集值映射的一种锥凸性及标量化

在一种集合偏序关系下提出了集值映射的标量锥拟凸概念, 讨论了它与各种锥凸性的关系. 然后对恰当锥拟凸性得到了某种水平集意义下的刻画. 同时建立了集值映射的各种锥凸性通过实值单调增加凸函数表示的标量化复合法则. 最后给出了利用Gerstewitz泛函表示的对集值映射的锥拟凸性的标量化刻画.     

集值映射的一种锥凸性及标量化

在一种集合偏序关系下提出了集值映射的标量锥拟凸概念, 讨论了它与各种锥凸性的关系. 然后对恰当锥拟凸性得到了某种水平集意义下的刻画. 同时建立了集值映射的各种锥凸性通过实值单调增加凸函数表示的标量化复合法则. 最后给出了利用Gerstewitz泛函表示的对集值映射的锥拟凸性的标量化刻画.     

限制容差关系下的集对变精度粗糙集模型

不完备信息系统中目前有多种扩充,如基于容差关系的扩充、基于相似关系的扩充等等,但是这些扩充都各自存在局限性。针对这些局限性,引入相对分类错误率的概念,提出了一种基于限制容差关系下的集对变精度粗糙集模型。这就将经典的粗糙集模型和限制容差关系下的集对粗糙集模型进行了推广。然后,讨论了该模型上、下近似算子的一些性质。最后,通过一个具体例子,说明了该模型在不完备信息系统中处理模糊和不确定性知识是可行、有效的。     

交C-连续偏序集

利用偏序集上的半拓扑结构,引入了交C-连续偏序集概念,探讨了交C-连续偏序集的性质、刻画及与C-连续偏序集、拟C-连续偏序集等之间的关系.主要结果有:(1)交C-连续的格一定是分配格;(2)有界完备偏序集(简记为bc-poset)L是交C-连续的当且仅当对任意x∈L及非空Scott闭集S,当∨S存在时有x∧∨S=∨{x∧s:s∈S};(3)完备格是完备Heyting代数当且仅当它是交连续且交C-连续的;(4)有界完备偏序集是C-连续的当且仅当它是交C-连续且拟C-连续的;(5)获得了反例说明分配的完备格可以不是交C-连续格,交C-连续格也可以不是交连续格.     

水雾化粉末质量预报系统的建模与知识获取

水雾化粉末质量预报系统具有原始数据不全的特点,是一个不完备的信息系统.本文依据此特点,结合变精度粗糙集方法,在相客关系的基础上引入集对分析方法,提出一种基于集对势容差关系的扩充粗糙集方法,并应用于该信息系统的建模中,通过对α的调节和控制,有效保证了制粉生产条件属性容差类划分的准确性和灵活性.最后,本文以该模型为基础,使用基于属性重要性的贪心算法讨论了制粉生产条件属性约简和知识获取的方法、步骤和决策规则.经实际生产验证了获取的预报知识的合理性和有效性,对制粉工艺和生产真正起到了优化作用.     

偏序集上一致连续性的等价刻画与性质

将一致小于关系移植到一般偏序集上,同时引入了上界小于关系,定义了偏序集的一致连续性和上界连续性.给出了一致连续偏序集的等价刻画,探讨了一致连续偏序集所具有的性质.主要结果有:(1)证明了偏序集上的一致连续性,上界连续性与s-超连续性均等价;(2)在交半格条件下,偏序集的一致连续性等价于它的每一主理想一致连续;(3)在并半格条件下,偏序集的一致连续性蕴含连续性,反之不成立;(4)一致完备的一致连续偏序集均是连续bc-dcpo,且每个主理想均为完全分配格;(5)在一致完备的条件下,一致连续性对主滤子,对闭区间,对Scott S-集以及对一致连续投射像均是可遗传的.文中也构造了若干实用的反例.     

集值决策表基于邻域关系的属性约简

集值信息系统是完备信息系统的广义形式,它当中的一些对象在某些属性下的取值可能不止一个,反映的是信息的不确定性.本文在集值信息系统上引入对象的邻域关系,并以每个对象的邻域作为基本集,建立了集值信息系统的粗糙集方法.为了简化的知识表示,我们进一步讨论了邻域协调集值决策表的正域约简与邻域不协调集值决策表的近似分布约简,给出了正域约简与近似分布约简的等价刻画条件,并借助区分函数给出了计算正域约简与近似分布约简的方法.     

模糊赋范线性空间的紧性与完备性

讨论了Fuzzy赋范线性中准紧集、完备集及有界集间的关系;给出完备Fuzzy赋范空间的闭球套定理与Baire定理;刻画了了有限维Fuzzy赋范空间的特征。     

模糊数学在飞机故障诊断中的应用

飞机故障征兆与故障原因问的隶属关系是模糊的，为此，将模糊数学方法引入到飞机故障诊断中，提出由历史数据及专家优序数综合确定模糊隶属度的方法，建立模糊诊断模型，并在计算机上实现飞机故障的模糊诊断。     

模糊偏序集上理想完备的幂等性

主要讨论模糊偏序集上理想完备性的本质.并得到以下结论:模糊偏序集的理想完备是幂等的当且仅当理想完备上的广义Scott拓扑与Alexandroff拓扑是一致的.     

