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An interval joint-probabilistic programming method for solid waste management: a case study for the city

Yi XU, Shunze WU, Hongkuan ZANG, Guiguang HOU

《环境科学与工程前沿（英文）》 2014年第8卷第2期页码 239-255 doi: 10.1007/s11783-013-0536-x

摘要： Currently, environmental protection and resources conservation continue to be challenges faced by solid-waste managers in China. These challenges are being further compounded by rapid socioeconomic development and population growth associated with increased waste generation rates and decreased waste disposal capacities. In response to these challenges, an interval joint-probabilistic mixed-integer programming (IJMP) method is developed for supporting long-term planning of waste management activities in the city of Tianjin, which is one of the largest municipalities in the northern part of China. In the IJMP, joint probabilistic constraints are introduced into an interval-parameter mixed-integer programming framework, such that uncertainties presented in terms of interval values and random variables can be reflected. Moreover, a number of violation levels for the waste-management-capacity constraints are examined, which can facilitate in-depth analyses of tradeoffs among economic objective and system-failure risk. The results indicate that reasonable solutions have been generated. They are valuable for supporting the adjustment of the city’s existing waste-management practices and the long-term planning of the city’s waste-management facilities.

关键词： interval analysis mixed integer joint probabilistic constraint planning uncertainty waste management

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An interval type-2 fuzzy logic controller for TCSC to improve the damping of power system oscillations

Manoj Kumar PANDA, Gopinath PILLAI, Vijay KUMAR

《能源前沿（英文）》 2013年第7卷第3期页码 307-316 doi: 10.1007/s11708-013-0269-3

摘要： In this paper an interval type-2 fuzzy logic controller (IT2FLC) was proposed for thyristor controlled series capacitor (TCSC) to improve power system damping. For controller design, memberships of system variables were represented using interval type-2 fuzzy sets. The three-dimensional membership function of type-2 fuzzy sets provided additional degree of freedom that made it possible to directly model and handle uncertainties. Simulations conducted on a single machine infinite bus (SMIB) power system showed that the proposed controller was more effective than particle swarm optimization (PSO) tuned and type-1 fuzzy logic (T1FL) based damping controllers. Robust performance of the proposed controller was also validated at different operating conditions, various disturbances and parameter variation of the transmission line parameters.

关键词： power system oscillations thyristor controlled series capacitor (TCSC) type-2 fuzzy logic system interval type-2 fuzzy logic controller (IT2FLC)

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A consensus model for group decision making under interval type-2 fuzzy environment

Xiao-xiong ZHANG,Bing-feng GE,Yue-jin TAN

《信息与电子工程前沿（英文）》 2016年第17卷第3期页码 237-249 doi: 10.1631/FITEE.1500198

摘要： We propose a new consensus model for group decision making (GDM) problems, using an interval type-2 fuzzy environment. In our model, experts are asked to express their preferences using linguistic terms characterized by interval type-2 fuzzy sets (IT2 FSs), because these can provide decision makers with greater freedom to express the vagueness in real-life situations. Consensus and proximity measures based on the arithmetic operations of IT2 FSs are used simultaneously to guide the decision-making process. The majority of previous studies have taken into account only the importance of the experts in the aggregation process, which may give unreasonable results. Thus, we propose a new feedback mechanism that generates different advice strategies for experts according to their levels of importance. In general, experts with a lower level of importance require a larger number of suggestions to change their initial preferences. Finally, we investigate a numerical example and execute comparable models and ours, to demonstrate the performance of our proposed model. The results indicate that the proposed model provides greater insight into the GDM process.

关键词： Group decision making (GDM) Interval type-2 fuzzy sets (IT2 FSs) Feedback mechanism

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MPC-based interval number optimization for electric water heater scheduling in uncertain environments

Jidong WANG, Chenghao LI, Peng LI, Yanbo CHE, Yue ZHOU, Yinqi LI

《能源前沿（英文）》 2021年第15卷第1期页码 186-200 doi: 10.1007/s11708-019-0644-9

摘要： In this paper, interval number optimization and model predictive control are proposed to handle the uncertain-but-bounded parameters in electric water heater load scheduling. First of all, interval numbers are used to describe uncertain parameters including hot water demand, ambient temperature, and real-time price of electricity. Moreover, the traditional thermal dynamic model of electric water heater is transformed into an interval number model, based on which, the day-ahead load scheduling problem with uncertain parameters is formulated, and solved by interval number optimization. Different tolerance degrees for constraint violation and temperature preferences are also discussed for giving consumers more choices. Furthermore, the model predictive control which incorporates both forecasts and newly updated information is utilized to make and execute electric water heater load schedules on a rolling basis throughout the day. Simulation results demonstrate that interval number optimization either in day-ahead optimization or model predictive control format is robust to the uncertain hot water demand, ambient temperature, and real-time price of electricity, enabling customers to flexibly adjust electric water heater control strategy.

