 3 型区间成员函数建模的实用方法,从而缩小了马姆达尼 3 型区间模糊系统理论与实际应用之间的差距。本文的主要目的不是证明 3 型区间模糊系统的优越性,而是提供一个框架并全面说明其理论概念,以帮助未来的研究工作开发此类系统的优化方法和新应用,以及发现其潜在的适用性,这可能源于其处理更复杂不确定性的能力。两个应用实例的仿真结果表明,所提出的方法具有高效实现区间-3 型模糊系统的潜力。
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引用次数: 0
Robust Fuzzy Model-Based $$H_2/H_infty$$ Control for Markovian Jump Systems with Random Delays and Uncertain Transition Probabilities 具有随机延迟和不确定转换概率的马尔可夫跃迁系统的基于模糊模型的鲁棒性 $$H_2/H_infty$$ 控制
IF 4.3 3区 计算机科学 Q2 AUTOMATION & CONTROL SYSTEMS Pub Date : 2024-04-10 DOI: 10.1007/s40815-024-01680-9
Cheng Tan, Binlian Zhu, Jianying Di, Yuhuan Fei

This paper studies the mixed (H_2/H_infty) control for Takagi–Sugeno (T–S) fuzzy Markovian jump systems (MJSs) subject to random delays and multiple uncertain transition probabilities. In contrast to existing research, this study presents uncertainty parameters, external disturbance, random delays, and uncertain transition probabilities simultaneously in a unified T–S fuzzy model. Specifically, this study examines multiple Markov chains with partially unknown transition probabilities. These complex imperfections have a substantial adverse impact on system performance and the associated challenge of mixed (H_2/H_infty) control remains unresolved. Our innovative contributions are described as follows. The proposed approach utilizes free-weighting matrix technique and Lyapunov–Krasovskii functional to get the (H_2/H_infty) controller, which ensures that the stochastic T–S fuzzy systems exhibit stochastic stability and comply with the (H_infty) performance index.

本文研究了高木-菅野(T-S)模糊马尔可夫跃迁系统(MJS)的混合(H_2/H_infty)控制,该系统受随机延迟和多种不确定过渡概率的影响。与现有研究不同的是,本研究在统一的 T-S 模糊模型中同时提出了不确定参数、外部干扰、随机延迟和不确定转换概率。具体来说,本研究考察了具有部分未知过渡概率的多个马尔可夫链。这些复杂的不完善因素对系统性能产生了巨大的不利影响,而混合(H_2/H_infty)控制的相关挑战仍未解决。我们的创新贡献如下。所提出的方法利用自由加权矩阵技术和Lyapunov-Krasovskii函数来得到(H_2/H_infty)控制器,从而确保随机T-S模糊系统表现出随机稳定性并符合(H_infty)性能指标。
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引用次数: 0
Complex Pythagorean Hesitant Fuzzy Aggregation Operators Based on Aczel-Alsina t-Norm and t-Conorm and Their Applications in Decision-Making 基于 Aczel-Alsina t-Norm 和 t-Conorm 的复杂毕达哥拉斯犹豫模糊聚合算子及其在决策中的应用
IF 4.3 3区 计算机科学 Q2 AUTOMATION & CONTROL SYSTEMS Pub Date : 2024-04-10 DOI: 10.1007/s40815-023-01613-y
Zaifu Sun, Zeeshan Ali, Tahir Mahmood, Peide Liu

Aggregation operators are used for aggregating the collection of finite information into a singleton set. The Aczel-Alsina t-norm and t-conorm are very useful for constructing any kind of new aggregation operators, which was presented by Aczel and Alsina in 1982. Moreover, complex Pythagorean fuzzy (CPF) sets and hesitant fuzzy (HF) sets are the most generalized and very useful techniques to cope with unreliable and awkward information in genuine life problems. In this manuscript, we combine the HF set and CPF set to derive the complex Pythagorean hesitant fuzzy (CPHF) set and its fundamental laws. Furthermore, we evaluate the Aczel-Alsina operational laws based on Aczel-Alsina norms and CPHF information. Additionally, based on the Aczel-Alsina operational laws for CPHF information, we investigate the CPHF Aczel-Alsina-weighted averaging (CPHFAAWA) operator, CPHF Aczel-Alsina-ordered weighted averaging (CPHFAAOWA) operator, CPHF Aczel-Alsina-weighted geometric (CPHFAAWG) operator, and CPHF Aczel-Alsina-ordered weighted geometric (CPHFAAOWG) operator. Some remarkable properties are also examined for the invented theory. Moreover, a multi-attribute decision-making (MADM) technique is presented based on discovered operators for CPHF information. Finally, we aim to illustrate some examples for comparing the proposed techniques with some existing ones to show the worth and feasibility of the discovered approaches.

