Connecting Many-valued Contexts to General Geometric Structures
نویسنده
چکیده
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 concept lattices which are closely tied to the corresponding context. The latter can be related to complete affine ordered sets using residuated mappings and the notion of a weak parallelism.
منابع مشابه
CONNECTING T AND LATTICE-VALUED CONVERGENCES
$top$-filters can be used to define $top$-convergence spaces in the lattice-valued context. Connections between $top$-convergence spaces and lattice-valued convergence spaces are given. Regularity of a $top$-convergence space has recently been defined and studied by Fang and Yue. An equivalent characterization is given in the present work in terms of convergence of closures of $top$-filters. M...
متن کاملUNCERTAINTY DATA CREATING INTERVAL-VALUED FUZZY RELATION IN DECISION MAKING MODEL WITH GENERAL PREFERENCE STRUCTURE
The paper introduces a new approach to preference structure, where from a weak preference relation derive the following relations:strict preference, indifference and incomparability, which by aggregations and negations are created and examined. We decomposing a preference relation into a strict preference, anindifference, and an incomparability relation.This approach allows one to quantify diff...
متن کاملCountable composition closedness and integer-valued continuous functions in pointfree topology
For any archimedean$f$-ring $A$ with unit in whichbreak$awedge (1-a)leq 0$ for all $ain A$, the following are shown to be equivalent: 1. $A$ is isomorphic to the $l$-ring ${mathfrak Z}L$ of all integer-valued continuous functions on some frame $L$. 2. $A$ is a homomorphic image of the $l$-ring $C_{Bbb Z}(X)$ of all integer-valued continuous functions, in the usual se...
متن کاملA COMMON FRAMEWORK FOR LATTICE-VALUED, PROBABILISTIC AND APPROACH UNIFORM (CONVERGENCE) SPACES
We develop a general framework for various lattice-valued, probabilistic and approach uniform convergence spaces. To this end, we use the concept of $s$-stratified $LM$-filter, where $L$ and $M$ are suitable frames. A stratified $LMN$-uniform convergence tower is then a family of structures indexed by a quantale $N$. For different choices of $L,M$ and $N$ we obtain the lattice-valued, probabili...
متن کاملGeometric Classification of Commutative Algebras of Ordinary
1. The purpose of this paper is to give a geometric classification of all commutative algebras consisting of linear ordinary differential operators whose coefficients are scalar-valued functions. The problem of determining commuting ordinary differential operators has a long history in mathematics – it started in 1879. Since then it has been studied by many people in various contexts and from d...
متن کامل