关键词： electric water heater load scheduling interval number optimization model predictive control uncertainty

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基于区间数的多指标灰靶决策模型的研究

党耀国,刘思峰,刘斌

《中国工程科学》 2005年第7卷第8期页码 31-35

摘要：

现实生活中遇到的许多问题都具有不确定性，使得在对系统进行决策评估时，指标值难以精确化。在此情形下，人们常常对指标值给出一个区间，到目前为止，尚未有人研究区间数灰靶决策。首先定义了区间数、m维区间数的距离及其距离性质，并证明了当区间数为实数时，区间数距离就是实数距离的推广；提出了区间数规范化方法，在此基础上, 建立了基于区间数的灰靶决策模型，从而把灰靶决策模型由实数序列拓展到区间数序列，使灰靶决策理论得到发展，同时为扩大灰靶决策的应用领域提供了理论根据。最后以实例验证了该模型的有效性与实用性。

关键词：区间数灰靶决策模型应用

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A refined risk explicit interval linear programming approach for optimal watershed load reduction withobjective-constraint uncertainty tradeoff analysis

Pingjian YANG,Feifei DONG,Yong LIU,Rui ZOU,Xing CHEN,Huaicheng GUO

《环境科学与工程前沿（英文）》 2016年第10卷第1期页码 129-140 doi: 10.1007/s11783-014-0683-8

摘要： To enhance the effectiveness of watershed load reduction decision making, the Risk Explicit Interval Linear Programming (REILP) approach was developed in previous studies to address decision risks and system returns. However, REILP lacks the capability to analyze the tradeoff between risks in the objective function and constraints. Therefore, a refined REILP model is proposed in this study to further enhance the decision support capability of the REILP approach for optimal watershed load reduction. By introducing a tradeoff factor ( ) into the total risk function, the refined REILP can lead to different compromises between risks associated with the objective functions and the constraints. The proposed model was illustrated using a case study that deals with uncertainty-based optimal load reduction decision making for Lake Qionghai Watershed, China. A risk tradeoff curve with different values of was presented to decision makers as a more flexible platform to support decision formulation. The results of the standard and refined REILP model were compared under 11 aspiration levels. The results demonstrate that, by applying the refined REILP, it is possible to obtain solutions that preserve the same constraint risk as that in the standard REILP but with lower objective risk, which can provide more effective guidance for decision makers.

关键词： refined risk explicit interval linear programming decision making objective-constraint uncertainty tradeoff aspiration level Lake Qionghai Watershed

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区间灰数表征与算法改进及其GM(1,1)模型应用研究

方志耕,刘思峰,陆芳,万军,刘斌

《中国工程科学》 2005年第7卷第2期页码 57-61

摘要：

针对目前区间灰数的表征和运算过程中存在着较为严重的问题，即：运算结果对灰数的灰度进行不必要的放大，造成信息的严重失真，笔者定义了标准区间灰数与第一和第二标准区间灰数的概念，分析了第一和第二标准区间灰数之间的关系，进一步设计了普通区间灰数与标准区间灰数之间的转换规则，提供了标准区间灰数之间的比较与运算法则，较好地解决了区间灰数之间的大小比较与运算问题。最后，将这一研究成果应用于基于区间数的GM (1, 1)模型预测问题，取得了良好的效果。

