物元可拓集集合性质研究

在可拓集合概念基础上,提出了向量可拓集和区间可拓集概念,研究了物元可拓集合的交、并、求补等集合运算及其性质.     

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.     

可拓集合及其应用研究

介绍了扩展的可拓集合概念 ,提出了可拓集合论需要进一步研究的内容 ,并综述了可拓集合在人工智能、市场、资源、检测和控制等领域的应用 .     

可拓集联系数的势及其关系

在可拓集联系数的基础上,提出了可拓集集对势的概念,并且对集合型可拓集联系数的关系做了定义.这使得可拓集合与集对分析的结合更加紧密,而且可以在实际中得到更好的应用.     

基于可拓集合的动态分类及其UML表示方法研究

可拓集合是分析事物的可变性和多变性的理论基础 .本文首先建立了物元与类之间的联系 ,在可拓集合零界的基础上建立了过渡类 ,为了形式化描述出多值分类 ,对关联函数进行约束 ,并利用可拓域与物元变换探讨了动态分类机制 ,最后采用 UML构造型扩展机制对动态分类的表示问题进行初步的研究 .     

可拓集的λ—域关于变换T的性质

本给出可拓集关于变换Ｔ的λ－无救域,λ－遗失域的概念,并得到可拓集关于变换Ｔ的各种域的若干性质。     

基于可拓分析的信息模式识别方法

采用可拓评判方法,应用物元概念和关联函数,确定了玉米螟种群动态分级识别的的经典域物元和节域物元,提出了一种新的基于可拓分析的信息模式识别方法,并探讨了其应用.应用结果表明,历史拟合率达100%,1995、1996两年预报,其结果与实际一致.说明该识别方法具有良好的应用前景,一种全新的模式识别分类器.     

可拓营销理论研究

利用物元理论、事元理论和可拓集合理论 ,对需要、产品、市场、资源、企业等进行可拓分析 ,提出可拓营销的基本理论——产品开拓规律、可拓市场、可拓资源、健全企业等     

可拓集合上的关系

本文给出可拓集合Ｘ到Ｙ上的关系Ｒ的概念，并讨论了可拓集合关系Ｒ的一般性质。     

一类物元可拓集的性质研究

提出了物元等价类概念,并利用子集合X和属性子集R对物元集合S(U,A,V,f)在集合论域U上构造了一类可拓集合A~,并讨论了A~关于X和R的一些相关性质.     

Soft set theory based on its extension

In this paper, we point out a defect that the definitions of soft subset and soft intersection in Maji’s paper are partial definitions, and then we introduce extension of soft set to redefine and simplify operations between soft sets. At last, we obtain some algebraic properties of new soft operations.     

On the Extension of PM-Ring

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Topological affine spaces

Some characterizations of the topological affine spaces are already known [2,5,6]; they are given via the topologies on the sets of points and hyperplanes. According to the definition made by Sörensen in [6], a topological affine space is an affine space whose sets of points and hyperplanes are endowed with non-trivial topologies such that the joining of n independent points, the intersection of n independent hyperplanes and the construction of parallel hyperplanes are continuous operations. In this paper we give a new characterization of such spaces by means of the topologies on the sets of points and lines.The author wishes to thank the University of Hannover, West Germany, for its hospitality during the time of this research. This work was supported by CNR (National Research Council of Italy).     

Convex extensions of the convex set valued maps

In this article the existence of the convex extension of convex set valued map is considered. Conditions are obtained, based on the notion of the derivative of set valued maps, which guarantee the existence of convex extension. The conditions are given, when the convex set valued map has no convex extension. The convex set valued map is specified, which is the maximal convex extension of the given convex set valued map and includes all other convex extensions. The connection between Lipschitz continuity and existence of convex extension of the given convex set valued map is studied.     

Arithmetical distributions and the sequential extension of binary relations

With the help of an iterative process, we define a fairly broad class of arithmetical distributions on which continuous operations of addition, multiplication, and differentiation are defined. The multiplication of arithmetical distributions that we introduce is made consistent with the known definitions of the product of distributions. The results obtained can be used to justify the passage to the limit in the study of nonlinear problems of mathematical physics. Formalizing our approach, we describe a construction of an extension of binary relations, which is called sequential extension, from a dense subset to the whole topological space. These results are extended to operations of the first order. We show that the sequential extension of differentiation from the set of infinitely differentiable functions to the set of distributions coincides up to isomorphism with the generalized differentiation of distributions. Translated fromMatematicheskie Zametki, Vol. 65, No. 6, pp. 836–853, June, 1999.     

基于语言值的变权综合决策方法

给出一种新的语言值乘法和加法运算,同时利用扩展原理、格贴近度和择近原则等理论论证所给运算法则的科学性,在此基础上建立一个基于二元组的纯语言值加权综合决策模型,随后,在语言值与实数集[0,1]之间定义两个转换函数,由此引入语言值效用向量等概念,借助语言值效用向量和实数型状态变权向量导出语言值状态变权向量,进而建立相应的语言值变权公式和变权综合决策模型。     

信息代数紧扩张的一种新方法

本文研究了从一般信息代数获取紧信息代数的一种新方法.通过在一个信息代数的定向集族上建立一个等价关系,证得相应的等价类全体之集关于联合和聚焦两种运算构成了原信息代数的一个紧扩张.     

The arithmetic extensions of a numerical semigroup

Abstract

In this paper we introduce the notion of extension of a numerical semigroup. We provide a characterization of the numerical semigroups whose extensions are all arithmetic and we give an algorithm for the computation of the whole set of arithmetic extension of a given numerical semigroup. As by-product, new explicit formulas for the Frobenius number and the genus of proportionally modular semigroups are obtained.