求模糊关系传递闭包的一种算法

根据模糊关系的传递性的特征,文章提出了利用相应的模糊矩阵求有限论域上模糊关系的传递闭包的一种计算方法,该算法可以加快获得传递闭包的速度。通过实例说明了该算法是简便、实用的。     

一种求布尔矩阵传递闭包的基于自反矩阵构造的平方算法

首先,介绍布尔矩阵传递闭包的概念及计算问题;随后,分析布尔矩阵的传递闭包和由该布尔矩阵与单位矩阵取并所得到的自反矩阵的传递闭包之间的关系;最后,利用上述结果给出一种求解布尔矩阵传递闭包的基于自反矩阵构造的平方算法,并通过实例说明了其具体计算过程.     

Fuzzy矩阵的广义传递闭包

本文给出了Fuzzy矩阵广义传递闭包的概念,并讨论了它的简单性质和计算方法     

模糊关系矩阵传递闭包的Warshall算法

通过对照关系的传递闭包和模糊关系的传递闭包，把求关系矩阵的传递闭包的算法完整地推广到模糊关系矩阵上。     

相似矩阵与等价矩阵的收敛性及其传递闭包

利用模糊矩阵的有向伴随图,探讨了模糊相似矩阵与模糊等价矩阵的收敛性,证明了模糊相似矩阵与模糊等价矩阵的收敛指数.然后通过计算模糊相似矩阵的传递闭包,给出了改造模糊相似矩阵使之成为模糊等价矩阵的一条简单途径.最后通过一个关于模糊聚类分析的算例,展现了基于模糊相似矩阵的传递闭包法在农业蝗灾防控中的应用.     

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。     

利用关系矩阵求传递闭包的一种方法

介绍了一种利用关系矩阵求有限集合上二元关系的传递闭包的方法 ,该方法简便、实用 .还可用此方法计算有向图的可达性矩阵 .     

模糊k-强传递阵

推广强传递阵 ,给出 k-强传递阵的概念 ,讨论它的等价刻画、与截阵性质一致问题 ,证明文献中几种传递性概念与强传递的等价性 ,丰富了模糊矩阵传递性的研究内容。     

模糊关系传递性有关指标之间的关系

研究模糊关系与传递性有关的指标,这些指标包括T-传递指标、S-负传递指标、T-S-半传递指标、T-S-Ferrers关系指标等,详细讨论了它们之间的关系,从而推广了Fodor和王有关传递性性质之间的相关结果.     

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。     

Transitive Limit Closures of Convex Dynamical Systems

Convex dynamical systems are iterated set-valued maps with convex graphs. The closed union of all finite powers of a given convex relation will be called its limit closure. We address the question of transitivity of limit closures and establish a sufficient condition for such transitivity (limit transitivity). We also present examples showing that the limit closure of a general compact convex system is not necessarily transitive. limit closure can be intransitive as well. It is also shown that the restriction of a linear single-valued map to a convex set containing an open neighborhood of the origin is always limit transitive.     

A method for obtaining transitive approximations of a binary relation

A binary relation R does not always possess the desirable property of transitivity. Consequently, this needs to be imposed artificially by deviating as little as possible from R. In this paper, three approaches to transitive approximation are analyzed within a common distance-based framework: exterior (transitive closure), interior (openings or maximal transitive sub-relations contained in R) and mixed (transitive fittings) approximation. Additionally, we propose a method for obtaining all these transitive approximations. The method is based on a distance function optimization framework that leads to straightforward goal programming models.     

On the transitivity property

In this short note general transitivity properties of fuzzy binary relations are discussed. It is shown that under some weak conditions any fuzzy binary relation can be regarded as a transitive one with respect to a properly chosen t-norm. A representation theorem for such relations is formulated.     

Operations on binary relations

The effects of five basic operations (asymmetrization, complementation, dualization, symmetrization, transitive closure) on binary relations are examined. Identifies between compound operations are developed (e.g. the symmetric part of the transitive closure of the complement of the transitive closure equals the transitive closure of the symmetric complement of the transitive closure), ordering aspects of compound operations are noted, and it is shown that in addition to the empty and universal relations at most 110 different relations can be generated from a given binary relation by sequential applications of the five basic operations. Moreover, 110 is the least upper bound, and none of these 110 requires more than seven applications of the basic operations for its expression. One of the potentially irreducible compound operations of length seven is cstcatc, the complement of the symmetric part of the transitive closure of the complement of the asymmetric part of the transitive closure of the complement.     

Making choices with a binary relation: Relative choice axioms and transitive closures

This article presents an axiomatic analysis of the best choice decision problem from a reflexive crisp binary relation on a finite set (a digraph). With respect to a transitive digraph, optimality and maximality are usually accepted as the best fitted choice axioms to the intuitive notion of best choice. However, beyond transitivity (resp. acyclicity), optimality and maximality can characterise distinct choice sets (resp. empty sets). Accordingly, different and rather unsatisfying concepts have appeared, such as von Neumann–Morgenstern domination, weak transitive closure and kernels. Here, we investigate a new family of eight choice axioms for digraphs: relative choice axioms. Within choice theory, these axioms generalise top-cycle for tournaments, gocha, getcha and rational top-cycle for complete digraphs. We present their main properties such as existence, uniqueness, idempotence, internal structure, and cross comparison. We then show their strong relationship with optimality and maximality when the latter are not empty. Otherwise, these axioms identify a non-empty choice set and underline conflicts between chosen elements in strict preference circuits. Finally, we exploit the close link between this family and transitive closures to compute choice sets in linear time, followed by a relevant practical application.     

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。     

模糊粗糙近似算子的拓扑性质

考虑论域上一二元关系所决定的模糊粗糙近似算子的拓扑性质,证明了任一自反二元关系可以决定一模糊拓扑.并且,当二元关系自反对称时,该模糊拓扑中的元是开集当且仅当它是闭集;当二元关系自反传递时,该模糊拓扑的闭包与内部算子恰为模糊粗糙上、下近似算子.     

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.     

Calculating Exact Transitive Closure for a Normalized Affine Integer Tuple Relation

An approach to calculate the exact transitive closure of a parameterized and normalized affine integer tuple relation is presented. A relation is normalized when it describes graphs of the chain topology only. The exact transitive closure calculation is based on resolving a system of recurrence equations being formed from the input and output tuples of a normalized relation. The approach permits for calculating an exact transitive closure for a relation when the constraints of this closure are represented by both affine and non-linear forms. An example of calculating the exact transitive closure of normalized affine integer tuple relation is presented.