Total ordering for intuitionistic fuzzy numbers

Intuitionistic fuzzy set plays a vital role in decision making, data analysis, and artificial intelligence. Many decision‐making problems consist of different types of datum, where fuzzy set theoretical approaches may fail to obtain the optimal decision. Numerous approaches for intuitionistic fuzzy decision‐making problem have been introduced in the literature to overcome these short comings. But there is no single approach that can be used to solve all kinds of problems because of the partial ordering defined on the collection of intuitionistic fuzzy numbers (IFNs). Even though ranking of fuzzy numbers have been studied from early seventies in the last century, a total order on the entire class of fuzzy numbers has been introduced by Wang and Wang (Fuzzy Sets Syst 2014, 243, 131–141) only on 2014. A total order on the collection of all IFN is an open problem till today. In this article, a total order on the entire class of IFN using upper lower dense sequence in the interval [0, 1] is proposed and compared with existing techniques using illustrative examples, further an algorithm (which is problem independent) for solving any intuitionistic fuzzy multicriteria decision‐making problem (Intuitionistic fuzzy MCDM) is introduced. This new total ordering on IFNs generalizes the total ordering defined in Wang and Wang ( 22 ) for fuzzy numbers. © 2016 Wiley Periodicals, Inc. Complexity 21: 54–66, 2016     

Tabu search heuristics for the order batching problem in manual order picking systems

In a manual order picking system, order pickers walk or ride through a distribution warehouse in order to collect items requested by (internal or external) customers. In order to perform these operations efficiently, it is usually required that customer orders be combined into (more substantial) picking orders that are limited in size. The order batching problem considered in this paper deals with the question of how a given set of customer orders should be combined into picking orders such that the total length of all picker tours necessary for all of the requested items to be collected is minimized. For the solution of this problem the authors suggest two approaches based on the tabu search principle. The first is a (classic) tabu search (TS), and the second is the attribute-based hill climber (ABHC). In a series of extensive numerical experiments, these approaches are benchmarked against other solution methods put forward in the current literature. It is demonstrated that the proposed methods are superior to the existing methods and provide solutions which may allow distribution warehouses to operate more efficiently.     

基于Fuzzy-Rough-TOPSIS的工程项目投标风险评价模型研究

在工程项目招投标阶段,项目风险评价是建筑施工企业进行投标决策和作出项目选择的重要依据.基于理想化与主客观相结合的思想,提出了一种确定风险评价指标综合权重的方法;采用梯形模糊数处理模糊性信息,并将其与粗集理论和TOPSIS(a technique for order preference by similarity to ideal solution)方法相融合,建立了工程项目风险评价的Fuzzy-Rough-TOPSIS模型.实例运行表明,模型可操作性强,适用于多个项目的风险分析和比较,并能够在一定程度上克服以往模型存在的主观性强、应用条件限制严格等不足.     

基于Hausdauff度量的模糊TOPSIS方法研究

针对模糊多属性决策中的模糊 TOPSIS方法 ,提出了一种基于 Hausdauff度量的模糊 TOPSIS方法 .首先由模糊极大集与模糊极小集确定模糊多属性决策问题的理想解与负理想解 ,进而由 Hausdauff度量获得不同备选方案到理想解与负理想解的距离及其贴近度 ,根据贴近度指标对方案进行排序 ,为决策者提供决策支持 .最后以 L-R梯形模糊数为例进行了实例研究 .     

离心风机梯形截面蜗壳内旋涡流动的数值分析

本文求解时均N-S方程和“Baldwin-Lomax”湍流模式,使用基于时间推进法的Jameson格式计算方法,对一离心风机的梯形截面蜗壳内部流场进行了数值模拟。计算结果表明,在蜗壳各径向截面上都存在着一个旋转方向相反、强度交替变化的涡对。该涡对会随着径向截面位置与蜗壳运行工的变化发生复杂的变化。对该涡对演化细节的研究有助于探讨蜗壳内流动损失的一些机理。     

On dual Schur domain decomposition method for linear first-order transient problems

