考虑白化权函数的区间灰数预测模型研究

针对区间灰数预测模型较少考虑灰数取值可能性对预测结果的影响,构建了白化权函数已知的区间灰数预测模型。首先,将区间灰数进行标准化,分别取其"白部"和"灰部"得到白部序列和灰部序列。然后,根据白化权函数与x轴所围图形得到面积序列以及计算白化权函数已知的区间灰数的"核"得到核序列。最后,通过充分挖掘白化权函数已知的区间灰数序列中蕴含的信息,建立灰色预测模型,并应用算例分析验证模型的有效性和实用性。     

基于核和灰度的灰色网络计划技术

针对工程项目工作持续时间具有灰色不确定性特征的实际问题,结合灰色系统理论,提出了基于核和灰度的灰色网络计划技术.考虑业主方进度偏好,构造灰工作三角形白化权函数,然后以三角形重心横坐标为灰工作的核,以要求工期为论域计算灰工作的灰度,并以核和灰度表示的简化形式构建了灰工作网络计划.给出了灰工作网络计划时间参数计算方法,并探讨了灰关键路径的判定方法.案例分析验证了方法的科学性和有效性.     

基于白化权函数的区间灰数预测模型

针对传统灰色预测模型无法进行白化权函数已知的区间灰数预测的缺陷,通过先将区间灰数进行标准化处理,分解成实数形式的"白部"和"灰部",然后分别对"白部"和"灰部"序列进行预测.再将已知的白化权函数映射为[0,1]区间上的函数,并用函数的面积和重心估计出预测值的白化权函数.模型不仅能解决典型白化权函数的类型,还能解决三角白化权函数的情况,且建模机理简单,计算简便.最后,将模型应用于黄河宁蒙河段巴彦高勒站的凌期日均流量的预测,验证了新模型的有效性及实用性.     

矿井瓦斯抽放效果的灰色聚类评估

为了对矿井瓦斯抽放效果进行合理评估,通过将中心点三角白化权函数中对应于两端灰类的白化权函数分别划分为下限测度白化权函数和上限测度白化权函数,构建矿井瓦斯抽放效果评估模型,并利用模型对矿井重点位置的瓦斯浓度值进行评估、诊断.模型计算结果表明,改进的中心点白化权函数评估模型可以确保各灰类聚类系数之和为1,而且在划分瓦斯抽放效果的灰类时较中心点三角白化权函数评估模型更为准确.     

基于区间灰数序列的多变量灰色预测模型

针对传统的多变量灰色预测模型仅适用于实数序列的问题,对多变量在区间灰数序列的情形下进行建模.以核和灰度两个维度为基础,分别建立核序列和灰度序列的MGM(1,m)模型,通过核和灰度的模拟预测值还原计算得到多变量中各个变量对应的灰数序列的上界和下界,从而构建基于区间灰数序列的MGM(1,m)模型.最后,将提出的灰色多变量模型应用于雾霾的判别因素能见度和相对湿度,建立基于区间灰数序列的MGM(1,2)模型,对区间灰数序列的模拟预测取得了较好的效果,结果表明提出的基于核和灰度的灰色多变量预测模型具有可行性和实用性.     

基于端点白化权函数聚类的水环境质量等级评价分析

为更准确地评价水环境质量,将端点三角白化权函数灰色评估引入到水质综合评价中.针对以往灰色白化权函数评估主要通过测定指标灰聚类系数判定被评价对象的优劣强弱等级进行等级识别评价,对三角白化权函数计算方法进一步扩展,完成多评价对象的准确等级定位及比较排序.将这种方法应用于山东省聊城市东昌湖水水质评价中,经实例计算证明基于三角白化权函数灰色评估评价模型的稳定性、合理性和实用性为水质评价研究方法提供了新的思路和借鉴.     

