Conceptual neighborhood graphs capture the similarity among qualitative relations. This paper derives the graphs for the thirty-three topological relations between two crisp, undirected lines and for the seventy-seven topological relations between two lines with uncertain boundaries. The analysis of the graphs shows that the normalized node degrees increases, from the crisp to the broad-boundar...

A current trend in the development of spatial-relation ontologies is to capture more and more details about the geometries of the spatial objects that are related, primarily by topological relations. In an effort to bridge between often disparate approaches, a reference system for topological relations between compound spatial objects is introduced. Its framework comprises the base relations’ c...

This paper derives and compares two strategies for minimizing topological constraints in a query expressed by a visual example: (1) elimination of topological relations that are implied uniquely by composition and (2) restriction to topological relations that relate near-neighbor objects, as determined by a Delaunay triangulation. In both cases, the query processing approach is to solve a const...

This paper is concerned with the existence of periodic travelling wave solutions of reactiondiffusion equations, which arise as models of predator-prey interactions in mathematical ecology. The relevant equations are somewhat similar to the Fitz-Hugh-Nagumo equations, and our results apply to this latter system as well. In studying the Fitz-Hugh-Nagumo equations, Conley ([ 3 I), initiated a new...

A self-organizing map (SOM) algorithm can generate a topographic map from a high-dimensional stimulus space to a low-dimensional array of units. Because a topographic map preserves neighborhood relationships between the stimuli, the SOM can be applied to certain types of information processing such as data visualization. During the learning process, however, topological defects frequently emerg...

Based on a complete Heyting algebra, we modify the definition of lattice-valued fuzzifying convergence space using fuzzy inclusion order and construct in this way a Cartesian-closed category, called the category of L−ordered fuzzifying convergence spaces, in which the category of L−fuzzifying topological spaces can be embedded. In addition, two new categories are introduced, which are called th...

This paper considers fuzzifying topologies, a special case of I-fuzzy topologies (bifuzzy topologies), introduced by Ying [25]. It investigates topological notions defined by means of  -open sets when these are planted into the framework of Ying’s fuzzifying topological spaces (by Łukasiewicz logic in [0, 1]). In this paper we introduce some sorts of operations, called general fuzzifying opera...

In spatial data models for various applications, such as geographical information systems (GISs), the importance of topological relations is widely recognized. Topology makes very general statements about the structure and the relations of spatial objects. A refinement of topology by means of other geometric aspects can help to bend the various models that have been developed for topological re...

The underlying idea of the ESOM [2] is to incorporate the topological neighborhood preserving property of Self-Organizing Map (SOM) and the convex-hull property (a global optimality) of TSP together. The learning rule of its generalized version is as follows: ! w j(t+ 1) = cj(t) [ ! w j(t) + j(t) ( ! x t !w j(t))] where !w j is the weight of jth neuron, !x t the input city coordinate, cj(t) the...