Syndetically proximal pairs

For continuous self-maps of compact metric spaces, we study the syndetically proximal relation, and in particular we identify certain sufficient conditions for the syndetically proximal cell of each point to be small. We show that any interval map f with positive topological entropy has a syndetically scrambled Cantor set, and an uncountable syndetically scrambled set invariant under some power of f. In the process of proving this, we improve a classical result about interval maps and establish that if f is an interval map with positive topological entropy and m?2, then there is n∈N such that the one-sided full shift on m symbols is topologically conjugate to a subsystem of fn² (the classical result gives only semi-conjugacy).     

一致性互反Fuzzy判断矩阵的传递性

研究矩阵元素为Fuzzy数的互反判断矩阵的传递性质.首先得到了判断两个Fuzzy数近似相等的等价条件,并得到了揭示Fuzzy数的核之间关系的一个充要条件.在此基础上,进一步证明了一致性互反Fuzzy判断矩阵具有传递性的两个结论.这两个结论说明:在层次分析法中,用一致性互反Fuzzy判断矩阵表示一组方案在同一目标下的两两重要性比较是符合理性决策的思维特征的.     

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。     

积逻辑系统中的广义重言式

讨论积逻辑系统中的广义重言式理论 ,给出积逻辑系统中子代数和广义重言式的一系列性质。本文的主要结果表明 ,在几个重要的逻辑系统中 ,标准积逻辑系统具有最简单的广义重言式结构 ,而在推理过程中 ,它具有较差的真值传递性。     

模糊量排序综述

对模糊量排序研究作一个全面回顾 ,包括排序问题的描述、应用背景、排序指标综述及分类、排序方法的合理性、排序方法之间的联系等方面。     

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。     

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.     

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.     

Rational choice based on vague preferences

This paper studies vague preferences. In contrast to the concept of fuzzy preferences, the more general notion of vague preferences does not entail the assumption that the different degrees of preference are completely ordered. It is shown that the more general concept of a vague preference order arises very naturally in the context of aggregating a set of (exact) weak orders. Furthermore, necessary and sufficient conditions for the rationalizability of an exact choice function by means of a vague preference order are given. It turns out that in the general case these conditions are weaker than in the case where the degrees of preference are completely ordered. Consequently, there exist choice functions which are rationalizable by a general vague preference order but which are not rationalizable by a fuzzy preference order, or more generally by any vague preference order which induces a complete ranking of the degrees of preference. Examples of such choice functions are provided.This is a revised version of a discussion paper which was written at the University of Karlsruhe. I am grateful to Georg Bol and an anonymous referee for valuable comments. The research has been made possible by a fellowship of the DFG (Deutsche Forschungsgemeinschaft) which is also gratefully acknowledged.