The Number of Representations of an Integer as a Sum of Eight Triangular Numbers

An infinite product is expanded to Laurent series by residue theorem.Applying this expansion, the formula for the number of representations of an integer as a sum of eight triangular numbers is easily obtained.

A novel similarity measure between intuitionistic fuzzy sets based on the mid points of transformed triangular fuzzy numbers with applications to pattern recognition and medical diagnosis

Similarity measure is an essential tool to compare and determine the degree of similarity between intuitionistic fuzzy sets (IFSs). In this paper, a new similarity measure between intuitionistic fuzzy sets based on the mid points of transformed triangular fuzzy numbers is proposed. The proposed similarity measure provides reasonable results not only for the sets available in the literature but also gives very reasonable results, especially for fuzzy sets as well as for most intuitionistic fuzzy sets. To provide supportive evidence, the proposed similarity measure is tested on certain sets available in literature and is also applied to pattern recognition and medical diagnosis problems. It is observed that the proposed similarity measure provides a very intuitive quantification.

Success Factors of Biotechnology Industry Based on Triangular Fuzzy Number

Based on the theory of competitive advantage and value chain, this paper establishes the indicator system, and develop the strategic framework using the fuzzy Delphi method. Then the triangular fuzzy number model is established using Fuzzy Analytic Hierarchy Process, and the key factors influencing biotechnology industry are extracted. The results show that in terms of weight, the key factors influencing the success of biotechnology industry are sequenced as follows: "open innovation capacity", "quality and cost control ability", "advanced customer-oriented product manufacturing capacity", "technology R & D personnel's capacity", "brand image building capacity", "logistics and sales capacity", "grasping the market demand trends". The manufacturers and government decision-making body can use this as the basis, to promote the development of the biotechnology industry.

Analysis of Syetem Reliability in Manufacturing Cell Based on Triangular Fuzzy Number

Due to lacking of test-data and field-data in reliability research during the design stage of manufacturing cell sys- tem.The degree of manufacturing cell system reliability research is increased.In order to deal with the deficient data and the un- certainty occurred from analysis and judgment,the paper discussed a method for studying reliability of manufacturing cell system through the analysis of fuzzy fault tree,which was based on triangular fuzzy number.At last,calculation case indicated that it would have great significance for ascertaining reliability index,maintenance and establishing keeping strategy towards manufac- turing cell system.

An Evaluation Model of Graduation Thesis Results Based on Triangular Fuzzy Number

The evaluation of thesis by undergraduate has the characteristics of multi-factor, multi-layer and easy to be affected by subjective factors. To reduce the subjectivity, triangular fuzzy number is used as index set to give weight, and on this basis, fuzzy comprehensive evaluation is used to evaluate the quality of graduation thesis. The empirical analysis shows that the combination of triangular fuzzy number and fuzzy comprehensive evaluation has certain practical value in the quality evaluation of graduation thesis.

Sums of Squares of Polygonal Numbers

Polygonal numbers and sums of squares of primes are distinct fields of number theory. Here we consider sums of squares of consecutive (of order and rank) polygonal numbers. We try to express sums of squares of polygonal numbers of consecutive orders in matrix form. We also try to find the solution of a Diophantine equation in terms of polygonal numbers.

基于Z-number谱的多属性决策方法

为了在多专家决策过程中综合各种客观因素和主观因素,提高决策的准确性,文章结合Z-number理论定义了Z-number的两种参数形式从而定义了Z-number频谱S(Z)。S(Z)代表了Z-number在不同频率分量处不确定信息成分的大小,是一种模态分析结果和已知谱相结合计算结构响应的分析方法,用于确定结构对数据随时间变化所含信息量的响应,从隶属域和频域两方面对数据进行分析得到相应的不确定信息成分的大小,它能提供更直观、丰富的信息。另外,以三角模糊数为案例结合Z-number谱进行多属性决策,模糊数向量化后算出选择方案与多属性之间的拟合指数,最后在两方案的不一致性系数和最小的目标下建立决策模型获得每一方案的优先权重和相关排序,进行多方案多属性决策分析,并通过实例分析验证该方法的有效性和可行性。

Solution of Matrix Game with Triangular Intuitionistic Fuzzy Pay-Off Using Score Function

Using score function in a matrix game is very rare. In the proposed paper we have considered a matrix game with pay-off as triangular intuitionistic fuzzy number and a new ranking order has been proposed using value judgement index, available definitions and operations. A new concept of score function has been developed to defuzzify the pay-off matrix and solution of the matrix game has been obtained. A numerical example has been given in support of the proposed method.

