This paper revisits conceptual neighborhood graphs for the topological relations between two regions, in order to bridge from the A-B-C neighborhoods defined for interval relations in R to region relations in R and on the sphere S. A categorization of deformation types—built from same and different positions, orientations, sizes, and shapes—gives rise to four different neighborhood graphs. They...

The original definition of a topological space given by Hausdorff used neighborhood systems. Lattice-valued maps appear in this context when you identify a topology with a monoid in the Kleisli category of the filter monad on SET. H?hle’s notion of a lattice-valued topology [2] uses the same idea and it’s inspired in the classical lattice-valued topologies. Ltopological spaces are motivated by ...

This paper, gives an answer for the Question 1.1 posed by Hitzler (Generalized metrics and topology in logic programming semantics, 2001) by means of "Topological aspects of d-metric space with d-neighborhood system". We have investigated the topological aspects of a d-neighborhood system obtained from dislocated metric space (simply d-metric space) which has got useful applications in the sema...

As explained in the lecture "Introduction", topological notions of connectedness and of the boundary of a subset are important for image analysis. The widely used concept of m, nadjacencies defines these notions not satisfactorily: different adjacencies for the foreground and background are only applicable for binary images. A subset has two boundaries: the inner and the outer ones. They do not...

This paper describes the definition and testing of a new type of median filter for images. The topological median filter implements some existing ideas and some new ideas on fuzzy connectedness to improve, over a conventional median filter, the extraction of edges in noise. The concept of alpha-connectivity is defined and used to create an algorithm for computing the degree of connectedness of ...

the neighborhood has had a long history in iranian urbanization. since urban plans wereintroduced by the authorities to shape urban development in iran half a century ago, the concept of iranian traditional neighborhood has been neglected gradually. the concept of neighborhood has not found the appropriate status in urban design and planning yet. one of the main reasons is that academics, profe...

We introduce the notion of N-topo nilpotent fuzzy set in a fuzzy neighborhood ring and develop some fundamental results. Here we show that a fuzzy neighborhood ring is locally inversely bounded if and only if for all 0 < α < 1, the α-level topological rings are locally inversely bounded. This leads us to prove a characterization theorem which says that if a fuzzy neighborhood ring on a division...

1. Interior Transformations.-The objective of the authors is to find out what properties of meromorphic functions are essentially topological in character, and by the introduction of appropriate topological concepts and methods to extend and simplify the present theory. To that end it is natural to replace the class of meromorphic functions by their topological generalizations, the interior tra...