Division of mappings between complete lattices
نویسنده
چکیده
The importance for image processing of a good theory for morphological operators in complete lattices is now well understood. In this paper we introduce inverses and quotients of mappings between complete lattices which are analogous to inverses and quotients of positive numbers. These concepts are then used to create a convenient formalism for dilations and erosions as well as for cleistomorphisms (closure operators) and anoiktomorphisms (kernel operators).
منابع مشابه
ALGEBRAIC GENERATIONS OF SOME FUZZY POWERSET OPERATORS
In this paper, let $L$ be a completeresiduated lattice, and let {bf Set} denote the category of setsand mappings, $LF$-{bf Pos} denote the category of $LF$-posets and$LF$-monotone mappings, and $LF$-{bf CSLat}$(sqcup)$, $LF$-{bfCSLat}$(sqcap)$ denote the category of $LF$-completelattices and $LF$-join-preserving mappings and the category of$LF$-complete lattices and $LF$-meet-preserving mapping...
متن کاملSome results on $L$-complete lattices
The paper deals with special types of $L$-ordered sets, $L$-fuzzy complete lattices, and fuzzy directed complete posets.First, a theorem for constructing monotone maps is proved, a characterization for monotone maps on an $L$-fuzzy complete lattice is obtained, and it's proved that if $f$ is a monotone map on an $L$-fuzzy complete lattice $(P;e)$, then the least fixpoint of $f$ is meet of a spe...
متن کاملConnecting Many-valued Contexts to General Geometric Structures
We study the connection between certain many-valued contexts and general geometric structures. The known one-to-one correspondence between attribute-complete many-valued contexts and complete affine ordered sets is used to extend the investigation to π-lattices and class geometries. The former are identified as a subclass of complete affine ordered sets, which exhibit a close relation to concep...
متن کاملQ-sup-algebras and their representation
The topic of sets with fuzzy order relations valuated in complete lattices with additional structure has been quite active in the recent decade, and a number of papers have been published (see [3, 5, 6] among many others). Based on a quantale-valued order relation and subset membership, counterparts to common order-theoretic notions can be defined, like monotone mappings, adjunctions, joins and...
متن کاملNote on formal contexts of generalized one - sided concept lattices ∗
Generalized one-sided concept lattices represent one of the conceptual data mining methods, suitable for an analysis of object-attribute models with the different types of attributes. It allows to create FCA-based output in form of concept lattice with the same interpretation of concept hierarchy as in the case of classical FCA. The main aim of this paper is to investigate relationship between ...
متن کامل