Abstract The Alexandrov L -fuzzy nearness is a new addition to the systems that base for intelligent and its wide applications in various fields. This paper represents connections among such as: rough sets, semi-topogenous orders uniformities complete residuated lattices. Moreover, we show there Galois correspondence between categories of those mentioned systems.

Considering a commutative unital quantale L as the truth value table and using the tool of L-generalized convergence structures of stratified L-filters, this paper introduces a kind of fuzzy upper topology, called fuzzy S-upper topology, on L-preordered sets. It is shown that every fuzzy join-preserving L-subset is open in this topology. When L is a complete Heyting algebra, for every completel...

This paper presents, by means of Alexandrov topology for fuzzy preordered sets and specialization order for fuzzy topological spaces, a systematic investigation of the interrelationship between fuzzy preordered sets, topological spaces, and fuzzy topological spaces. © 2006 Elsevier B.V. All rights reserved.

Let X be a topological space equipped with a collection P of continuous paths. Associated to the pair (X,P) we define a path topology that generalizes the P-topology of Hawking et al. [1] Moreover, we axiomatize a collection P that generates an order that we call an NRT full order. This in turn generalizes the chronology order of spacetime defined via timelike paths. We also investigate the ass...

As a contribution to higher dimensional spatial data modelling this article introduces a novel approach to spatial database design. Instead of extending the canonical Solid-Face-Edge-Vertex schema of topological data, these classes are replaced altogether by a common type SpatialEntity, and the individual “bounded-by” relations between two consecutive classes are replaced by one separate binary...

We study hierarchies of partitions in a topological space where the interiors of the classes and their frontiers are simultaneously represented. In both continuous and discrete spaces our approach rests on tessellations whose classes are R-open sets. In the discrete case, the passage from partitions to tessellations is expressed by the Alexandrov topology and yields double resolutions. A new to...

The purpose of this paper is to present an optimal sphere theorem for metric spaces analogous to the celebrated Rauch-Berger-Klingenberg Sphere Theorem and the Diameter Sphere Theorem in riemannian geometry. There has lately been considerable interest in studying spaces which are more singular than riemannian manifolds. A natural reason for doing this is because Gromov-Hausdorff limits of riema...

We continue to study one of the classic problems in general topology raised by P. S. Alexandrov: when a Hausdorff space X has continuous bijection (a condensation) onto compactum? concentrate on situation not only but also $$X\setminus Y$$ can be condensed compactum whenever cardinality Y does exceed certain $$\tau$$ .

In this paper, we investigate the properties of L-lower approximation operators as a generalization of fuzzy rough set in complete residuated lattices. We study relations lower (upper, join meet, meet join) approximation operators and Alexandrov L-topologies. Moreover, we give their examples as approximation operators induced by various L-fuzzy relations.