In this study the author discusses the problem of defuzzification by minimizing the weighted distance between two fuzzy quantities. Also, this study obtains the nearest point with respect to a fuzzy number and shows that this point is unique relative to the weighted distance. By utilizing this point, a method is presented for effectively ranking fuzzy numbers and their images to overcome the de...

This paper addresses the problem of finding k nearest neighbors for moving query point (we call it k-NNMP). It is an important issue in both mobile computing research and real-life applications. The problem assumes that the query point is not static, as in k-nearest neighbor problem, but varies its position over time. In this paper, four different methods are proposed for solving the problem. D...

We propose a nearest point algorithm (NPA) for optimization of a family of Support Vector Machines (SVM) methods. Geometrically, optimizing SVM corresponds to finding the nearest points between two polyhedrons. In classification, the hard margin case corresponds to finding the closest points of the convex hull of each class. The soft margin case corresponds to finding the closest points in the ...

In this paper, we provide a simple approximation for the distance from an arbitrary location to the kth nearest point. Distance is measured as the Euclidean and the rectilinear distances on a continuous plane. The approximation demonstrates that the kth nearest distance is proportional to the square root of k and inversely proportional to the square root of the density of points. The accuracy o...

If we pick n random points uniformly in [0, 1]d and connect each point to its k−nearest neighbors, then it is well known that there exists a giant connected component with high probability. We prove that in [0, 1]d it suffices to connect every point to cd,1 log logn points chosen randomly among its cd,2 logn−nearest neighbors to ensure a giant component of size n− o(n) with high probability. Th...

Consider that the coordinates of N points are randomly generated along the edges of a d-dimensional hypercube (random point problem). The probability that an arbitrary point is the mth nearest neighbor to its own nth nearest neighbor (Cox probabilities) plays an important role in spatial statistics. Also, it has been useful in the description of physical processes in disordered media. Here we p...