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。     

关于模糊严格偏好关系的传递性

给定一个模糊关系,Ovchinnikov和Roubens引进了非常一般的模糊严格偏好关系定义,本文将详细讨论该偏好关系的弱传递性,一致性,强传递性以及非循环性等传递性有关的性质。     

-可分解Fuzy关系及其*-传递性

对［０，１］上一般的算子‘＊’引入＊－紧Ｆｕｚｚｙ关系及其○＊－可分解Ｆｕｚｙ关系的概念，证明了有单位元１的保序算子‘＊’及有单位元０的保序算子‘＊－’所定义的○＊－可分解和○＊－－可分解Ｆｕｚｚｙ关系在某种意义上构成了新的可传递Ｆｕｚｚｙ关系类，并且还给出了这些类在不同类型的传递性之间的一种位置关系，特别地，对二元○∨－可分解Ｆｕｚｚｙ关系，该文还得到了一个关于其传递性的完全刻画．     

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。     

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。     

少数服从多数规则的特性

假定投票人的人数是奇数，E．S．Maskin引入传递性刻画了少数服从多数规则的特性．Campbell和Kelly试图将E．S．Maskin的理论推广到投票人的人数是任意整数的情形，用有限传递性来刻画少数服从多数规则的特性．我们发现存在这样的少数服从多数规则，它满足无关方案独立性条件并且认为任意两个不同的备选方案都是有差异的，但却不一定满足有限传递性．所以，用有限传递性来刻画少数服从多数规则的特性就有一定缺陷．本文对满足无关方案独立性的少数服从多数规则特性进行了重新刻画，并弱化了有关条件．     

Schubert修正的紧凑形式

在本文中我们推导出了Schubert修正的紧凑形式，该紧凑形式保留了Schubert修正的稀疏传递性，还可使我们利用有记忆算法有效的求解一定的非线性方程组。     

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 .     

关于Morse对度量传递性的猜想

度量传递性蕴含拓扑传递性为一已知的结论,然而,反之如何,则是一个没有得到解决的问题,在1946和1973年,Morse曾先后两次提到这个问题,并猜想说:对于解析系统或具有某种光滑性的系统,上述逆定理恐怕是对的,本文对几乎处处解析的C^∞系统否定了Morse的猜想,而对二维环面上的解析系统证实了他的猜想是正确的。     

争鸣

问 题 问题29 某人为了说明充分条件不具有传递性,举了如下两个反例: 例1 矩形(?)平行四边形(?)对角线不一定相等.我们看出,矩形不是“对角线不一定相等的四边形”的充分条件,也就是说 A(?)B(?)C,不一定有A(?)C.     

Fuzzy partitions and relations; an axiomatic basis for clustering

In this paper some connections between fuzzy partitions and similarity relations are explored. A new definition of transitivity for fuzzy relations yields a relation-theoretic characterization of the class of all psuedo-metrics on a fixed (finite) data set into the closed unit interval. This notion of transitivity also links the triangle inequality to convex decompositions of fuzzy similarity relations in a manner which may generate new techniques for fuzzy clustering. Finally, we show that every fuzzy c-partition of a finite data set induces a psuedo-metric of the type described above on the data.     

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.     

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。     

CELLULAR AUTOMATA FOR THE NETWORK RESEARCHER

Cellular automata (CA) can be used in simulations of network processes and network evolution by identifying adjacent vertices in a network with neighboring cells in a CA. However, there are restrictions on networks that can be represented by two dimensional CAs. For example, the degree of a vertex, the maximum number of unconnected neighbors, and the maximum size of a clique, are limited. Moreover, a high degree of transitivity is built into the two dimensional CA. Increasing the number of dimensions beyond two relaxes all the constraints. Moreover, the reduced transitivity of higher dimensional CAs allows us to vary in a systematic way the “localness” of the connections. Thus, we can examine the differences between strong (local and transitive) versus weak (non-transitive) ties, a difference that Granovetter and others have shown to be important. The paper offers equations describing how maximum degree, maximum clique size, maximum number of unconnected neighbors, and transitivity vary with the dimensions of the CA.     

Fuzzy Transitive Relations

A modified definition of fuzzy transitivity is given.Several properties of this new definition are obtained.Effect of these new properties of transitivity on equivalence relations is also studied.     

Learning intransitive reciprocal relations with kernel methods

In different fields like decision making, psychology, game theory and biology, it has been observed that paired-comparison data like preference relations defined by humans and animals can be intransitive. Intransitive relations cannot be modeled with existing machine learning methods like ranking models, because these models exhibit strong transitivity properties. More specifically, in a stochastic context, where often the reciprocity property characterizes probabilistic relations such as choice probabilities, it has been formally shown that ranking models always satisfy the well-known strong stochastic transitivity property. Given this limitation of ranking models, we present a new kernel function that together with the regularized least-squares algorithm is capable of inferring intransitive reciprocal relations in problems where transitivity violations cannot be considered as noise. In this approach it is the kernel function that defines the transition from learning transitive to learning intransitive relations, and the Kronecker-product is introduced for representing the latter type of relations. In addition, we empirically demonstrate on two benchmark problems, one in game theory and one in theoretical biology, that our algorithm outperforms methods not capable of learning intransitive reciprocal relations.     

Some observations on fuzzy relations over fuzzy subsets

This paper considers fuzzy relations defined over fuzzy subsets and settles some open problems regarding the distributivity and transitivity of such relations