Related papers: Soft Rough Graphs
Tree sets are abstract structures that can be used to model various tree-shaped objects in combinatorics. Finite tree sets can be represented by finite graph-theoretical trees. We extend this representation theory to infinite tree sets.…
In recent years, deep neural networks (DNNs) have known an important rise in popularity. However, although they are state-of-the-art in many machine learning challenges, they still suffer from several limitations. For example, DNNs require…
We introduce one dimensional sets to help describe and constrain the integral curves of an $n$ dimensional dynamical system. These curves provide more information about the system than the zero-dimensional sets (fixed points) do. In fact,…
Graph databases are becoming widely successful as data models that allow to effectively represent and process complex relationships among various types of data. As with any other type of data repository, graph databases may suffer from…
Causal abstraction provides a theory describing how several causal models can represent the same system at different levels of detail. Existing theoretical proposals limit the analysis of abstract models to "hard" interventions fixing…
In this paper, we introduce the notion of fuzzy soft numbers. Here defined fuzzy soft number and four arithmetic operations $ \tilde{+}, \tilde{-}, \tilde{\times}, \tilde{\div} $ and related properties. Also introduce Hausdorff distance,…
Better representation of the uncertainty in a data visualisation is a focus of recent research activity. A problem with the current literature is that there is a lack of clarity about the definition of uncertainty and what it means to…
A point visibility graph is a graph induced by a set of points in the plane where the vertices of the graph represent the points in the point set and two vertices are adjacent if and only if no other point from the point set lies on the…
In this paper we study a new product of graphs called {\em tight product}. A graph $H$ is said to be a tight product of two (undirected multi) graphs $G_1$ and $G_2$, if $V(H)=V(G_1)\times V(G_2)$ and both projection maps $V(H)\to V(G_1)$…
Graphs and networks provide a canonical representation of relational data, with massive network data sets becoming increasingly prevalent across a variety of scientific fields. Although tools from mathematics and computer science have been…
Graphical models can represent a multivariate distribution in a convenient and accessible form as a graph. Causal models can be viewed as a special class of graphical models that not only represent the distribution of the observed system…
In reliable decision-making systems based on machine learning, models have to be robust to distributional shifts or provide the uncertainty of their predictions. In node-level problems of graph learning, distributional shifts can be…
Graphs are ubiquitous in encoding relational information of real-world objects in many domains. Graph generation, whose purpose is to generate new graphs from a distribution similar to the observed graphs, has received increasing attention…
In the branch of mathematics known as graph theory, graphs are considered as a set of points, called vertices, with connections between these points, called edges. The purpose of this paper is to study mappings between two graphs that have…
Since physical theories employ mathematical models to describe and predict physical phenomena, our knowledge depends on the models available to that end. To increase their scope we present a particular type of simplified models, serial…
This research paper delves into the innovative integration of Shannon entropy and rough set theory, presenting a novel approach to generalize the evaluation approach in machine learning. The conventional application of entropy, primarily…
In this paper, we define a soft somewhat open set using the soft interior operator. We study main properties the class of soft somewhat open sets that is contained in the class soft somewhere dense sets. Then, we introduce the classes of…
We define a free product of connected simple graphs that is equivalent to several existing definitions when the graphs are vertex-transitive but differs otherwise. The new definition is designed for the automorphism group of the free…
The study of machine learning-based logical query answering enables reasoning with large-scale and incomplete knowledge graphs. This paper advances this area of research by addressing the uncertainty inherent in knowledge. While the…
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…