二级传递性与二级传递模糊矩阵

推广传递性概念,给出二级传递性的定义;研究二级传递模糊矩阵的性质,给出其若干等价刻画;证明二级传递模糊矩阵或者收敛或者周期为2,指数不大于n 1;讨论二级传递与强传递、k-传递和泛传递等概念之间的关系,指出二级传递是传递性概念的一种新的推广形式。     

k-强传递阵

给出k-强传递阵的几个性质，讨论k-强传递阵与强传递阵的关系，并且指出强传递与准传递是等价的。     

广义模糊传递性和形式三传递模糊矩阵

提出广义模糊传递性和形式三传递阵的概念，给出已有模糊传递定义的一种统一形式，确定所有的三传递模糊矩阵，初步理清它们的层次和部分等价关系，为模糊矩阵传递性进一步研究和应用提供背景和方法。     

绝对距离d（R,T）最小的模糊等价矩阵

通常根据样本间某种相关关系得到的模糊关系矩阵不具有传递性，因而不是等价阵，本文讨论了在绝对距离意义下，与最近的模糊等价阵，从图的角度出发，建立与赋权图Ｇ＿、等价阵与树Ｔ之间的联系，得出最优解Ｔ必可在Ｇ＿的生成树集合中找到的结论，同时给出Ｔ必须满足的条件，     

λ型传递矩阵与多因素模糊决策

基于已知常用的模糊矩阵传递性概念定义了λ型传递。给出了它的几个等价条件。研究它的图论特征，指出λ型传递矩阵的圈都过强对边二元圈。随后证明了与全传递模糊矩阵的等价性。进一步研究与截矩阵的性质一致问题，证明了λ型传递满足一致性。最后给出λ型传递在模糊排充中的应用，表明它是一种新的实用的多因素模糊决策的数学模型。     

可控阵的k—泛传递刻画

研究k-泛传递的性质及其图的特征，证明acyclicity阵是可控阵，实现对可控阵的传递性刻画，得到可控阵的图的特征。     

强反传递模糊矩阵及其性质

首先探讨反传递模糊矩阵在网络分析中的意义,进而引入强反传递模糊矩阵概念,给出它的性质及其在网络分析中的应用;其次,研究强反传递模糊矩阵的等价刻画、图论特性、截阵性质、标准形以及周期与指数等问题;最后,给出的判定方法及强反传递圈的求法。     

二元关系的传递性和传递闭包探讨

探讨了二元关系传递性的判定和传递闭包的计算及其教学的有关问题 ,提出了中途点的概念 ,得到传递性在乘幂运算下的不变性 ,以及简化了计算传递闭包的算法 .     

二元关系传递性泛系研究新探

本文基于泛系数学研究和一般事物机理分析的需要，讨论了二元关系对多元关系的传递性，引进一种被叫作“ｇ－传递性”的广义传递概念，考察了它的基本性质，ｇ－传递性不但是普通传递性、拟传递性、半序、拟半序等泛序概念的推广，还包容闭性、凸性、拓扑、对偶性等基本概念为其特例，从而表明这一概念的普适性。     

使无穷小等价成为一个等价关系

修订等价无穷小的定义,可使无穷小量的等价真正成为一种等价关系,即满足自反性,对称性和传递性。     

超空间与原空间动力系统之间的关系

设(X,d,f)为拓扑动力系统,其中X为局部紧可分的可度量化空间,d为紧型度量,f为完备映射,用2X表示由X的所有非空闭子集构成的集族,(2X,ρ,2f)为由(X,d,f)所诱导的赋予hit-or-miss拓扑的超空间动力系统.本文引入了余紧点传递和弱拓扑传递的定义.特别的,在X满足一定的条件时,给出了点传递,弱拓扑传递和余紧点传递之间的关系,并研究了(X,d,f)的余紧传递点,回复点和几乎周期点分别与(2X,ρ,2f)的传递点,回复点和几乎周期点之间的蕴含关系.这些结论丰富了赋予hit-or-miss拓扑的超空间的研究内容.     

Behavior in Repeated Prisoner's Dilemma Games with Shifted Outcomes Analyzed with a Statistical Learning Model

A fuzzy set theoretical framework is proposed for the analysis of sociometric structure characterized by vagueness of liking between individuals and a person's relative degree of belonging to a social group. Max‐min transitivity of a fuzzy relation is employed as a basic concept to examine the degree of liking and clustering in group structures. A distance model based on min‐max transitivity is also formulated as a special case of transitivity analysis. Other notions of transitivity such as the max‐product and the max‐* are also discussed. An empirical analysis is performed to examine the applicability of the proposed transitivity concepts. It appears that the current methodological construct provides a more appropriate perspective in the analysis of the group structure properties.     

关于T传递性与S负传递性之间关系

首先指出文献[1]中关于T传递性与S负传递性的两个不正确的结论，然后在不同的条件下对二者之间的关系进行详细的讨论。     

Hereditarily hypercyclic operators and mixing

We show that hereditary transitivity (respectively strongly hereditary transitivity) is equivalent to weak mixing (respectively strong mixing) in a discrete dynamical system with Polish phase space. We also study the connection between local orbit structure and hypercyclicity, and obtain a “local hypercyclicity criterion.”     

Several transitive properties and Devaney’s chaos

The relation among transitivity, indecomposability and Z-transitivity is discussed. It is shown that for a non-wandering system (each point is non-wandering), indecomposability is equivalent to transitivity, and for the dynamical systems without isolated points, Z-transitivity and transitivity are equivalent. Besides, a new transitive level as weak transitivity is introduced and some equivalent conditions of Devaney's chaos are given by weak transitivity. Moreover, it is proved that both d-shadowing property and d-shadowing property imply weak transitivity.     

直觉模糊度量空间上的半群作用

讨论在直觉模糊度量空间上的拓扑半群作用,引入诸如拓扑传递性,点传递性及点稠传递性等概念.考虑非敏感性与传递性,等度连续等动力学性质的相互关系.     

Fuzzy processing in transitivity development

We review the literature on the development of transitive reasoning, and note three historical stages. Stage 1 was dominated by the Piagetian idea that transitive inference is logical reasoning in which relationships between adjacent terms figure as premises. Stage 2 was dominated by the information-processing view that memory for relationships between adjacent terms is determinative in transitivity performance. Stage 3 has produced data that are inconsistent with both the logic and memery positions, leading to a new theory that is designed to account for such findings, fuzzy-trace theory. The basic assumption of fuzzytrace theory is that reasoners rely on global patterns, or gist. We describe the tenets of fuzzytrace theory, and explore its implications for different theoretical conceptions of logical competence, concluding that young children possess transitivity competence. We discuss the connection between transitivity competence (cognition) and intransitive preferences (metacognition).     

Transitive and fully transitive groups

The notions of transitivity and full transitivity for abelian -groups were introduced by Kaplansky in the 1950s. Important classes of transitive and fully transitive -groups were discovered by Hill, among others. Since a 1976 paper by Corner, it has been known that the two properties are independent of one another. We examine how the formation of direct sums of -groups affects transitivity and full transitivity. In so doing, we uncover a far-reaching class of -groups for which transitivity and full transitivity are equivalent. This result sheds light on the relationship between the two properties for all -groups.

     

On the enumeration of distinct fuzzy switching functions

This paper entails the development of bound equations on the number of minimized fuzzy switching functions. A triangular matrix representing the transitivity between fundamental fuzzy phrases is discussed and applied in the enumeration process. Improved upper and lower bounds have been developed by use of the transitivity matrix. In addition, an algorithm is described to calculate the number of distinct fuzzy switching functions for any number of variables.