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An overview on the applications of the hesitant fuzzy sets in group decision-making: Theory, support

Zeshui XU, Shen ZHANG

《工程管理前沿（英文）》 2019年第6卷第2期页码 163-182 doi: 10.1007/s42524-019-0017-4

摘要： Due to the characteristics of hesitant fuzzy sets (HFSs), one hesitant fuzzy element (HFE), which is the basic component of HFSs, can express the evaluation values of multiple decision makers (DMs) on the same alternative under a certain attribute. Thus, the HFS has its unique advantages in group decision making (GDM). Based on which, many scholars have conducted in-depth research on the applications of HFSs in GDM. We have viewed lots of relevant literature and divided the existing studies into three categories: theory, support and methods. In this paper, we elaborate on hesitant fuzzy GDM from these three aspects. The first aspect is mainly about the introduction of HFSs, HFPRs and some hesitant fuzzy aggregation operators. The second aspect describes the consensus process under hesitant fuzzy environment, which is an important support for a complete decision-making process. In the third aspect, we introduce seven hesitant fuzzy GDM approaches, which can be applied in GDM under different decision-making conditions. Finally, we summarize the research status of hesitant fuzzy GDM and put forward some directions of future research.

关键词： hesitant fuzzy set hesitant fuzzy preference relation group decision-making

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基于犹豫模糊决策矩阵的犹豫模糊多准则共识群决策方法 Article

Jie DING, Ze-shui XU, Hu-chang LIAO

《信息与电子工程前沿（英文）》 2017年第18卷第11期页码 1679-1692 doi: 10.1631/FITEE.1601546

摘要：本文建立了两种关于犹豫模糊多准则群共识决策的方法，并使用犹豫模糊决策矩阵（hesitant fuzzy decision matrices, HFDMs）表示专家的偏好。

关键词：多准则群决策；群共识；共识达成方法；犹豫模糊决策矩阵；集成算子

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An enhanced environmental multimedia modeling system based on fuzzy-set approach: I.

Chesheng ZHAN,Rongrong ZHANG,Xiaomeng SONG,Baolin LIU

《环境科学与工程前沿（英文）》 2015年第9卷第3期页码 494-505 doi: 10.1007/s11783-013-0609-x

摘要： Multimedia environmental modeling is extremely complex due to the intricacy of the systems with the consideration of many related factors. Traditional environmental multimedia models (EMMs) are usually based on one-dimensional and first-order assumptions, which may cause numerical errors in the simulation results. In this study, a new user-friendly fuzzy-set enhanced environmental multimedia modeling system (FEEMMS) is developed, and includes four key modules: an air dispersion module, a polluting source module, an unsaturated zone module, and a groundwater module. Many improvements over previous EMMs have been achieved through dynamically quantifying the intermedia mass flux; incorporating fuzzy-set approach into environmental multimedia modeling system (EMMS); and designing a user-friendly graphic user interface (GUI). The developed FEEMMS can be a useful tool in estimating the time-varying and spatial-varying chemical concentrations in air, soil, and groundwater; characterizing the potential risk to human health presented by contaminants released from a contaminated site; and quantifying the uncertainties associated with modeling systems and subsequently providing robustness and flexibility for the remediation-related decision making.

关键词： environmental multimedia modelling fuzzy-set approach theoretical framework environmental protection

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Reliability assessment of three-dimensional bearing capacity of shallow foundation using fuzzy set theory