Optimality conditions in set optimization employing higher-order radial derivatives

There are two approaches of defining the solutions of a set-valued optimization problem:vector criterion and set criterion.This note is devoted to higher-order optimality conditions using both criteria of solutions for a constrained set-valued optimization problem in terms of higher-order radial derivatives.In the case of vector criterion,some optimality conditions are derived for isolated (weak) minimizers.With set criterion,necessary and sufficient optimality conditions are established for minimal solutions relative to lower set-order relation.     

与Schrödinger算子相关的等价集合及应用

本文不仅给出了锥中无穷远点处与Schr?dinger算子相关等价集合的定义而且证明了相应的判定准则.作为应用,本文得到一个定义在锥中的点列是无穷远点处与Schr?dinger算子相关等价集合的充要条件.     

犹豫模糊集的截集及其性质

通过引入犹豫模糊集的截集概念并研究截集的性质,建立了沟通犹豫模糊集合与经典集合之间的桥梁.进一步,讨论了犹豫模糊关系的截关系及其性质.     

模糊软映射及其应用

在模糊软集合的基础上,提出了模糊软关系和模糊软映射的定义,并研究了它们的性质,最后给出了模糊软映射在医疗诊断中的应用实例.     

The stability of the solution sets for set optimization problems via improvement sets

ABSTRACT

The aim of this paper is to investigate the stability of the solution sets for set optimization problems via improvement sets. Firstly, we consider the relations among the solution sets for optimization problem with set optimization criterion. Then, the closeness and the convexity of solution sets are discussed. Furthermore, the upper semi-continuity, Hausdorff upper semi-continuity and lower semi-continuity of solution mappings to parametric set optimization problems via improvement sets are established under some suitable conditions. These results extend and develop some recent works in this field.     

基于可拓集的可拓分类知识获取研究

以可拓集理论为依据,给出基于可拓变换的可拓分类知识的定义,并在信息元集和评价信息元集的基础上,探讨可拓分类知识的获取方法,包括质变域知识的获取、量变域知识的获取和有关拓界的知识的获取.这是可拓数据挖掘的主要内容之一,为从数据库中获取变化的分类知识提供了新的思路.     

SEMIGROUP APPROACH TO A DOUBLY DEGENERATE PARABOLIC EQUATION

1.IntroductionWeareconcernedwiththesemigroupapproachtotheinitialvalueproblemfordoublynonlineardegenerateparabolicequationoftheformwhicharisesfromdifferentphysicalbackgroundssuchasthemodelingofthemotionofnon-Newtonianfluids.Inthepastyears,thenonlinear...     

Rough sets for pattern classification using pairwise-comparison-based tables

Rough set theory is a useful mathematical tool to deal with vagueness and uncertainty in available information. The results of a rough set approach are usually presented in the form of a set of decision rules derived from a decision table. Because using the original decision table is not the only way to implement a rough set approach, it could be interesting to investigate possible improvement in classification performance by replacing the original table with an alternative table obtained by pairwise comparisons among patterns. In this paper, a decision table based on pairwise comparisons is generated using the preference relation as in the Preference Ranking Organization Methods for Enrichment Evaluations (PROMETHEE) methods, to gauges the intensity of preference for one pattern over another pattern on each criterion before classification. The rough-set-based rule classifier (RSRC) provided by the well-known library for the Rough Set Exploration System (RSES) running under Windows as been successfully used to generate decision rules by using the pairwise-comparisons-based tables. Specifically, parameters related to the preference function on each criterion have been determined using a genetic-algorithm-based approach. Computer simulations involving several real-world data sets have revealed that of the proposed classification method performs well compared to other well-known classification methods and to RSRC using the original tables.     

A remark on uniform spaces with invariant nonstandard hulls

Let (X , Γ) be a uniform space with its uniformity generated by a set of pseudo‐metrics Γ. Let the symbol ? denote the usual infinitesimal relation on *X , and define a new infinitesimal relation ≈ on *X by writing x ≈ y whenever *? (x, p ) ? *? (y, p ) for each ? ∈ Γ and each p ∈ X . We call (X , Γ) an S‐space if the relations ? and ≈ coincide on fin(*X ). S ‐spaces are interesting because their nonstandard hulls have representations within Nelson's internal set theory (IST, [5]). This was shown in [1], where it was also observed that the class of uniform spaces that have invariant nonstandard hulls is contained in the class of S ‐spaces. The question of whether there are S ‐spaces that do not have invariant nonstandard hulls was left open in [1]. In this note we show that when the uniformity of an S ‐space is given by a single pseudometric, the space has invariant nonstandard hulls. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

凸集的广义Reuleaux三角形

常宽凸集的面积最小者为Reulaux三角形，而非常宽凸集的面积最小者为何呢？它就是本文将给出的广义Reuleaux三角形△R。