灰色白化权函数定权聚类模型在合并村庄脆弱性评估中的应用北大核心

灰色白化权函数定权聚类模型是根据灰色关联矩阵或灰数的白化权函数值将一些意义、量纲、样本值数量相差较大的观测指标或观测对象划分成若干个可定义类别的方法。文中利用灰色白化权函数定权聚类模型数理意义与合并村庄脆弱性评估目标高度契合的技术特点,运用该模型从外部扰动、敏感性、适应力三个维度对研究区域内8个合并村庄进行脆弱性评估,完善地解决合并村庄脆弱性评估时多维度、多评估对象、多评估指标、多评估等级交织在一起的复杂问题,从而为合并村庄的可持续发展提供决策与参考。     

灰色不确定性白化模型的扩展补充

针对以前的研究文献中提出的灰数的白化模型存在局限性,研究了基于灰云的灰数白化模型的进一步扩展和补充.首先概述了已有的灰数白化模型存在局限性,然后给出了"非中点单一最大重要性权值"正态灰云模型、"多最大重要性权值"正态灰云模型和非正态不确定性灰云模型表示和生成方法,最后给出了结论和进一步研究的展望.     

基于相对核的三参数区间灰数信息下多属性决策方法

针对属性值为三参数区间灰数且部分权亘信息已知的多属性决策问题,提出了基于三参数区间灰数相对核的决策方法.首先考虑"亘心"点的影响给出三参数区间灰数核的定义,其次结合三参数区间灰数的核和灰度,定义了三参数区间灰数的相对核及比较法则,同时根据方差最大化思想,构建求解属性权亘的单目标线性规划模型,进而得到方案的综合属性值并进行排序.最后通过一个实例采验证所提方法的有效性和可行性.     

多源异构不确定数据下威布尔分布可靠度函数及收敛性研究

威布尔分布可以作为绝大多数机电产品的失效分布,但实践中难以获得威布尔分布的参数精确数值.采用不同方法所得到的估计结果往往有所差异,不同来源的参数估计结果其形式也往往难以统一.考虑广义标准灰数思想,对多源异构不确定数据进行统一表征,得到参数灰区间,构建灰参量威布尔可靠度函数;然后基于信息补充导致区域收敛的正态分布假设,将灰参量可靠度函数的白化问题转化为封闭区域的面积收敛问题,并构建以封闭区域面积最小和总信息补充成本最低为目标函数的多目标规划模型,得出封闭区域收敛时威布尔分布参数白化为灰参量区间的核的结论.最后采用Matlab对案例求得5组结果,验证了所述方法的有效性.     

Examination and prediction of fog and haze pollution using a Multi-variable Grey Model based on interval number sequences

In this study, a new Multivariable Grey Model (1,m) aimed at interval grey number sequences with known possibility functions is built using the kernel and degree of greyness under new definitions. Based on the new model, formulae are deduced to calculate and predict the upper and lower bounds of interval grey numbers. Since the grey system model and fog- and haze-prone weather have the same characteristics of uncertainty, this model was applied to simulate and predict the measurable indicators of fog and haze in Nanjing, China. We selected visibility data and particulate matter data with a diameter of 2.5 µm to build a new Multivariable Grey Model (1,2) with a new kernel and degree of greyness sequence. In addition, we established the traditional Multivariable Grey Model (1,2) with the original kernel and degree of greyness and the Auto-Regressive Integrated Moving Average Model (1,1,0). The results show that the new Multivariable Grey Model (1,2) has the best simulation and prediction effects among the three models, with average relative errors of simulation and prediction at 1.32% and 0.32%, respectively. To further verify the validity and feasibility of the proposed model, we added another real-world example to establish the three models mentioned above. The results prove that the proposed model has evidently superior performance to another two models.     

主客观组合赋权的灰色决策模型及其在消费者决策中的运用

现实中许多抽象系统的数值并不能精确地得到,在多属性决策过程中,其属性值多以模糊数或者区间灰数的形式表示,属性权重也受到主观因素和客观因素的影响,针对此类问题,以属性值为区间灰数的多属性决策问题为出发点,采用主客观结合的赋权方式,提出了基于区间距离的灰色相对关联度分析方法,构建了灰色决策模型,并通过消费者决策实例进行了分析,模型是对传统灰色决策模型的拓展,具有更广泛的应用性和实用性.     

