Related papers: Near approximations via general ordered topologica…
Uniformity and proximity are two different ways for defining small scale structures on a set. Coarse structures are large scale counterparts of uniform structures. In this paper, motivated by the definition of proximity, we develop the…
Universal approximation theory offers a foundational framework to verify neural network expressiveness, enabling principled utilization in real-world applications. However, most existing theoretical constructions are established by…
Some properties of generalized convexity for sets and for functions are identified in case of the reliability polynomials of two dual minimal networks. A method of approximating the reliability polynomials of two dual minimal network is…
Rough sets are efficient for data pre-processing in data mining. As a generalization of the linear independence in vector spaces, matroids provide well-established platforms for greedy algorithms. In this paper, we apply rough sets to…
Neural network width and depth are fundamental aspects of network topology. Universal approximation theorems provide that with increasing width or depth, there exists a neural network that approximates a function arbitrarily well. These…
The inverse problem of general rough sets, considered by the present author in some of her earlier papers, in one of its manifestations is essentially the question of when an agent's view about crisp and non crisp objects over a set of…
Nearness theory comes into play in homotopy theory because the notion of closeness between points is essential in determining whether two spaces are homotopy equivalent. While nearness theory and homotopy theory have different focuses and…
Graph Spectral Clustering methods (GSC) allow representing clusters of diverse shapes, densities, etc. However, the results of such algorithms, when applied e.g. to text documents, are hard to explain to the user, especially due to…
Visual attributes are great means of describing images or scenes, in a way both humans and computers understand. In order to establish a correspondence between images and to be able to compare the strength of each property between images,…
Mathematicians tend to use the phrase "arbitrarily close" to mean something along the lines of "every neighborhood of a point intersects a set". Taking the latter statement as a technical definition for arbitrarily close leads to an…
In this paper we first introduce the unified definition of the sharp constant that includes constants in three major problems of approximation theory, such as, inequalities for approximating elements, approximation of individual elements,…
Matrix approximation is a common tool in machine learning for building accurate prediction models for recommendation systems, text mining, and computer vision. A prevalent assumption in constructing matrix approximations is that the…
The introduction of covering-based rough sets has made a substantial contribution to the classical rough sets. However, many vital problems in rough sets, including attribution reduction, are NP-hard and therefore the algorithms for solving…
In this paper, using the concept of natural density, we have introduced the notion of rough statistical convergence which is an extension of the notion of rough convergence in a partial metric space. We have defined the set of rough…
This paper investigates the mining of class association rules with rough set approach. In data mining, an association occurs between two set of elements when one element set happen together with another. A class association rule set (CARs)…
Subsethood, which is to measure the degree of set inclusion relation, is predominant in fuzzy set theory. This paper introduces some basic concepts of spatial granules, coarse-fine relation, and operations like meet, join, quotient meet and…
Models for near-rigid shape matching are typically based on distance-related features, in order to infer matches that are consistent with the isometric assumption. However, real shapes from image datasets, even when expected to be related…
A central problem in machine learning is often formulated as follows: Given a dataset $\{(x_j, y_j)\}_{j=1}^M$, which is a sample drawn from an unknown probability distribution, the goal is to construct a functional model $f$ such that…
An S-approximation space is a novel approach to study systems with uncertainty that are not expressible in terms of inclusion relations. In this work, we further examined these spaces, mostly from a topological point of view by a…
This paper further studies the fuzzy rough sets based on fuzzy coverings. We first present the notions of the lower and upper approximation operators based on fuzzy coverings and derive their basic properties. To facilitate the computation…