关键词：区间灰数标准区间灰数表征 GM(1 1)模型运算规则

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原油成品油管道同沟敷设新技术中的热力分析

凌霄,王艺,宇波,张劲军,达鑫,张争伟

《中国工程科学》 2008年第10卷第11期页码 30-36

摘要：

采用非结构化有限容积法，对原油成品油双管同沟敷设新技术进行数值模拟，详细研究了不同管间距下成品油管道对加热输送原油管道的热力影响，尤其是对热油油温的影响。

关键词：输油管道双管同沟敷设热力分析数值模拟管间距

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用考虑置信区间长度影响的最小二乘法拟合S-N曲线

杨晓华,金平,姚卫星

《中国工程科学》 2004年第6卷第4期页码 41-43

摘要：

S-N曲线是用名义应力法预测结构疲劳寿命的基础。基于试验疲劳寿命分散的物理机制，提出了一个S-N曲线试验数据处理的加权最小二乘法，此方法中每组数据的权重与该组数据的置信区间成反比。计算结果表明用考虑置信区间长度影响的最小二乘法拟合得到的S-N曲线比用一般最小二乘法得到的S-N曲线具有更高的可靠度，给出的寿命预测结果也更安全。

关键词：置信区间疲劳寿命最小二乘法 S-N曲线

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区间值信息系统中基于信息熵的属性约简 Article

Jian-hua DAI,Hu HU,Guo-jie ZHENG,Qing-hua HU,Hui-feng HAN,Hong SHI

《信息与电子工程前沿（英文）》 2016年第17卷第9期页码 919-928 doi: 10.1631/FITEE.1500447

摘要：概要：区间值数据用来表示包含观察值的不确定性。区间值信息系统的处理有助于拓展粗糙集理论的应用范畴。属性约简是区间值数据分析的一个关键问题。现有针对传统单值数据的方法不适用于区间值数据。目前，关注区间值数据约简的研究还相对较少。本文从信息论的角度提出了一个区间值数据的属性约简框架，定义了区间值信息系统中的熵、条件熵以及联合熵等概念，继而构造了属性约简算法。实验结果表明所构造的方法是有效的。

关键词：粗糙集理论；区间值数据；属性约简；熵

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每个输入具有两个非线性模糊集合的区间二型模糊控制器解析结构的推导与分析 Article

Bin-bin LEI,Xue-chao DUAN,Hong BAO,Qian XU

《信息与电子工程前沿（英文）》 2016年第17卷第6期页码 587-602 doi: 10.1631/FITEE.1601019

摘要：二型模糊控制器一直被视为“黑盒”，因此揭示二型模糊控制器的解析结构不仅能够加深对二型模糊控制器内部工作原理的理解，而且能够对控制器进行更加系统的分析和设计。本文推导并分析了一种区间二型模糊控制器的解析结构。该区间二型模糊控制器具有以下结构特点：每个输入采用两个非线性区间二型模糊集合模糊化、规则后件为区间二型单点模糊集合、扎德AND算子和Karnik-Mendel(KM)降型器。其次，通过将区间二型模糊控制器的输入空间划分为15个分区并推导每个分区上的输入输出关系，证明文中区间二型模糊控制器近似等效为具有变增益的非线性PI或PD控制器。再者，通过与对应一型模糊控制器的解析结构进行对比，分析了文中区间二型模糊控制器的潜在优势。最后，通过仿真和实验验证了理论分析结果的可靠性和文中区间二型模糊集合的有效性。

关键词：区间二型模糊控制器；解析结构；Karnik-Mendel降型

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探测高超声速滑翔飞行器的区间二型模糊逻辑雷达任务优先级分配方法 Research Articles

孟繁卿1,田康生2

《信息与电子工程前沿（英文）》 2022年第23卷第3期页码 488-501 doi: 10.1631/FITEE.2000560

摘要：针对相控阵雷达探测临近空间高超声速滑翔飞行器时的资源管理问题，设计了一种基于区间二型模糊逻辑系统的雷达任务优先级分配方法。详细阐述了雷达任务数学模型、高超声速滑翔目标的运动模型和探测模型。将高超声速滑翔飞行器的目标威胁划分为机动威胁、速度威胁、方位威胁和距离威胁。此方法中，机动因子、速度、方位、距离和初始优先级为输入变量，雷达任务优先级为输出变量。为减少模糊规则数、避免规则爆炸，设计了分层结构的区间二型模糊逻辑系统。最后，通过仿真验证该方法可行性。结果表明，基于区间二型模糊逻辑系统的任务优先级分配方法具有更高的精确跟踪率、平均初始优先级和目标威胁度以及更短的偏移时间。

