LLT polynomials,chromatic quasisymmetric functions and graphs with cycles

We use a Dyck path model for unit-interval graphs to study the chromatic quasisymmetric functions introduced by Shareshian and Wachs, as well as unicellular LLT polynomials, revealing some parallel structure and phenomena regarding their $\mathrm{e}$-positivity.The Dyck path model is also extended to circular arc digraphs to obtain larger families of polynomials, giving a new extension of LLT polynomials. Carrying over a lot of the non-circular combinatorics, we prove several statements regarding the $\mathrm{e}$-coefficients of chromatic quasisymmetric functions and LLT polynomials, including a natural combinatorial interpretation for the $\mathrm{e}$-coefficients for the line graph and the cycle graph for both families. We believe that certain $\mathrm{e}$-positivity conjectures hold in all these families above.Furthermore, beyond the chromatic analogy, we study vertical-strip LLT polynomials, which are modified Hall–Littlewood polynomials.     

利用近红外及中红外融合技术对小麦产地和烘干程度的同时鉴别

小麦是制作馒头的主要原料之一,小麦中水、蛋白质、淀粉会因产地以及烘干程度的差异而不同,进而影响到加工成馒头的品质。所以实现对小麦产地和烘干程度的快速鉴别就显得尤为重要。感官评定是鉴别小麦产地和烘干程度常用的方法,对比感官评定,光谱分析可以识别样品中的分子结构等信息。基于此,尝试利用近红外和中红外光谱融合技术实现对不同产地和不同烘干程度的小麦同时鉴别。首先选取了两个不同产地的小麦,再利用微波干燥法对两个不同产地的小麦做烘干预处理,使烘干的小麦水含量为12%±0.5%,原麦水含量为18%±0.5%。分别标记为原麦A,烘干A,原麦B,烘干B,再将小麦研磨成粉末,过100目筛网筛选后,置于自封袋中备用。随后分别采集四种小麦样品的近红外和中红外光谱信息,在Matlab 7.10的环境下使用标准正态变量变换(standard normal variable transformation, SNVT)对采集到的原始光谱数据进行预处理,利用主成分分析对预处理后的数据进行降维处理,再结合线性判别分析（linear discriminant analysis,LDA）和支持向量机（support vector machine, SVM）分别建立小麦近红外、中红外光谱数据识别模型。另外利用联合区间偏最小二乘法（synergy interval partial least square, SiPLS）筛选出利用标准正态变量变换(SNVT)预处理后的小麦近红外和中红外光谱数据特征光谱区间,将筛选出的近红外和中红外光谱数据特征光谱区间融合后再结合线性判别分析（LDA）和支持向量机（SVM）建立小麦融合光谱信息的识别模型。然后比较同种光谱数据下利用线性判别分析（LDA）和支持向量机（SVM）建立的小麦识别模型识别率、比较同种建模方法下近红外和中红外光谱数据建立小麦识别模型识别率、比较同种建模方法下光谱数据融合和单一光谱数据建立小麦识别模型识别率。结果表明,同种光谱分析方法,利用SVM建立的四种小麦识别模型识别率高于利用LDA建立的小麦识别模型识别率。同种建模方法,近红外光谱数据建立的小麦识别模型识别率优于中红外光谱数据建立的小麦识别模型识别率。而在同种建模方法下,利用SiPLS筛选出近红外和中红外光谱数据的特征光谱区间数据融合后建立小麦识别模型识别率最高,光谱数据融合后结合LDA建立的小麦识别模型校正集识别率为98.75%,预测集识别率为97.50%;而将此选择的变量结合SVM建立的小麦识别模型的校正集和预测集识别率都达到100.0%。对比利用单一光谱数据建立的小麦识别模型识别率,光谱数据融合之后建立的小麦识别模型识别率得到显著提高,该研究从纵向和横向上全面地比较了光谱数据建立的小麦模型识别率,结果可为更准确地运用光谱融合技术建立小麦产地以及烘干程度识别模型提供参考。     

可能度及其在多指标区间决策中的应用

在对区间数比较的可能度进行综述的基础上提出了可能度公理,构建了多指标区间决策的综合评价模型,并运用区间数比较的可能度,给出了一种简便实用的方案排序方法.最后通过实例说明了方法的合理性和可行性.     

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.     

Variable sampling interval Shewhart control charts for monitoring the multivariate coefficient of variation

In many industrial manufacturing processes, the ratio of the variance to the mean of a quantity of interest is an important characteristic to ensure the quality of the processes. This ratio is called the coefficient of variation (CV). A lot of control charts have been designed for monitoring the CV of univariate quantity in the literature. However, the CV control charts for multivariate quantity have not received much attention yet. In this paper, we investigate a variable sampling interval (VSI) Shewhart control chart for monitoring multivariate CV. The time between two consecutive samples is allowed to vary according to the previous value of the multivariate CV, which will help the chart to detect the process shifts faster. The comparison with the fixed sampling interval Shewhart chart is implemented to highlight the advantage of the VSI method. Finally, an illustrative example is demonstrated on real data.     

TH型区间值模糊正规子群

本文在区间值模糊集空间上，引入了幂等区间范数ＴＨ，在此基础上，定义了ＴＨ型区间值模糊正规子群，并研究了它的一些性质和结构特征，从而拓广了区间值模糊集的理论。     

基于区间效率的贷款定价研究

以存款利息支出率、费用支出率、预期违约损失率、目标利润率等4个定价指标作为输入,以贷款利率作为输出,采用支持向量机回归算法建立基于区间效率的贷款定价模型.创新与特色一是通过区间数形式来反映预期违约损失率、目标利润率、费用支出率等,改变了现有研究将目标利润、贷款费用、违约损失等变量看作确定性数值来定价的现状.使贷款利率更具有竞争性.二是通过比较不同核函数、核参数下的训练样本的贷款效率区间与合理的贷款效率区间的匹配程度,确定贷款定价模型最优的核函数和核参数,进而建立了贷款定价模型.间接解决了在考虑贷款价格能否被银行、客户接受情况下贷款利率确定的问题.     

Interval Valued Intuitionistic （S, T）-fuzzy Hv-submodules

On the basis of the concept of the interval valued intuitionistic fuzzy sets introduced by K. Atanassov, the notion of interval valued intuitionistic fuzzy Hv-submodules of an Hv-module with respect to a t-norm T and an s-norm S is given and the characteristic properties are described. The homomorphic image and the inverse image are investigated. In particular, the connections between interval valued intuitionistic （S, T）-fuzzy Hv-submodules and interval valued intuitionistic （S, T）-fuzzy submodules are discussed.     

The necessary and sufficient condition for the convergence of Ishikawa iteration on an arbitrary interval

As an important iteration, the Mann and Ishikawa iteration has extensive application in fixed point theory. In 1991, David Borwein and Jonathan Borwein proved the convergence of the Mann iteration on a closed bounded interval in their paper. In this paper, we will extend their result to an arbitrary interval and to the Ishikawa iteration, indicating the necessary and sufficient condition for the convergence of Ishikawa iteration of continuous functions on an arbitrary interval.     

基于模糊语言的多属性联系数决策方法

针对属性权重已知,属性值以模糊语言给出的多属性决策问题,提出了一种基于模糊语言标度的区间数表示形式,并利用集对分析方法将区间数进行转化为联系数的表示方式,通过联系数中同、异、反的关系,给出相应集势值,由集势值的大小进行择优排序.最后,通过实例分析,验证了该方法的可行性和有效性.