模糊关系的迹与其性质指标之间的关系

讨论用模糊关系的迹去刻画模糊关系的各种性质指标,从而揭示模糊关系的迹与一些性质指标如自反、T-非对称、S-强完全、T-传递、S-负传递指标之间的联系.通过我们的讨论,推广了文献中迹与模糊关系性质联系的相关结果.     

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。     

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。     

模糊关系的对偶合成及其在传递性中的应用

引入了模糊关系的一种新的合成：对偶合成。这种新的合成使我们十分容易地刻画反向传递性。利用合成和对偶合成,我们建立了传递性、反向传递性、半传递性和Ferrers性质的若干有趣的等价条件。     

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。     

-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．     

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.     

求极大T-传递内部的新方法

利用Fodor等的基本思想,从另一个角度构造了一个有限论域上模糊关系的极大T-传递内部,求得另一个与Fodor等的方法不同的极大T-传递内部,并在计算机上加以实现,从而为将一个非传递的模糊关系改造为传递的模糊关系提供了一个新的方法.     

传递系统的伪分解函数和应用

令X为一个紧致度量空间,fX→X为(拓扑)传递的映射.通过对传递系统(X,f)在fn,n∈N的作用下的伪分解,先引入一个新的拓扑不变量"传递系统的PD函数(伪分解函数)".然后,讨论关于此不变量的一些重要性质.最后,把关于周期轨道的Sharkovskii定理推广到传递子系统上.     

传递系统的伪分解函数和应用

令X为一个紧致度量空间,f:x→X为(拓扑)传递的映射.通过对传递系统(X,f)在fn,n∈N的作用下的伪分解,先引入一个新的拓扑不变量“传递系统的PD函数(伪分解函数)”. 然后,讨论关于此不变量的一些重要性质.最后,把关于周期轨道的Sharkovskii定理推广到传递子系统上.     

高等数学中几个概念之间的关系

对高等数学中导数的单侧极限与单侧导数、可导与连续、函数单调性与函数极值之间的关系进行探讨,对相关命题的正误进行辨析,以利于学生对概念的理解和相关知识的掌握.     

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.     

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     

The fluted fragment with transitive relations

The fluted fragment is a fragment of first-order logic (without equality) in which, roughly speaking, the order of quantification of variables coincides with the order in which those variables appear as arguments of predicates. It is known that this fragment has the finite model property. We consider extensions of the fluted fragment with various numbers of transitive relations, as well as the equality predicate. In the presence of one transitive relation (together with equality), the finite model property is lost; nevertheless, we show that the satisfiability and finite satisfiability problems for this extension remain decidable. We also show that the corresponding problems in the presence of two transitive relations (with equality) or three transitive relations (without equality) are undecidable, even for the two-variable sub-fragment.     

Categories of Relations and Functional Relations

We define relations and their composition in a category with (E, M)-factorization structure, with M consisting of monomorphisms, but E not restricted to epimorphisms. We obtain an associativity criterion for composition of relations, and we study functional and induced relations. We show that under our assumptions, the categories of relations on functional and induced relations are isomorphic to the category of relations for the given category.     

Scoring rule and majority agreements for large electorates with arbitrary preferences

This paper examines elections among three candidates when the electorate is large and voters can have any of the 26 nontrivial asymmetric binary relations on the candidates as their preference relations. Comparisons are made between rule-λ rankings based on rank-order ballots and simple majorities based on the preference relations. The rule-λ ranking is the decreasing point total order obtained when 1, λ and 0 points are assigned to the candidates ranked first, second and third on each voter's ballot, with 0 ? λ ? 1.Limit probabilities as the number of voters gets large are computed for events such as ‘the first-ranked rule-λ candidate has a majority over the second-ranked rule-λ candidate’ and ‘the rule-λ winner is the Condorcet candidate, given that there is a Condorcet candidate’. The probabilities are expressed as functions of λ and the distribution of voters over types of preference relations. In general, they are maximized at λ = 1/2 (Borda) and minimized at λ = 0 (plurality) and at λ = 1 for any fixed distribution of voters over preference types. The effects of more indifference and increased intransitivity in voter's preference relations are analyzed when λ is fixed.     

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.