关键词：高超声速滑翔飞行器；相控阵雷达；区间二型模糊逻辑系统；优先级分配

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自适应最优相关间隔选择的多普勒频偏估计算法

张彭,毕光国,曹秀英,袁晓辉

《中国工程科学》 2007年第9卷第6期页码 71-76

摘要：利用该特性提出一种逐次缩小搜索范围的迭代（CIO，correlation唱interval optimized）算法，实现对其搜索和最大多普勒频偏的估计。通过仿真证明理论分析的正确及算法的有效性。

关键词：多普勒频偏自相关最优化迭代

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三参数区间数研究及其在决策分析中的应用

胡启洲,张卫华,于莉

《中国工程科学》 2007年第9卷第3期页码 47-51

摘要：

在定义三参数区间数的基础上，给出了三参数区间数的运算关系；然后将权重为区间数的多指标决策问题转化为指标取值为三参数区间数的多指标决策问题；在三参数区间数理想方案点定义的基础上，给出了权重为三参数区间数的逼近理想点法；最后将其应用于某城市公交线网的优化调整中。结果表明，该法科学合理、切实可行。

关键词：多指标决策三参数区间数逼近理想点法

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Performance design of a cryogenic air separation unit for variable working conditions using the lumped parameter model

Jinghua XU, Tiantian WANG, Qianyong CHEN, Shuyou ZHANG, Jianrong TAN

《机械工程前沿（英文）》 2020年第15卷第1期页码 24-42 doi: 10.1007/s11465-019-0558-6

摘要： Large-scale cryogenic air separation units (ASUs), which are widely used in global petrochemical and semiconductor industries, are being developed with high operating elasticity under variable working conditions. Different from discrete processes in traditional machinery manufacturing, the ASU process is continuous and involves the compression, adsorption, cooling, condensation, liquefaction, evaporation, and distillation of multiple streams. This feature indicates that thousands of technical parameters in adsorption, heat transfer, and distillation processes are correlated and merged into a large-scale complex system. A lumped parameter model (LPM) of ASU is proposed by lumping the main factors together and simplifying the secondary ones to achieve accurate and fast performance design. On the basis of material and energy conservation laws, the piecewise-lumped parameters are extracted under variable working conditions by using LPM. Takagi–Sugeno (T–S) fuzzy interval detection is recursively utilized to determine whether the critical point is detected or not by using different thresholds. Compared with the traditional method, LPM is particularly suitable for “rough first then precise” modeling by expanding the feasible domain using fuzzy intervals. With LPM, the performance of the air compressor, molecular sieve adsorber, turbo expander, main plate-fin heat exchangers, and packing column of a 100000 Nm O /h large-scale ASU is enhanced to adapt to variable working conditions. The designed value of net power consumption per unit of oxygen production (kW/(Nm O )) is reduced by 6.45%.

关键词： performance design air separation unit (ASU) lumped parameter model (LPM) variable working conditions T–S fuzzy interval detection

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标题作者时间类型操作

An interval joint-probabilistic programming method for solid waste management: a case study for the city

Yi XU, Shunze WU, Hongkuan ZANG, Guiguang HOU

期刊论文

An interval type-2 fuzzy logic controller for TCSC to improve the damping of power system oscillations

Manoj Kumar PANDA, Gopinath PILLAI, Vijay KUMAR

期刊论文

A consensus model for group decision making under interval type-2 fuzzy environment

Xiao-xiong ZHANG,Bing-feng GE,Yue-jin TAN

期刊论文

MPC-based interval number optimization for electric water heater scheduling in uncertain environments

Jidong WANG, Chenghao LI, Peng LI, Yanbo CHE, Yue ZHOU, Yinqi LI

期刊论文

基于区间数的多指标灰靶决策模型的研究

党耀国,刘思峰,刘斌

期刊论文

A refined risk explicit interval linear programming approach for optimal watershed load reduction withobjective-constraint uncertainty tradeoff analysis

Pingjian YANG,Feifei DONG,Yong LIU,Rui ZOU,Xing CHEN,Huaicheng GUO

期刊论文

区间灰数表征与算法改进及其GM(1,1)模型应用研究

方志耕,刘思峰,陆芳,万军,刘斌

期刊论文

原油成品油管道同沟敷设新技术中的热力分析

凌霄,王艺,宇波,张劲军,达鑫,张争伟

期刊论文

用考虑置信区间长度影响的最小二乘法拟合S-N曲线

杨晓华,金平,姚卫星

期刊论文

区间值信息系统中基于信息熵的属性约简