$L$-fuzzy rough sets are extensions of the classical rough sets by relaxing theequivalence relations to $L$-relations. The topological structures induced by$L$-fuzzy rough sets have opened up the way for applications of topological factsand methods in granular computing. In this paper, we firstly prove thateach arbitrary $L$-relation can generate an Alexandrov $L$-topology.Based on this fact, w...

Introduction: Graph theoretical analysis of functional Magnetic Resonance Imaging (fMRI) data has provided new measures of mapping human brain in vivo. Of all methods to measure the functional connectivity between regions, Linear Correlation (LC) calculation of activity time series of the brain regions as a linear measure is considered the most ubiquitous one. The strength of the dependence obl...

Self−similarity is a conspicuous feature of many plants. Geometric self−similarity is commonly expressed in terms of affine transformations that map a structure into its components. Here we introduce topological self−similarity, which deals with the configurations and neighborhood relations between these components instead. The topological self−similarity of linear and branching structures is c...

Nowadays, geospatial information systems (GIS) are widely used to solve different spatial problems based on various types of fundamental data: spatial, temporal, attribute and topological relations. Topological relations are the most important part of GIS which distinguish it from the other kinds of information technologies. One of the important mechanisms for representing topological relations...

If Geographic Information Systems (GISs) contain multiple representations of the same geographic objects at different levels of detail, it becomes necessary to compare the different representations and assess whether they contradict each other or not. Topological information is generally considered first-class geographic information and as such the preservation of topological relations among ob...

Turbo similarity searching uses information about the nearest neighbours in a conventional chemical similarity search to increase the effectiveness of virtual screening, with a data fusion approach being used to combine the nearest-neighbour information. A previous paper suggested that the approach was highly effective in operation; this paper further tests the approach using a range of differe...

This work defines and compares three content measures that characterize topological relations between rectangular regions in a two-dimensional space. These content measures use simplified views of spatial objects in order to create an efficient mechanism for capturing the topological content of spatial configurations. The content measures are compared based on the correlation between two simila...