直觉模糊GM(1,1)模型及其在灰色发展决策的应用

研究了以直觉模糊数为对象的GM(1,1)模型并运用到灰色发展决策方法。利用灰色系统理论中核和灰度的内涵,将直觉模糊数的犹豫度和记分函数结合构建了直觉模糊数序列 GM(1,1)预测模型,从而实现了直觉模糊数的预测。在此基础上结合变权原理提出了基于直觉模糊数的灰色发展决策方法。最后,算例分析说明了该方法的合理性和可行性。     

基于标准区间灰数的发展带离散DDGM预测模型

由于区间灰数运算体系尚不完善,灰数间的代数运算将导致结果灰度增加,难以有效构建基于"区间灰数"的灰色发展带预测模型.对此,通过将区间灰数进行标准化处理,分解成基于实数形式的"白部"和"灰部"两个部分;然后分别对"白部"和"灰部"建立发展带预测模型,再推导并还原得到区间灰数的发展带预测模型;最后,将模型用于摆动幅度大且整体趋势增长的区间灰数在未来时刻的预测,预测效果验证了所提出模型的有效性.     

Extended rough set model based on known same probability dominant valued tolerance relation

Classical rough set theory is based on the conventional indiscernibility relation. It is not suitable for analyzing incomplete information. Some successful extended rough set models based on different non-equivalence relations have been proposed. The data-driven valued tolerance relation is such a non-equivalence relation. However, the calculation method of tolerance degree has some limitations. In this paper, known same probability dominant valued tolerance relation is proposed to solve this problem. On this basis, an extended rough set model based on known same probability dominant valued tolerance relation is presented. Some properties of the new model are analyzed. In order to compare the classification performance of different generalized indiscernibility relations, based on the category utility function in cluster analysis, an incomplete category utility function is proposed, which can measure the classification performance of different generalized indiscernibility relations effectively. Experimental results show that the known same probability dominant valued tolerance relation can get better classification results than other generalized indiscernibility relations.     

不完备信息下的灰色粗糙集成决策模型侯亚林

In this paper, for multiple attribute decision-making problem in which attribute values are interval grey numbers and some of them are null values, a decision model based on grey rough sets integration with incomplete information is proposed. We put forward incidence degree coefficient formula for grey interval, by information entropy theory and analysis technique, the method and principle is presented to fill up null values. We also establish the method of grey interval incidence cluster. Because grey system theory and Rough set theory are complementary each other, decision table with preference information is obtained by the result of grey incidence cluster. An algorithm for inducing decision rules based on rough set theory and the dominance relationship is presented. In some extent, this algorithm can deal with decision-making problem in which the attribute values are interval grey numbers and some of them are null values. Contrasted with classical model of cluster decision-making, the algorithm has an advantage of flexibility and compatibility to new information.     

一种基于三参数区间灰色语言变量的多属性群决策方法

针对属性值为三参数区间灰色语言变量的不确定型多属性决策问题进行了研究,本文将语言变量和三参数区间数融合, 提出了三参数区间灰色语言变量的概念, 定义了三参数区间灰色语言变量的运算规则和可能度公式,在此基础上建立了基于投影模型的三参数区间灰色语言变量的多属性群决策方法。最后,通过对移动银行服务质量评估案例验证本模型的有效性。     

灰色正项几何规划研究

In the model of geometric programming, values of parameters cannot be gotten owing to data fluctuation and incompletion. But reasonable bounds of these parameters can be attained. This is to say, parameters of this model can be regarded as interval grey numbers. When the model contains grey numbers, it is hard for common programming method to solve them. By combining the common programming model with the grey system theory, and using some analysis strategies, a model of grey polynomial geometric programming, a model of θpositioned geometric programming and their quasi-optimum solution or optimum solution are put forward. At the same time, we also developed an algorithm for the problem. This approach brings a new way for the application research of geometric programming. An example at the end of this paper shows the rationality and feasibility of the algorithm.     

灰色GM(1,1,k,k2)模型背景值及时间响应函数优化

本文提出了一种新的带有时间幂次项的灰色GM(1,1,k,k²)模型,给出了其灰微分方程和白化微分方程基本形式。基于最小二乘法获得了该模型参数估计值,并推导了该模型时间响应函数。鉴于GM(1,1,k,k²)模型灰微分方程与白化微分方程之间存在跳跃关系,首先对灰微分方程的背景值进行了优化,并推导了优化后的背景值计算公式。为了克服初始值的影响,根据误差平方和最小,进一步优化了GM(1,1,k,k²)模型时间响应函数。最后,该优化后的GM(1,1,k,k²)模型被应用于软土地基沉降预测,获得了较好的模拟预测效果,说明模型是可行的。