Rajarshi PRAMANIK, Dilip Kumar BAIDYA, Nirjhar DHANG

《结构与土木工程前沿（英文）》 2021年第15卷第2期页码 478-489 doi: 10.1007/s11709-021-0698-8

摘要： The aim of this study is to investigate the applicability of reliability theory on surface square/rectangular footing against bearing capacity failure using fuzzy set theory in conjunction with the finite element method. Soil is modeled as a three-dimensional spatially varying medium, where its parameters (cohesion, friction angle, unit weight, etc.) are considered as fuzzy variables that maintain some membership functions. Soil is idealized as an elastic-perfectly plastic material obeying the Mohr–Coulomb failure criterion, where both associated and non-associated flow rules are considered in estimating the ultimate bearing capacity of the footing. The spatial variability of the soil is incorporated for both isotropic and anisotropic fields, which are determined by the values of scales of fluctuation in both the horizontal and vertical directions. A new parameter namely, limiting applied pressure at zero failure probability is proposed, and it indirectly predicts the failure probability of the footing. The effect of the coefficient of variation of the friction angle of the soil on the probability of failure is analyzed, and it is observed that the effect is significant. Furthermore, the effect of the scale of fluctuation on the probability of failure is investigated, and the necessity for considering spatial variability in the reliability analysis is well proven.

关键词： finite element method square footing reliability analysis fuzzy set theory coefficient of variation spatial variability

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An enhanced environmental multimedia modeling system based on fuzzy-set approach: II.

Rongrong ZHANG,Chesheng ZHAN,Xiaomeng SONG,Baolin LIU

《环境科学与工程前沿（英文）》 2015年第9卷第6期页码 1025-1035 doi: 10.1007/s11783-014-0655-z

摘要： Part I of this study develops an enhanced environmental multimedia modeling system (EMMS) based on fuzzy-set approach. Once the model development is complete, the composite module and the entire modeling system need to be tested and validated to ensure that the model can simulate natural phenomena with reasonable and reliable accuracy. The developed EMMS is first tested in a complete case study. And then verification results are conducted to compare with extensively researched literature data. In the third step, the data from an experimental landfill site is used for a pilot-scale validation. The comparisons between EMMS outputs and the literature data indicate that the EMMS can perform accurate modeling simulation. The modules of EMMS could support the entire environmental multimedia modeling system. Further field-scale validation is finished. The results are satisfactory. Most of the modeling yields closely match the monitoring data collected from sites. In addition, with the aid of fuzzy-set approach, EMMS can be a reliable and powerful tool to address the complex environmental multimedia pollution problems and provide an extensive support for decision makers in managing the contaminated environmental systems.

关键词： environmental multimedia modelling system fuzzy-set approach application model validation uncertainty analysis

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基于Rough集理论的模糊神经网络构造方法

黄显明,易继锴

《中国工程科学》 2004年第6卷第4期页码 44-50

摘要：

提出了在模糊神经网络中使用Rough集理论进行网络结构设计的方法。由于Rough集理论有强大的数值分析能力，而模糊神经网络具有准确的逼近收敛能力和较高的精度，所以通过两者的结合，可以得到一种可理解性好、计算简单、收敛速度快的神经网络模型。这种网络构造方法的主要过程为：首先，利用Rough集理论对给定数据集进行规则获取；然后，根据这些规则构造模糊神经网络各层的神经元个数及相关参数初始值；最后，用BP算法迭代求出网络的各种参数，完成网络的设计。给出了一个二维非线性函数拟合的实例，进一步验证了方法的正确性。

关键词：模糊神经网络 Rough集规则获取函数拟合

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不完备模糊信息系统

杨习贝,杨静宇,吴陈,傅凡

《中国工程科学》 2006年第8卷第7期页码 47-53

摘要：

以不完备模糊信息系统为研究对象，建立了其中的模糊相容关系及模糊粗糙上、下近似集。在此基础上，探讨了论域上的模糊覆盖问题并提出了覆盖的3种运算形式；定义了2种新的模糊粗糙熵以讨论不完备模糊信息系统中的不确定性因素，证明了不确定因素的变化与度量强度之间的重要关系；建立了一种度量部分模糊知识依赖的新方法，获得了一些新的定理结果证明。

