在因素空间理论基础上,提出直觉模糊概念,从原概念及其对立概念的表现外延出发,构造了直觉模糊概念外延的两种逼近,并在此基础上提出了基于反馈外延双层包络的DFE决策方法,最后,给出操作步骤并通过实例对上述理论方法进行了应用.

为解决多标记学习中的维度灾难问题,采用分而治之的方法,充分考虑标记间的相关性,提出一种基于改进快速密度聚类的多标记学习层次树模型(ML-HTM).该模型降低了聚类过程中的计算复杂度,提高了多标记学习效率.为检验模型效果,在6个高维数据集、12个多标记分类评价指标上进行多标记学习实验,并与6种经典多标记学习算法的评价指标值进行算法对比.实验结果表明,该模型对多标记学习中高维数据的处理,明显提高了预测性能和学习效率,充分挖掘标记间的相关性,使得标记预测的结果更加准确.

The existence of strongly polynomial-time algorithm for linear programming is a cross century international mathematical problem, whose breakthrough will solve a major theoretical crisis for the development of artificial intelligence. In order to make it happen, this paper proposes three solving techniques based on the cone-cutting theory: 1. The selection of cutter: principles highest vs. deepest; 2. The algorithm of column elimination, which is more convenient and effective than the Ye-column elimination theorem; 3. A step-down algorithm for a feasible point horizontally shifts to the center and then falls down to the bottom of the dual feasible region D. There will be a nice work combining three techniques, the tri-skill is variant Simplex algorithm to be expected to help readers building the strong polynomial algorithms. Besides, a variable weight optimization method is proposed in the paper, which opens a new window to bring the linear programming into uncomplicated calculation.

为解决模糊数排序中普遍存在的错误风险问题,采用模糊数的隶属函数分布方法,给出两个模糊数排序的风险度和可信度定义.在此基础上,将两个模糊数的排序风险拓展到多个模糊数中,针对模糊多属性决策中多个模糊数排序提出了一种基于风险最小化或基于可信度最大化的排序方法,并给出一个排序方案的综合风险度的计算.通过一个算例说明所提出方法的可行性和有效性.研究结果表明:基于风险的模糊数排序原则是可行且有效的,模糊数的风险排序计算得到的结果与事实相符.

为了更充分的利用数据信息,本文提出了以犹豫模糊集作为概念的反馈外延.进而给出了考虑犹豫度的犹豫模糊集间的关系与运算;基于此运算,定义了模糊概念的外延包络,并利用包络来集结多因素的偏好信息,最后给出群决策步骤,并通过实例对上述理论方法进行了应用.

为解决在稀疏规则库条件下KH插值推理方法不能保证推理结果的正规性与凸性问题,基于模糊结构元理论,将模糊数的运算转换为单调函数的运算,定义一种新的模糊数距离的计算方法,提出一种新的稀疏规则库插值推理方法.在此基础上,将该方法从单变量拓展到多变量的情况,提出一种多变量模糊插值推理方法.通过一个算例说明所提出方法的可行性和有效性.研究结果表明:该方法在保证推理结论正规性与凸性的基础上,避免了用α-截集的方法求得结果,简便了推理运算.

针对目前关于犹豫模糊运算与测度的研究中存在的不足,首先给出犹豫模糊熵函数的定义,并将其作为犹豫模糊信息不确定性测度,进而提出犹豫模糊信息特征向量概念,以信息特征向量为出发点对犹豫模糊距离测度和相似性测度展开研究;为优化群决策过程,提出基于完全优先关系的群一致性测度概念并研究其性质;最后,提出基于相似性测度和群一致性测度的群决策方法并结合算例验证所提出方法的有效性.

为了从不同维度综合刻画事物的模糊性,用三角结构元线性表示了区间值模糊数,定义了区间值模糊数的运算及排序;通过对称变换实现了成本型指标的效益型转化,通过平移与压缩实现了属性的归一化,确定了标准评判矩阵.结果表明,区间值模糊数的模糊多属性决策,综合考虑了多个专家意见的融合以及概念的模糊性.研究结论拓展了模糊多属性决策研究的思路,使之更贴近实际.

At present, research on hesitant fuzzy operations and measures is based on equal length processing, and an equal length processing method will inevitably destroy the original data structure and change the data information. This is an urgent problem to be solved in the development of hesitant fuzzy sets. Aiming at solving this problem, this paper firstly defines a hesitant fuzzy entropy function as the measure of the degree of uncertainty of hesitant fuzzy information and then proposes the concept of hesitant fuzzy information feature vector. The hesitant fuzzy distance measure and similarity measure are studied based on the information feature vector. Finally, the hesitant fuzzy network clustering method based on similarity measure is given, and the effectiveness of our algorithm through a numerical example is illustrated.

在大数据的背景下,运用模糊数据统计分析的理论与方法越来越受到重视.本文论述了模糊数据统计中存在的自然扩张和联合扩张问题,指出了统计量自然扩张的错误并给出了联合扩张的解决方案,利用模糊数的结构元表达方法构建了几个重要样本公式,它们是模糊数据统计分析的重要工具.

