山区高速铁路初步设计阶段方案比选的模糊数学方法

在山区高速铁路建设中,初步设计阶段常遇到多方案比选问题.而方案选择涉及因素众多,难以定量分析.针对此问题,引入模糊综合评价模型对各方案进行比选.以渝万铁路客运专线为例,应用模糊综合评价模型对有关方案进行了比选研究,最终得到了首选方案.     

直觉模糊变换半群的积与覆盖关系

提出了直觉模糊变换半群的(全)直积,圈积,直觉模糊变换半群的覆盖的定义,利用代数的手段讨论了直觉模糊变换半群的积的结合性质,研究了直觉模糊变换半群的积的覆盖关系.     

基于集对分析的水库诱发地震综合风险评价模型

在水库诱发地震综合风险评价指标体系建立的基础上,根据评价指标的物理含义及其对水库诱发地震的作用情况,建立了水库诱发地震综合风险评价等级标准.用基于加速遗传算法的模糊层次分析法确定水库诱发地震综合风险评价系统中各指标和各子系统的权重,建立了基于集对分析的水库诱发地震综合风险评价模型(SPA-IRAM).SPA-IRAM在克孜尔诱发地震综合风险评价中的应用结果表明:基于集对分析的级别特征值法和属性评判法的评价结果具有一致性和互补性,联合应用可保障SPA-IRAM评价结果的可靠性;该水库诱发地震综合风险评价等级接近于2到3级、介于弱险与中险之间,需要密切监测该水库所在地区的断层活动、水库周围断裂发育和库区岩层裂隙发育的情况,进一步提高水库所在地区人均GDP和水库所在地区钢筋混凝土房屋比例,降低第一产业产值在国民生产总值中的比重和水库所在地区砖木房屋比例.SPA-IRAM综合利用了评价指标、子系统和样本与评价等级标准间联系数的丰富的结构信息和层次信息,可从指标、子系统和样本3个层次定量地分析水库诱发地震综合风险的复杂状态,在水库诱发地震风险管理中具有重要意义.     

基于粗糙集与模糊集理论的图书馆最优购书算法

本文将粗糙集理论与模糊集理论结合起来,给出一种图书馆最优选书算法.该算法首先从已知数据的初始信息系统出发,计算各选书方案之间的相似度,从而构造相似矩阵,然后根据相似矩阵的传递闭包对各方案进行聚类,并根据粗糙集理论求各属性重要性,最后利用加权综合的思想及最小距离方法选择最优买书方案.     

含弹性约束的多目标模糊线性规划求解

本文讨论了一类含弹性约束的多目标模糊线性规划问题.利用模糊结构元方法引入模糊数的加权特征数概念和序关系,应用Verdegay的模糊线性规划方法及模糊数的加权特征数将此类多目标模糊线性规划问题转化成一类含参数约束条件的清晰多目标线性规划模型,并应用一种基于线性加权函数的规划算法求其α-拟最优可行解.最后,给出了一个数值实例来说明如何求解此类多目标模糊线性规划问题.     

模糊数互补判断矩阵的乘性一致性研究

指出了文献[13]中乘性一致性区间数互补判断矩阵定义的不足,并重新提出了较为合理的定义,进而定义了乘性一致性模糊数互补判断矩阵.通过引入Q-算子和Q-矩阵,给出了判断一个模糊数互补判断矩阵是否满足乘性一致性的较为实用的检验方法.最后通过一个算例说明了此方法的可行性和简洁性.     

Leap-frogging Newton's method

Using Newton's method as an intermediate step, we introduce an iterative method that approximates numerically the solution of f (x) = 0. The method is essentially a leap-frog Newton's method. The order of convergence of the proposed method at a simple root is cubic and the computational efficiency in general is less, but close to that of Newton's method. Like Newton's method, the new method requires only function and first derivative evaluations. The method can easily be implemented on computer algebra systems where high machine precision is available.     

n-tribonacci triangles and applications

In this note we introduce n-tribonacci triangle, which is similar to Pascal's triangle, to derive an explicit formula for the tribonacci numbers by using some properties of our triangle.     

The Tits Alternative for Groups Defined by Periodic Paired Relations

The class of groups defined by periodic paired relations, as introduced by Vinberg, includes the generalized triangle groups, the generalized tetrahedron groups, and the generalized Coxeter groups. We observe that any group defined by periodic paired relations Γ can be realized as a so-called “Pride group”. Using results of Howie and Kopteva we give necessary and sufficient conditions for this Pride group to be non-spherical. Under such conditions, we show that Γ satisfies the Tits alternative.

Communicated by A. Olshanskiy     

Ranking generalized fuzzy numbers in fuzzy decision making based on the left and right transfer coefficients and areas

Although a number of recent studies have proposed ranking fuzzy numbers based on the deviation degree, most of them have exhibited several shortcomings associated with non-discriminative and counter-intuitive problems. In fact, none of the existing deviation degree methods has guaranteed consistencies between the ranking of fuzzy numbers and that of their images under all situations. They have also ignored decision maker’s attitude toward risk, which significantly influences final ranking result. To overcome the above-mentioned drawbacks, this study proposes a new approach for ranking fuzzy numbers that ensures full consideration for all information of fuzzy numbers. Accordingly, an overall ranking index is obtained by the integration of the information from the left and the right (LR) areas between fuzzy numbers, the centroid points of fuzzy numbers and the decision maker’s attitude toward risk. This new method is efficient for evaluating generalized fuzzy numbers and distinguishing symmetric fuzzy numbers. It also overcomes the shortcomings of the existing approaches based on deviation degree. Several numerical examples are provided to illustrate the superiority of the proposed approach. Lastly, a new fuzzy MCDM approach for generalized fuzzy numbers is proposed based on the proposed ranking approach and the concept of generalized fuzzy numbers. The proposed fuzzy MCDM approach does not require the normalization process and thus avoids the loss of information results from transforming generalized fuzzy numbers to normal form.