关键词：不完备模糊信息系统模糊相容关系模糊粗糙集模糊覆盖模糊粗糙熵模糊知识依赖

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基于模糊集理论的二维线性鉴别分析新方法

郑宇杰,杨静宇,吴小俊,李勇智

《中国工程科学》 2007年第9卷第2期页码 49-53

摘要：

二维线性鉴别分析（２DLDA）是一种直接基于矩阵的特征提取方法，跳过传统的基于Fisher鉴别准则的线性鉴别分析方法中必须先将二维矩阵转化成一维矢量的过程，有效地提高了特征提取速度且避免了小样本问题，其识别率优于传统的Fisherface方法。结合模糊集理论，提出了一种新的２DLDA算法——模糊２DLDA （F１DLDA）算法。首先采用FKNN算法得到相应的样本分布信息，并按其对最后得到的特征向量所作的贡献融入到特征抽取过程中，得到有效的样本特征向量集。实验表明，F２DLDA算法的性能优于传统的２DLDA算法和Fisherface算法。

关键词：二维线性鉴别分析模糊二维线性鉴别分析模糊集理论特征提取模糊k近邻

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Level set band method: A combination of density-based and level set methods for the topology optimization

Peng WEI, Wenwen WANG, Yang YANG, Michael Yu WANG

《机械工程前沿（英文）》 2020年第15卷第3期页码 390-405 doi: 10.1007/s11465-020-0588-0

摘要： The level set method (LSM), which is transplanted from the computer graphics field, has been successfully introduced into the structural topology optimization field for about two decades, but it still has not been widely applied to practical engineering problems as density-based methods do. One of the reasons is that it acts as a boundary evolution algorithm, which is not as flexible as density-based methods at controlling topology changes. In this study, a level set band method is proposed to overcome this drawback in handling topology changes in the level set framework. This scheme is proposed to improve the continuity of objective and constraint functions by incorporating one parameter, namely, level set band, to seamlessly combine LSM and density-based method to utilize their advantages. The proposed method demonstrates a flexible topology change by applying a certain size of the level set band and can converge to a clear boundary representation methodology. The method is easy to implement for improving existing LSMs and does not require the introduction of penalization or filtering factors that are prone to numerical issues. Several 2D and 3D numerical examples of compliance minimization problems are studied to illustrate the effects of the proposed method.

关键词： level set method topology optimization density-based method level set band

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Multi-objective optimization of a hybrid distributed energy system using NSGA-II algorithm

Hongbo REN, Yinlong LU, Qiong WU, Xiu YANG, Aolin ZHOU

《能源前沿（英文）》 2018年第12卷第4期页码 518-528 doi: 10.1007/s11708-018-0594-7

摘要：

In this paper, a multi-objective optimization model is established for the investment plan and operation management of a hybrid distributed energy system. Considering both economic and environmental benefits, the overall annual cost and emissions of CO₂ equivalents are selected as the objective functions to be minimized. In addition, relevant constraints are included to guarantee that the optimized system is reliable to satisfy the energy demands. To solve the optimization model, the non-dominated sorting generic algorithm II (NSGA-II) is employed to derive a set of non-dominated Pareto solutions. The diversity of Pareto solutions is conserved by a crowding distance operator, and the best compromised Pareto solution is determined based on the fuzzy set theory. As an illustrative example, a hotel building is selected for study to verify the effectiveness of the optimization model and the solving algorithm. The results obtained from the numerical study indicate that the NSGA-II results in more diversified Pareto solutions and the fuzzy set theory picks out a better combination of device capacities with reasonable operating strategies.

关键词： multi-objective optimization hybrid distributed energy system non-dominated sorting generic algorithm II fuzzy set theory Pareto optimal solution

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Maximum independent set in planning freight railway transportation

Gainanov Damir N., Mladenovic NENAD, Rasskazova V. A.

《工程管理前沿（英文）》 2018年第5卷第4期页码 499-506 doi: 10.15302/J-FEM-2018031

摘要：

This work is devoted to the problem of planning of freight railway transportation. We define a special conflict graph on the basis of a set of acceptable train routes. The investigation aims to solve the classical combinatorial optimization problem in relation to the maximum independent set of vertices in undirected graphs. The level representation of the graph and its tree are introduced. With use of these constructions, the lower and upper bounds for the number of vertices in the maximum independent set are obtained.