Obtaining Crisp Priorities for Triangular and Trapezoidal Fuzzy Judgments

This paper proposes anoptimal fuzzy-based model for obtaining crisp priorities for Fuzzy-AHP comparison matrices.Crisp judgments cannot be given for real-life situations,as most of these include some level of fuzziness and com-plexity.In these situations,judgments are represented by the set of fuzzy numbers.Most of the fuzzy optimization models derive crisp priorities for judgments repre-sented with Triangular Fuzzy Numbers(TFNs)only.They do not work for other types of Triangular Shaped Fuzzy Numbers(TSFNs)and Trapezoidal Fuzzy Numbers(TrFNs).To overcome this problem,a sum of squared error(SSE)based optimization model is proposed.Unlike some other methods,the proposed model derives crisp weights from all of the above-mentioned fuzzy judgments.A fuzzy number is simulated using the Monte Carlo method.A threshold-based constraint is also applied to minimize the deviation from the initial judgments.Genetic Algorithm(GA)is used to solve the optimization model.We have also conducted casestudiesto show the proposed approach’s advantages over the existingmethods.Results show that the proposed model outperforms other models to minimize SSE and deviation from initial judgments.Thus,the proposed model can be applied in various real time scenarios as it can reduce the SSE value upto 29%compared to the existing studies.

THE STRUCTURE SENSITIVITY ANALYSIS FOR TRIANGULAR SYSTEMS

Triangular systems play a fundamental role in matrix computations. It has become commonplace that triangular systems are solved to be more accurate even if they are ill-conditioned. In this paper, we define structured condition number and give structured (forward) perturbation bound. In addition, we derive the representation of optimal structured backward perturbation bound.

Application of Nonlinear Triangular Fuzzy Fault Tree Algorithm in Predicting Lithium Battery Air Transport Accidents

The traditional triangular fuzzy fault tree prediction model adopts the linear approximation method.Therefore,the accident prediction error is large.Based on the analysis of the error sources and the fuzzy set,the precise calculation method of the event at the top of the fault tree is given.By using the numerical calculation software,an accurate calculation method of nonlinear triangular fuzzy accident prediction was adopted to predict lithium battery air transport fire accidents,and the fuzzy importance of the cause event was calculated.

砖木结构古建筑火灾风险影响因子评估研究

提出模糊DEMATEL-ISM的方法,在建立古建筑火灾评价指标体系的基础上,对归属于4大类风险因素的25个潜在风险因子进行关联性分析,得出因子的因果属性及因子间的逻辑层次结构关系,从而对古建筑火灾风险进行评估。利用模糊DEMATEL-ISM法对华阴市西岳庙灏灵殿进行实例分析,结果表明:疏散与扑救条件、电器设备隐患的原因度较大,需要对其予以控制;耐火等级、火灾荷载的结果度大,为事故发生的主要原因;疏散与扑救条件、易燃易爆危险品、电器设备隐患、安全责任制、灭火应急预案和演练为古建筑火灾事故的关键风险因子,可为古建筑火灾风险管控工作提供相应参考。

基于组合赋权云模型的塔台管制系统运行安全评估

随着我国民航业的迅猛发展,空中交通流量不断攀升,机场塔台管制系统的运行安全面临严峻考验,因此,正确识别和评估风险成为有效提高塔台管制系统运行安全水平的重要前提。为精准且有效地完成对塔台管制系统运行的安全评估,构建了基于模糊决策实验室分析法(Decision-Making Trial and Evaluation Laboratory,DEMATEL)网络层次分析法(Analytic Network Process,ANP)熵权法云模型的塔台管制系统运行安全评估模型。首先,通过流程图法并结合人机环管的思想建立塔台管制系统运行安全评估指标体系,并采用模糊DEMATEL法确定评估指标间的相互影响关系,绘制评估指标之间的网络结构图;然后,通过ANP法确定各评估指标的主观权重,采用熵权法确定各评估指标的客观权重,并通过博弈论方法计算评估指标的综合权重;最后,将权重结果与评语层云模型结合使用对各级安全评估指标进行安全评估,通过MATLAB软件完成算例的仿真分析。结果表明:该塔台管制系统运行安全等级在一般和良好之间,仍需采取有效措施对某些风险因素进行控制;同时验证了该模型在塔台管制系统运行安全评估中具有可行性和准确性,对塔台管制系统安全评估具有指导意义。

基于联系数投影的三角模糊数组合预测模型及其应用

在模糊预测中,三角模糊数比区间数更能准确刻画不确定信息。针对三角模糊数组合预测,本文首先引入集对分析中联系数,找出三角模糊数与三元联系数的转换关系,巧妙回避三角模糊数组合预测运算的模糊性和复杂性。其次定义三元联系数运算规则,构建联系数投影作为最优准则,建立联系数投影的定权系数三角模糊数组合预测模型。然后依据高精度预测方法应赋予较大权系数的原则,构建联系数广义诱导有序加权平均(CNGIOWA)算子,研究其性质定理,再结合联系数投影的最优准则,建立基于联系数投影和CNGIOWA算子的变权系数三角模糊数组合预测模型。最后将两类三角模糊数组合预测模型应用到模糊预测实证分析中,结果显示两类组合预测模型都能有效提高预测准确性。

