$L$-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...

This paper proposes a new methodology for computing Hausdorff distances between sets of points in a robust way. In a first step, robust nearest neighbor distance distributions between the two sets of points are obtained by considering reliability measures in the computations through a Monte Carlo scheme. In a second step, the computed distributions are operated using random variables algebra in...

in this manuscript, we study the inverse problem for non self-adjoint sturm--liouville operator $-d^2+q$ with eigenparameter dependent boundary and discontinuity conditions inside a finite closed interval. by defining  a new hilbert space and  using its spectral data of a kind, it is shown that the potential function can be uniquely determined by part of a set of values of eigenfunctions at som...

We determine the Euclidean distance degree of a projective toric variety. This extends the formula of Matsui and Takeuchi for the degree of the A-discriminant in terms of Euler obstructions. Our primary goal is the development of reliable algorithmic tools for computing the points on a real toric variety that are closest to a given data point.

In this manuscript, we consider the inverse problem for non self-adjoint Sturm--Liouville operator $-D^2+q$ with eigenparameter dependent boundary and discontinuity conditions inside a finite closed interval. We prove by defining a new Hilbert space and using spectral data of a kind, the potential function can be uniquely determined by a set of value of eigenfunctions at an interior point and p...

In the k-nearest neighbor (KNN) classifier, nearest neighbors involve only labeled data. That makes it inappropriate for the data set that includes very few labeled data. In this paper, we aim to solve the classification problem by applying transduction to the KNN algorithm. We consider two groups of nearest neighbors for each data point — one from labeled data, and the other from unlabeled dat...

w0-Nearest Points and w0-Farthest Point in Normed Linear Spaces

The problem of k-nearest neighbors (kNN) search is to find nearest k neighbors from a given data set for a query point. To speed up the finding process of nearest k neighbors, many fast kNN search algorithms were proposed. The performance of fast kNN search algorithms is highly influenced by the number of dimensions, number of data points, and data distribution of a data set. In the extreme cas...