六元gcd封闭集上Smith矩阵的整除性

我们给出了关于六元gcd封闭集S的充分必要条件,使得在整数矩阵环M_6(Z)中,定义在S上的e次幂GCD矩阵(S~e)整除e次幂LCM矩阵[S~e].这部分解决了Hong在2002年提出的一个公开问题.     

弱分离条件下的自共形迭代函数系统

开集条件是分形几何的一个重要概念,弱分离条件(WSC)在研究有重叠的迭代函数系统(IFS)中扮演着重要角色.本文考虑满足弱分离条件的自共形迭代函数系统,并给出确定其不变集的Hausdorff维数的一种方式.     

Centrality as a gradual notion: A new bridge between fuzzy sets and statistics

This paper aims at formalizing the intuitive idea that some points are more central in a probability distribution than others. Our proposal relies on fuzzy events to define a fuzzy set of central points for a distribution (or a family of distributions, including imprecise probability models). This framework has a natural interpretation in terms of fuzzy logic and unifies many known notions from statistics, including the mean, median and mode, interquantile intervals, the Lorenz curve, the halfspace median, the zonoid and lift zonoid, the coverage function and several expectations and medians of random sets, and the Choquet integral against an infinitely alternating or infinitely monotone capacity.     

Diverse reduct subspaces based co-training for partially labeled data

Rough set theory is an effective supervised learning model for labeled data. However, it is often the case that practical problems involve both labeled and unlabeled data, which is outside the realm of traditional rough set theory. In this paper, the problem of attribute reduction for partially labeled data is first studied. With a new definition of discernibility matrix, a Markov blanket based heuristic algorithm is put forward to compute the optimal reduct of partially labeled data. A novel rough co-training model is then proposed, which could capitalize on the unlabeled data to improve the performance of rough classifier learned only from few labeled data. The model employs two diverse reducts of partially labeled data to train its base classifiers on the labeled data, and then makes the base classifiers learn from each other on the unlabeled data iteratively. The classifiers constructed in different reduct subspaces could benefit from their diversity on the unlabeled data and significantly improve the performance of the rough co-training model. Finally, the rough co-training model is theoretically analyzed, and the upper bound on its performance improvement is given. The experimental results show that the proposed model outperforms other representative models in terms of accuracy and even compares favorably with rough classifier trained on all training data labeled.     

Topology vs generalized rough sets

This paper investigates the relationship between topology and generalized rough sets induced by binary relations. Some known results regarding the relation based rough sets are reviewed, and some new results are given. Particularly, the relationship between different topologies corresponding to the same rough set model is examined. These generalized rough sets are induced by inverse serial relations, reflexive relations and pre-order relations, respectively. We point that inverse serial relations are weakest relations which can induce topological spaces, and that different relation based generalized rough set models will induce different topological spaces. We proved that two known topologies corresponding to reflexive relation based rough set model given recently are different, and gave a condition under which the both are the same topology.     

Fuzzy closure systems on L—ordered sets

In this paper, notions of fuzzy closure system and fuzzy closure L —system on L —ordered sets are introduced from the fuzzy point of view. We first explore the fundamental properties of fuzzy closure systems. Then the correspondence between fuzzy closure systems (fuzzy closure L —systems) and fuzzy closure operators is established. Finally, we study the connections between fuzzy closure systems and fuzzy Galois connections. © 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim     

On a positive set theory with inequality

We introduce a quite natural Frege‐style set theory, which we call Strong‐Frege‐2 $(\mathsf {SF}_2)$, a sort of simplification of the theory considered in 13 (under the name Strong‐Frege‐3) and 1 (under the name F2). We give a model of a weaker variant of $\mathsf {SF}_2$, called $\mathsf {SF}_2\mathsf {AC}$, where atoms and coatoms are allowed. To construct the model we use an enumeration “almost without repetitions” of the Π¹₁ sets of natural numbers; such an enumeration can be obtained via a classical priority argument much in the style of 5 and 15 . © 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim     

有向网络下多个体系统的整体行为

研究非时变有向通讯网络背景下一阶线性多个体动力学系统的整体行为.根据通讯网络的结构,系统可以区分为独立基本子系统和非独立基本子系统.当系统的控制规则为一类平凡的线性类型时,系统的独立基本子系统将趋于自身的一致状态,也即子系统中的每个个体趋于子系统的带权中心.独立基本子系统带权中心由子系统的系数矩阵的零特征根归一化左特征向量确定.非独立子系统中个体将趋于独立基本子系统带权中心的凸集内.当且仅当系统的独立基本子系统唯一时,系统实现一致性行为.     

基于Vague集的水电工程方案模糊综合评价

水利工程建设方案决策是多目标综合评价问题,系统指标信息具有复杂、多变,模糊、不确定等特点,采用Vague集相似度量评价模型构建水利工程建设方案综合决策模型,建立基于Vlague集的指标隶属度计算方法,构造基于Vague集相似度的多目标方案评价.针对建设方案决策评价指标的不确定性,通过肯定、踌躇、否定的Vague集相似度量概念延伸了传统模糊集的评价、分析方式.将方法应用于水利工程建设方案决策实例,取得较为满意的结果,表明了方法的合理可行性,为水利工程的建设方案评价提供了科学决策的新途径.     

半环上的粗糙集

利用同余关系把粗糙集理论引入到半环里,给出了半环中的一个子集的上,下近似的概念,并研究了其一系列性质;另外我们还讨论了半环中的粗糙理想及性质.