为了更加完整地刻画出传统Fisher Score在某些分布不均匀情况下未体现出的类间差异,同时弥补对两类间交叉关系的考虑,采取新的类间散度度量公式,加入度量两类重复度的交叉系数,并引入最大互信息系数对公式进行修正,提出了改进的Fisher Score,对比实验验证了改进方法的有效性.结果表明:改进的Fisher Score 可以度量出更多的数据分布情况,在分布不均匀但同属于一个类中心的数据中,改进方法可以将更重要的特征辨识出来,完善了传统的Fisher Score特征选择方法.

针对等区间离散化方法的刚性划分问题,提出一种具有柔性的2-Flou数因素值离散化算法.利用提出的2-Flou数理论及其连接算法,采用双参数调节策略和四元组表示策略,对给定连续型数据进行柔性离散化.以iris数据集为例进行离散化实验,实验过程简单、结果符合预期.结果表明:2-Fou数的离散化方法比经典等区间离散化法更有柔性,比模糊区间离散化法表达更简单,是一种更有效的离散化方法.

Conceptual generation is a key point and basic problem in artificial intelligence, which has been probed in the Formal Concept Analysis (FCA) established by G. Wille. Factors Space (FS) is also a branch of cognition math initiated by P.Z. Wang at the end of last century, which has been applied in information processing with fuzzy concepts effectively. This paper briefly introduces the historic background of FS and its relationship with FCA. FS can be seen as a good partner of FCA on conceptual description and structure extraction; combining FCA with FS, we can get more clear and simple statements and more fast algorithms on conceptual generation.

本文提出了在因素空间上概念的区间集表示方法,包括定性表达和定量描述.给出一种基于结构元的区间数的比较与排序方法,进而根据概念的区间集表示给出了一种群决策方法,并通过实例对上述理论方法进行了应用.

研究离散线性切换系统非脆弱H∞滤波器设计问题,假设滤波器增益含有区间不确定性,采用平均驻留时间技术,并利用LMIs给出非脆弱H∞滤波器的设计方案.当采用经典的顶点方法时,需要求解的LMI数量呈指数级增长,系统维数较高时,可能超过当前的运算能力,故提出一种明确有效的概率算法.预先制定的概率水平可以保证鲁棒性,并给出为达到所需概率水平而需要的采样数量.该算法可以显著减少参与设计的LMI的数量.最后用数值仿真证明了方法的有效性.

库存系统中存在众多决策参数,这些决策参数往往难以准确确定而只能凭决策者的经验给出,由此产生了对模糊库存模型的研究.在库存决策参数中影响最大也是最难确定的是库存需求量,研究库存需求量为时变模糊需求,即库存需求量是模糊值函数时的模糊库存模型,利用模糊值函数及模糊数的结构元表示,给出了模糊值函数在不确定性区间上的积分表示,得到-循环模糊库存模型总费用的模糊解析表达,最后利用模糊数结构元加权排序进行逆模糊化,得出模糊值函数的极值模糊点,进而得到在模糊库存总费用最小时的订货周期和订货批量的可靠解.

利用模糊数与模糊值函数的结构元计算方法研究一类具有单元模糊失效率的系统,分析和讨论模糊参数系统的可靠性计算.本文提出求解系统模糊可靠度及其隶属函数表达形式的三种方法,并给出并联系统、串联系统、串-并联系统、并-串联系统的模糊可靠度及其隶属函数,利用这些方法也可以类似地解决其他具有模糊失效率的较复杂的系统可靠度计算问题.

针对高盐饮食人群易患高血压的问题,论文采用因素空间理论中的决定度方法对高盐饮食与高血压之间的关系进行分析.基于对辽宁阜新农村高盐饮食人群中选取的45315个样本数据进行初步处理,通过确定样本性别、年龄、民族、每日吃咸菜或大酱次数、食盐量、腌制咸菜的大酱或大粒盐等6个条件因素,并利用Matlab程序计算1个高血压结果因素的方式来分析高血压病因的决定度.研究结果表明:高盐饮食是高血压病高发的主要诱因,为我国高盐饮食人群高血压的防治提供基础依据.

To analyze the effects the history of familiar chronic diseases without infectivity have on the risk of having stroke,a resident group of individuals aged older than 35 in the countryside of Fuxin city,Liaoning province were investigated.Based on the baseline data,select the appropriate factors,analyze the correlation between the factors and reduce dimensions after knowing their features.Using 10-fold cross-validation,an intelligent inference algorithm —— factor analysis,is applied to compatible data to get the inference rules.Then combining the 10 group of inference rules gotten based on different training data together so that the final inference rules can be available and the accuracy on the test data are calculated.After being analyzed,it is known that having family history of hypertension、history of hyperlipidemia、history of coronary heart disease or history of diabetes can increase the risk of having stroke;If the father has hypertension,then the rate of having stroke will increase.If only the mother has hypertension,then the older will have higher rate of having stroke.If brothers or sisters have hypertension,then the rate of having stroke is not too high.People with the history of hyperlipidemia have higher rate of having cerebral infraction.

The core idea of big data processing based on factor space is placing data as sampling S of background relation R,and taking the target of data-cultivation as the approximation of R by the enclosure [S].And then the thinking functions of concept generation,rules extraction and logical inference can be done on data.To realize such strategy,the key point is information compression.For this reason,Prof.P Z Wang has presented the concept of background bases and an algorithm named angle criterion,which is simple and fast,but is approximation.This paper will promote it to be an accurate algorithm by adding a rather weaker condition.The algorithm enables that factor space theory can handle big data effectively.