基于TFN-AHP和云模型的母舰对气垫船保障能力评价

母舰对气垫船的保障能力是气垫船任务执行能力的重要组成部分,对母舰的保障能力进行综合评价是提升气垫船与母舰保障适配能力的重要环节。母舰对气垫船的保障活动具有高度的随机性、复杂性和动态性,导致其保障能力的评价也存在不确定性和模糊性。为此,基于三角模糊数(triangular fuzzy number,TFN)-层次分析法(analytic hierarchy process,AHP)与云模型提出了一种新的母舰对气垫船保障能力评价方法,并对某型母舰对气垫船的保障能力进行了评价。该方法通过特定的结构算法完成定性概念与定量表示的相互结合,降低了保障能力评价中权重计算的主观性和随机性,为母舰对气垫船保障能力评价提供了借鉴。

基于SERVQUAL理论的研究生教育质量提升路径研究

基于SERVQUAL理论,从研究生的视角对研究生教育质量提升路径进行分析。在既有研究的基础上,分析SERVQUAL理论对研究生教育质量提升的适用性。基于SERVQUAL量表和国内研究生教育现状构建评价指标体系,设计五维度调查问卷,并对问卷结果进行可靠性分析。采用三角模糊数,将研究生的主观感知以分次均值积分的形式数值化,得到感受值与期望值的差值。通过分析不同维度的数据结果及影响研究生教育质量提升的因素,并针对相应影响因素对研究生教育质量的提升路径给出相关建议。

基于TFN-AHP熵权的铁钻工工业设计方案评价

针对铁钻工工业设计方案评价综合性强、存在一定主观性、评价影响因素多的问题,提出一种基于三角模糊数层次分析法和熵权法主、客观方法相结合的铁钻工方案评价模型。该模型在层次分析法框架下,根据专家意见构建铁钻工工业设计方案评价指标体系,划分4项1级指标和12项2级指标,以模糊决策矩阵为评价信息载体,引入三角模糊数优化传统层次分析法不能准确表征带有模糊不确定性特征的评价信息的问题,并使用客观方法熵权法组合赋权确定综合权重。将此评价模型运用于实际铁钻工设计项目方案评价,将评价结果与相关传统评价法进行对比,并将筛选出来的方案进行深入优化设计,证明了评价模型的有效性。研究结果能够有效辅助企业进行铁钻工工业设计方案决策。

Finite Element Analysis of Magnetohydrodynamic Natural Convection within Semi-Circular Top Enclosure with Triangular Obstacles

The phenomena of magneto-hydrodynamic natural convection in a two-dimensional semicircular top enclosure with triangular obstacle in the rectangular cavity were studied numerically. The governing differential equations are solved by using the most important method which is finite element method (weighted-residual method). The top wall is placed at cold Tc and bottom wall is heated Th. Here the sidewalls of the cavity assumed adiabatic. Also all the wall are occupied to be no-slip condition. A heated triangular obstacle is located at the center of the cavity. The study accomplished for Prandtl number Pr = 0.71;the Rayleigh number Ra = 103, 105, 5 × 105, 106 and for Hartmann number Ha = 0, 20, 50, 100. The results represent the streamlines, isotherms, velocity and temperature fields as well as local Nusselt number.

一种基于三角数分解的可配置2-D卷积器优化方法

多尺寸2-D卷积通过特征提取在检测、分类等计算机视觉任务中发挥着重要作用。然而,目前缺少一种高效的可配置2-D卷积器设计方法,这限制了卷积神经网络(CNN)模型在边缘端的部署和应用。该文基于乘法管理以及奇平方数的三角数分解方法,提出一种高性能、高适应性的卷积核尺寸可配置的2-D卷积器。所提2-D卷积器包含一定数量的处理单元(PE)以及相应的控制单元,前者负责运算任务,后者负责管理乘法运算的组合,二者结合以实现不同尺寸的卷积。具体地,首先根据应用场景确定一个奇数列表,列表中为2-D卷积器所支持的尺寸,并利用三角数分解得到对应的三角数列表;其次,根据三角数列表和计算需求,确定PE的总数量;最后,基于以小凑大的方法,确定PE的互连方式,完成电路设计。该可配置2-D卷积器通过Verilog硬件描述语言(HDL)设计实现,由Vivado 2 022.2在XCZU7EG板卡上进行仿真和分析。实验结果表明,相比同类方法,该文所提可配置2-D卷积器,乘法资源利用率得到显著提升,由20%~50%提升至89%,并以514个逻辑单元实现1 500 MB/s的吞吐率,具有广泛的适用性。

考虑三方满意度的同城网络货运平台车货匹配研究

针对同城网络货运平台存在的费用不透明、优质资源分配不均等问题,首先结合竞价模式、派单模式与抢单模式,对同城网络货运平台运作模式进行优化。其次引入车货双边满意度的计算方法,基于匹配双方的需求偏好,建立综合满意度评价指标体系,结合区间三角模糊数与灰色关联分析法,设计满意度量化方法。最后兼顾货主、车主和平台,构建三方满意度最大化的一对多车货匹配模型,通过案例实现匹配结果输出,验证模型的可行性与合理性。结果表明,只考虑货主或车主满意度最大,将导致模型求解结果失衡;平台满意度权重调整对匹配结果的直接影响较小,结果倾向于满足双边用户的需求。敏感性分析发现,当货主、车主以及平台满意度权重配置分别为0.6、0.3、0.1时,匹配结果呈现最优化。