Nowak QUASIORDERS , TOLERANCE RELATIONS AND CORRESPONDING “ PARTITIONS ”
نویسنده
چکیده
The paper deals with a generalization of the notion of partition for wider classes of binary relations than equivalences: for quasiorders and tolerance relations. The counterpart of partition for the quasiorders is based on a generalization of the notion of equivalence class while it is shown that such a generalization does not work in case of tolerances. Some results from [5] are proved in a much more simple way. The third kind of “partition” corresponding to tolerances, not occurring in [5], is introduced.
منابع مشابه
Jagged partitions
By jagged partitions we refer to an ordered collection of non-negative integers (n 1 , n 2 , · · · , n m) with n m ≥ p for some positive integer p, further subject to some weakly decreasing conditions that prevent them for being genuine partitions. The case analyzed in greater detail here corresponds to p = 1 and the following conditions n i ≥ n i+1 − 1 and n i ≥ n i+2. A number of properties f...
متن کاملSearching for Relational Patterns in Data
We consider several basic classes of tolerance relations among objects. These (global) relations are deened from some predeened similarity measures on values of attributes. A tolerance relation in a given class of tolerance relations is optimal with respect to a given decision table A if it contains only pairs of objects with the same decision and the number of such pairs contained in the relat...
متن کاملHierarchical Image Feature Extraction by an Irregular Pyramid of Polygonal Partitions
We present an algorithmic framework for hierarchical image segmentation and feature extraction. We build a successive fine-to-coarse hierarchy of irregular polygonal partitions of the original image. This multiscale hierarchy forms the basis for object-oriented image analysis. The framework incorporates the Gestalt principles of visual perception, such as proximity and closure, and exploits spe...
متن کاملBasics of a formal theory of fuzzy partitions
A theory of fuzzy partitions is an important part of any theory meant to provide a formal framework for fuzzy mathematics. In [3], Henkin-style higher-order fuzzy logic is introduced and proposed as a foundational theory for fuzzy mathematics. Here we investigate the properties of fuzzy partitions within its formal framework. We follow closely the methodology of [2]. Therefore the notions intro...
متن کاملCombinatorics on Brauer-type semigroups
The Brauer semigroup Bn of partitions of a 2n-element set into two-element subsets, can be generalized in various ways. For example we may consider arbitrary partitions to obtain the semigroup Cn. The visualization of elements of these semigroups as chips leads us to the Temperley-Lieb semigroup TLn and its analogue TLCn. We study combinatorial properties of these four semigroups. For example, ...
متن کامل