关键词： independent set algorithm planning of transportation two-sided estimate

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Operating mechanism and set pair analysis model of a sustainable water resources system

Chaoyang DU,Jingjie YU,Huaping ZHONG,Dandan WANG

《环境科学与工程前沿（英文）》 2015年第9卷第2期页码 288-297 doi: 10.1007/s11783-014-0642-4

摘要： There is no alternative to the world’s water resources, and their increasing scarcity is making it difficult to meet the world population’s water needs. This paper presents a sustainable water resources system (SWRS) and analyzes the operating mechanism that makes it possible to evaluate the status of such a system. A SWRS can be described as a complex coupling system that integrates water resources, social, economic and ecological systems into a whole. The SWRS’s operating mechanism is composed of dynamic, resistance and coordination components, and it interacts with and controls the system’s evolution process. The study introduces a new approach, set pair analysis theory, to measure the state of a SWRS, and an evaluation index system is established using the subsystems and operating mechanism of a SWRS. The evaluation index system is separated into three levels (goal level, criteria level and index level) and divides the index standard into five grades. An evaluation model of the SWRS based on set pair analysis theory is constructed, and an example of SWRS evaluation in Shanghai is presented. The connection degrees of the index in the three levels are calculated, and the connection degree of the goal index is calculated to be 0.342, which classifies the city’s SWRS condition as grade 2. The sustainable use of water resources in the region is determined to be at a relatively adequate level that meets the requirements of sustainable development.

关键词： sustainable water resources system operating mechanism set pair analysis model Shanghai

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XFEM schemes for level set based structural optimization

Li LI, Michael Yu WANG, Peng WEI

《机械工程前沿（英文）》 2012年第7卷第4期页码 335-356 doi: 10.1007/s11465-012-0351-2

摘要：

In this paper, some elegant extended finite element method (XFEM) schemes for level set method structural optimization are proposed. Firstly, two- dimension (2D) and three-dimension (3D) XFEM schemes with partition integral method are developed and numerical examples are employed to evaluate their accuracy, which indicate that an accurate analysis result can be obtained on the structural boundary. Furthermore, the methods for improving the computational accuracy and efficiency of XFEM are studied, which include the XFEM integral scheme without quadrature sub-cells and higher order element XFEM scheme. Numerical examples show that the XFEM scheme without quadrature sub-cells can yield similar accuracy of structural analysis while prominently reducing the time cost and that higher order XFEM elements can improve the computational accuracy of structural analysis in the boundary elements, but the time cost is increasing. Therefore, the balance of time cost between FE system scale and the order of element needs to be discussed. Finally, the reliability and advantages of the proposed XFEM schemes are illustrated with several 2D and 3D mean compliance minimization examples that are widely used in the recent literature of structural topology optimization. All numerical results demonstrate that the proposed XFEM is a promising structural analysis approach for structural optimization with the level set method.

关键词： structural optimization level set method extended finite element method (XFEM) computational accuracy and efficiency

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Level set-based isogeometric topology optimization for maximizing fundamental eigenfrequency

Manman XU, Shuting WANG, Xianda XIE

《机械工程前沿（英文）》 2019年第14卷第2期页码 222-234 doi: 10.1007/s11465-019-0534-1

摘要： Maximizing the fundamental eigenfrequency is an efficient means for vibrating structures to avoid resonance and noises. In this study, we develop an isogeometric analysis (IGA)-based level set model for the formulation and solution of topology optimization in cases with maximum eigenfrequency. The proposed method is based on a combination of level set method and IGA technique, which uses the non-uniform rational B-spline (NURBS), description of geometry, to perform analysis. The same NURBS is used for geometry representation, but also for IGA-based dynamic analysis and parameterization of the level set surface, that is, the level set function. The method is applied to topology optimization problems of maximizing the fundamental eigenfrequency for a given amount of material. A modal track method, that monitors a single target eigenmode is employed to prevent the exchange of eigenmode order number in eigenfrequency optimization. The validity and efficiency of the proposed method are illustrated by benchmark examples.

关键词： topology optimization level set method isogeometric analysis eigenfrequency