聚合算子用于将有限信息集合聚合成单子集。Aczel-Alsina t-norm 和 t-conorm 对于构建任何一种新的聚合算子都非常有用,它们是由 Aczel 和 Alsina 于 1982 年提出的。此外,复杂毕达哥拉斯模糊(CPF)集和犹豫模糊(HF)集是最通用、最有用的技术,可用于处理真实生活问题中的不可靠和尴尬信息。在本手稿中,我们将 HF 集和 CPF 集结合起来,推导出复杂毕达哥拉斯犹豫模糊集(CPHF)及其基本规律。此外,我们还根据 Aczel-Alsina 准则和 CPHF 信息评估了 Aczel-Alsina 运算定律。此外,基于 CPHF 信息的 Aczel-Alsina 运算定律,我们研究了 CPHF Aczel-Alsina 加权平均(CPHFAAWA)算子、CPHF Aczel-Alsina 有序加权平均(CPHFAAOWA)算子、CPHF Aczel-Alsina 加权几何(CPHFAAWG)算子和 CPHF Aczel-Alsina 有序加权几何(CPHFAAOWG)算子。研究还考察了所发明理论的一些显著特性。此外,我们还介绍了一种基于所发现的 CPHF 信息算子的多属性决策(MADM)技术。最后,我们将举例说明所提出的技术与一些现有技术的比较,以显示所发现方法的价值和可行性。
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引用次数: 0
Research on the Comprehensive Allocation Method for a Vehicle Hydraulic Braking System Based on Partial Fuzzy Ratings and Considering Failure Correlation 基于部分模糊评级并考虑故障相关性的汽车液压制动系统综合分配方法研究
IF 4.3 3区 计算机科学 Q2 AUTOMATION & CONTROL SYSTEMS Pub Date : 2024-04-09 DOI: 10.1007/s40815-024-01699-y
Zhou Yang, Hui Bai, Hongju Wang, Jing Zhang

Vehicle hydraulic braking systems are widely used, structurally complex. Reliability allocation during the design phase is crucial, yet there is a relatively limited body of research on this subject. In response, a new method for vehicle hydraulic braking system is proposed: the comprehensive reliability allocation method based on partial fuzzy ratings and considering failure correlation (CRA-PFRAFC). Based on the analysis of reliability allocation criteria impacting the braking system, the fuzzy set theory is introduced into the comprehensive allocation method, and the criteria with strong subjective dependence are fuzzy evaluated. The braking system allocation model is established by Gumbel Copula function. According to the set reliability target, the model is solved to allocate the failure rates to each subsystem according to the allocation vector. An example illustrates the advantages of this method. The results show that the reliability of the brake assembly is the lowest, while the reliability of the vacuum booster system is the highest. By fuzzy rating the failure severity and failure occurrence, the subjective quantification problem in traditional method is avoided. Meanwhile, compared with the traditional subsystem independent assumption model, this method is more realistic, and the failure rate of subsystem allocation is increased by 20% on average. Therefore, this study provides necessary and effective theoretical basis for reducing the design and manufacturing costs of vehicle hydraulic braking systems.

汽车液压制动系统应用广泛,结构复杂。设计阶段的可靠性分配至关重要,但这方面的研究却相对有限。为此,针对车辆液压制动系统提出了一种新方法:基于部分模糊评级并考虑故障相关性的综合可靠性分配方法(CRA-PFRAFC)。在分析影响制动系统可靠性分配标准的基础上,将模糊集理论引入综合分配方法,对主观依赖性较强的标准进行模糊评价。利用 Gumbel Copula 函数建立制动系统分配模型。根据设定的可靠性目标,对模型进行求解,按照分配向量将故障率分配到各个子系统。一个例子说明了这种方法的优点。结果表明,制动器总成的可靠性最低,而真空助力器系统的可靠性最高。通过对故障严重性和故障发生率进行模糊评级,避免了传统方法中主观量化的问题。同时,与传统的子系统独立假设模型相比,该方法更符合实际情况,子系统分配的故障率平均提高了 20%。因此,本研究为降低汽车液压制动系统的设计和制造成本提供了必要而有效的理论依据。
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引用次数: 0
Predictive Control for Takagi–Sugeno Fuzzy Large-Scale Networked Control Systems 高木-菅野模糊大规模网络控制系统的预测控制
IF 4.3 3区 计算机科学 Q2 AUTOMATION & CONTROL SYSTEMS Pub Date : 2024-04-09 DOI: 10.1007/s40815-023-01636-5
Xiaoxiao Guo, Jianwei Xia, Hao Shen, Tianjiao Liu, Chengyuan Yan

