Related papers: Multi-granular Perspectives on Covering
Networks can be highly complex systems with numerous interconnected components and interactions. Granular computing offers a framework to manage this complexity by decomposing networks into smaller, more manageable components, or granules.…
Covering-based rough set theory is an extension to classical rough set. The main purpose of this paper is to study covering rough sets from a topological point of view. The relationship among upper approximations based on topological spaces…
In digital-based information boom, the fuzzy covering rough set model is an important mathematical tool for artificial intelligence, and how to build the bridge between the fuzzy covering rough set theory and Pawlak's model is becoming a…
Covering-based rough set theory is a useful tool to deal with inexact, uncertain or vague knowledge in information systems. Topology, one of the most important subjects in mathematics, provides mathematical tools and interesting topics in…
Concise granule descriptions for definable granules and approaching descriptions for indefinable granules are challenging and important issues in granular computing. The concept with only common attributes has been intensively studied. To…
The connection between the theory of permutation orbifolds, covering surfaces and uniformization is investigated, and the higher genus partition functions of an arbitrary permutation orbifold are expressed in terms of those of the original…
The arrangements of particles and forces in granular materials have a complex organization on multiple spatial scales that ranges from local structures to mesoscale and system-wide ones. This multiscale organization can affect how a…
The quest for regular models of arithmetic surfaces allows different viewpoints and approaches: using valuations or a covering by charts. In this article, we sketch both approaches and then show in a concrete example, how surprisingly…
Consider a graph with a rotation system, namely, for every vertex, a circular ordering of the incident edges. Given such a graph, an angle cover maps every vertex to a pair of consecutive edges in the ordering -- an angle -- such that each…
Covering is an important type of data structure while covering-based rough sets provide an efficient and systematic theory to deal with covering data. In this paper, we use boolean matrices to represent and axiomatize three types of…
An abundance of real-world problems manifest as covering edges and/or vertices of a graph with cliques that are optimized for some objectives. We consider different structural parameters of graph, and design fixed-parameter tractable…
Theories of rough sets and soft sets are powerful mathematical tools for modelling various types of vagueness. Hybrid model combining a rough set with a soft set which is called soft rough set proposed by Feng et al. [3] in 2010. In this…
Covering theory is an important tool in representation theory of algebras, however, the results and the proofs are scattered in the literature. We give an introduction to covering theory at a level as elementary as possible.
Multi-scale structures are prevalent in both natural and artificial systems, as they can handle increasing complexity. Several terms are employed almost interchangeably across various application domains to refer to the multi-scale concept…
In this paper, we provide a comprehensive rigorous modeling for multidimensional spaces with hierarchically structured dimensions in several layers of abstractions and data cubes that live in such spaces. We model cube queries and their…
Many different and complementary strategies for translating the basic principle of multiple topological imaging into observational analysis are now available, both for three-dimensional and two-dimensional catalogues.
Polymer materials have the characteristic feature that they are multiscale systems by definition. Already the description of a single molecules involves a multitude of different scales, and cooperative processes in polymer assemblies are…
This article is a gentle introduction to the mathematical area known as circle packing, the study of the kinds of patterns that can be formed by configurations of non-overlapping circles. The first half of the article is an exposition of…
Collective classification models attempt to improve classification performance by taking into account the class labels of related instances. However, they tend not to learn patterns of interactions between classes and/or make the assumption…
Multi-view clustering has been widely used in recent years in comparison to single-view clustering, for clear reasons, as it offers more insights into the data, which has brought with it some challenges, such as how to combine these views…