This paper addresses some numerical and theoretical aspects of dual Schur domain decomposition methods for linear first-order transient partial differential equations. The spatially discrete system of equations resulting from a dual Schur domain decomposition method can be expressed as a system of differential-algebraic equations (DAEs). In this work, we consider the trapezoidal family of schemes for integrating the ordinary differential equations (ODEs) for each subdomain and present four different coupling methods, corresponding to different algebraic constraints, for enforcing kinematic continuity on the interface between the subdomains. Unlike the continuous formulation, the discretized formulation of the transient problem is unable to enforce simultaneously the continuity of both the primary variable and its rate along the subdomain interface (except for the backward Euler method).Method 1 (d-continuity) is based on the conventional approach using continuity of the primary variable and we show that this method is unstable for a lot of commonly used time integrators including the mid-point rule. To alleviate this difficulty, we propose a new Method 2 (modified d-continuity) and prove its stability for coupling all time integrators in the trapezoidal family (except the forward Euler). Method 3 (v-continuity) is based on enforcing the continuity of the time derivative of the primary variable. However, this constraint introduces a drift in the primary variable on the interface. We present Method 4 (Baumgarte stabilized) which uses Baumgarte stabilization to limit this drift and we derive bounds for the stabilization parameter to ensure stability. Our stability analysis is based on the “energy” method, and one of the main contributions of this paper is the extension of the energy method (which was previously introduced in the context of numerical methods for ODEs) to assess the stability of numerical formulations for index-2 differential-algebraic equations (DAEs). Finally, we present numerical examples to corroborate our theoretical predictions.     

金属覆层保偏光纤偏振器的五层波导模型及理论分析

对金属履层保偏光纤偏振器建立了五层波导变参量物理模型,设计了自适应套孔爬山法的数值计算方法求解含多层波导本征值的复超越方程,计算结果揭示了金属覆层偏光纤偏振器的物理机制,并对器件进行了优化设计,给出了实验结果。     

基于微梯形弹光晶体的大光程差PEM研究

针对目前基于弹光调制器(photoelastic modulator,PEM)的傅里叶变换光谱测量技术(PEM-FTS)的光谱分辨率低,并且PEM调制光程差有限、多次反射对入射光斑大小要求高且光能利用率低等缺点。提出一种基于微梯形八角结构弹光晶体的大光程差PEM方法。通过改进弹光晶体结构,使其为微梯形八角结构,两个通光面略微成一定夹角,该结构PEM不仅可以有效提高PEM调制的最大光程差,而且对入射光斑要求较小。理论推导分析了该PEM的最大调制光程差,并推导得出任意角、任意位置入射时PEM的最大调制光程差公式;通过多物理场耦合仿真软件COMSOL Multiphysics 4.3a对PEM的振动模态和应力分布进行分析;结合PEM的最大调制光程差和光能利用率,分析了寻找最佳入射角的方法。设计加工该PEM,其中弹光晶体选用硒化锌晶体,压电晶体选用压电石英晶体。采用波长为632.8 nm的氦氖激光进行实验分析,实验结果显示,在相同驱动电压下,该PEM的最大调制光程差是普通PEM的19.25倍,与理论仿真的相对误差为1.3%。     

Beam dynamics and RF design of trapezoidal IH-RFQ with low energy spread

Beam dynamics and RF design have been performed of a new type trapezoidal IH-RFQ operating at 104 MHz for acceleration of ¹⁴C⁺ in the framework of RFQ based ¹⁴C AMS facility at Peking University. Low energy spread RFQ beam dynamics design was approached by the method of internal discrete bunching. ¹⁴C⁺ will be accelerated from 40 keV to 500 keV with the length of about 1.1 m. The designed transmission efficiency is better than 95% and the energy spread is as low as 0.6%. Combining the beam dynamics design, a trapezoidal IH-RFQ structure was proposed, which can be cooled more easily and has better mechanical performance than traditional RFQ. Electromagnetic field distribution was simulated by using CST Microwave Studio (MWS). The specific shunt impedance and the quality factor were optimized primarily.     

梯形模糊有序加权几何算子及其在决策中的应用

针对梯形模糊数据信息的集成问题,给出了梯形模糊数两两比较的可能度公式和梯形模糊有序加权几何(TFOWG)算子.基于可能度公式和TFOWG算子,提出了一种准则权重信息完全未知且准则值以梯形模糊数形式给出的不确定多准则决策方法.最后,实例分析表明了该方法的可行性和有效性.