In this paper, the issue of exponential stabilization and sampled-data controller design for Takagi–Sugeno fuzzy large-scale networked control systems is studied by using the reduction-based ordinary differential equation prediction method. For the problem that matrices cannot be multiplied directly during the process of designing the sampled-data controller in this paper, a matrix dimensional transformation method is proposed. Firstly, a type of two-sided mode-dependent loop-based Lyapunov–Krasovskii functional is constructed, which compensates for the large delay and makes fuller use of the information in sampled-data interval. Secondly, the proposed method is used to give the design scheme of an aperiodic sampled-data controller, and furthermore, an iterative algorithm to verify the effectiveness of the requested control gains is provided. Finally, two coupled vehicle pendulum systems and two-area interconnected power systems are applied to demonstrate the efficiency of the presented approach.

本文采用基于还原的常微分方程预测方法,研究了高木-菅野模糊大规模网络控制系统的指数稳定和采样数据控制器设计问题。针对本文在设计采样数据控制器过程中矩阵不能直接相乘的问题,提出了一种矩阵维数变换方法。首先,构建了一种基于双侧模态依赖环路的 Lyapunov-Krasovskii 函数,补偿了大延迟,更充分地利用了采样数据区间的信息。其次,利用所提出的方法给出了非周期性采样数据控制器的设计方案,并进一步提供了一种迭代算法来验证所要求的控制增益的有效性。最后,应用两个耦合车辆摆动系统和两个区域互联电力系统来证明所提方法的有效性。
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引用次数: 0
A Multi-view Semi-supervised Takagi–Sugeno–Kang Fuzzy System for EEG Emotion Classification 用于脑电图情感分类的多视角半监督高木-菅野-康模糊系统
IF 4.3 3区 计算机科学 Q2 AUTOMATION & CONTROL SYSTEMS Pub Date : 2024-04-08 DOI: 10.1007/s40815-023-01666-z
Xiaoqing Gu, Yutong Wang, Mingxuan Wang, Tongguang Ni

Electroencephalogram (EEG)-based emotion recognition plays an important role in brain-computer interface and mental health monitoring. The large amount of EEG data but the lacks of labeling, multi-feature attribute, and data uncertainty are the difficulties in its recognition problem. A multi-view semi-supervised Takagi–Sugeno–Kang (MV-SS-TSK) fuzzy system is developed for EEG emotion classification in this paper. In the learning of fuzzy system consequent, firstly, a novel joint learning of semi-supervised learning, sparse representation, and low-rank coding is developed for semi-supervised sparse consequent factor learning, which makes the consequent parameter learning as a pseudo-label-only optimization problem. In particular, to simplify fuzzy rules, the sparse constraint term ensures the consequent parameters to be sparse in rows. Secondly, the consequent factor learning in a single feature view is extended into the multi-view learning model. In particular, low-rank coding is considered in multi-view semi-supervised consequent parameter learning. The low-rank constraint on view-shared component of consequent factor is implemented to exploit global data structure. The sparse constraint on view-dependent component of consequent factor is implemented to retain the feature diversity representation. By minimizing the intersection between view-shared component and view-specific components for different views, MV-SS-TSK can take advantage of the intrinsic relationship between various features and capture the consistency from multi-view features. Experiments on the SEED dataset show the superior performance of the proposed fuzzy system.

基于脑电图(EEG)的情绪识别在脑机接口和心理健康监测中发挥着重要作用。脑电图数据量大,但缺乏标记、多特征属性和数据不确定性是其识别问题的难点。本文开发了一种多视角半监督高木-菅野-康(MV-SS-TSK)模糊系统,用于脑电图情绪分类。在模糊系统后果学习方面,首先,针对半监督稀疏后果因子学习开发了一种新颖的半监督学习、稀疏表示和低秩编码联合学习方法,使后果参数学习成为一个伪标签优化问题。其中,为了简化模糊规则,稀疏约束项确保了结果参数在行中的稀疏性。其次,将单特征视图中的后果因子学习扩展为多视图学习模型。特别是在多视图半监督后果参数学习中考虑了低秩编码。对随即因子的视图共享分量实施低秩约束,以利用全局数据结构。对随之因子中与视图相关的分量实施稀疏约束,以保留特征多样性表示。通过最小化不同视图的视图共享分量和视图特定分量之间的交集,MV-SS-TSK 可以利用各种特征之间的内在关系,捕捉多视图特征的一致性。在 SEED 数据集上的实验表明,所提出的模糊系统性能优越。
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引用次数: 0
An Adaptive Event-Triggered Filtering for Fuzzy Markov Switching Systems with Quantization and Deception Attacks: A Non-stationary Approach 具有量化和欺骗攻击的模糊马尔可夫开关系统的自适应事件触发滤波:一种非稳态方法
IF 4.3 3区 计算机科学 Q2 AUTOMATION & CONTROL SYSTEMS Pub Date : 2024-04-08 DOI: 10.1007/s40815-024-01711-5
Mourad Kchaou, Obaid Alshammari, Houssem Jerbi, Rabeh Abassi, Sondess Ben Aoun

This paper examines the event-triggered filtering problem related to discrete-time nonlinear systems that are described by interval type-2 (IT2) fuzzy models. The filter being studied is prone to a non-stationary Markovian process when both quantization output and deception attack are taken into account simultaneously. It is proposed to implement an asynchronous IT2 fuzzy filter characterized by two different piecewise-stationary Markov chains specifying the deception attacks and the modes of the system. A new event-triggering protocol (ETP) is investigated as a means of reducing unnecessary signal transmissions on the communication channel. Based on the linear matrix inequality analysis and using the information on upper and lower membership functions, it is demonstrated that stochastic sufficient conditions exist for the desired filter such that it exhibits mean square stability and achieves the prescribed mixed (H_infty ) and passivity performance index. Moreover, an optimization-based problem for computing filter gains is proposed. An experimental numerical illustration based on a truck-trailer system is used to validate the developed scheme.

本文研究了与离散时间非线性系统有关的事件触发滤波问题,该系统由区间 2 型(IT2)模糊模型描述。当同时考虑量化输出和欺骗攻击时,所研究的滤波器容易出现非平稳马尔可夫过程。我们提出了一种异步 IT2 模糊过滤器,该过滤器由两个不同的片静态马尔可夫链组成,分别指定欺骗攻击和系统模式。研究了一种新的事件触发协议(ETP),以减少通信信道上不必要的信号传输。基于线性矩阵不等式分析,并利用上下成员函数的信息,证明了所需滤波器存在随机充分条件,使其表现出均方稳定性,并达到规定的混合(H_infty )和被动性能指标。此外,还提出了计算滤波器增益的优化问题。基于卡车拖车系统的实验数值说明用于验证所开发的方案。
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引用次数: 0
Location Selection for Dry Hot Rock Exploration Based on Large-Scale Group Decision-Making with Three-way Decision 基于三方决策的大规模群体决策的干热岩勘探选址方法
IF 4.3 3区 计算机科学 Q2 AUTOMATION & CONTROL SYSTEMS Pub Date : 2024-04-08 DOI: 10.1007/s40815-024-01690-7
Fang Liu, Zhongli Zhou, Ju Wu, Yi Liu

In large-scale group decision-making (LSGDM) for dry hot rock exploration location selection, decision-makers are limited by their professional fields and knowledge background, and it is difficult to provide complete evaluation information. However, brainstorming is the main advantage of LSGDM. To maximize the professional contributions of various decision-makers, a multi-attribute LSGDM method based on three-way decision (TWD) and intuitionistic fuzzy concept-oriented (IFC) is proposed. Firstly, according to the characteristics of IFC, a description of the LSGDM problem based on IFC is given; then, an LSGDM model based on TWD is proposed to classify and rank alternatives. Two algorithmic descriptions are given, namely consensus reaching process algorithm and algorithm for classifying and ranking alternatives. Then, taking dry hot rock exploration location selection as an example, the execution steps of this model were elaborated in detail, and the final classification and ranking results were obtained. Finally, the effectiveness and feasibility of this model were analyzed based on experimental results, and the influence of various parameters on the results was also studied.

在干热岩勘探选址的大规模群体决策(LSGDM)中,决策者受其专业领域和知识背景的限制,很难提供完整的评价信息。然而,集思广益是 LSGDM 的主要优势。为了最大限度地发挥不同决策者的专业贡献,本文提出了一种基于三向决策(TWD)和直觉模糊概念导向(IFC)的多属性 LSGDM 方法。首先,根据直觉模糊概念的特点,描述了基于直觉模糊概念的 LSGDM 问题;然后,提出了基于 TWD 的 LSGDM 模型,对备选方案进行分类和排序。给出了两种算法说明,即共识达成过程算法和备选方案分类与排序算法。然后,以干热岩勘探选址为例,详细阐述了该模型的执行步骤,并得出了最终的分类和排序结果。最后,根据实验结果分析了该模型的有效性和可行性,并研究了各种参数对实验结果的影响。
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引用次数: 0
期刊
International Journal of Fuzzy Systems
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