Related papers: Fuzzy, Neutrosophic, and Uncertain Graph Theory: P…

Graph theory provides fundamental concepts for many fields of science like statistical physics, network analysis and theoretical computer science. Here we give a pedagogical introduction to graph theory, divided into three sections. In the…

Probabilistic graphical modeling is a branch of machine learning that uses probability distributions to describe the world, make predictions, and support decision-making under uncertainty. Underlying this modeling framework is an elegant…

Conceptual Graphs (CG) are a graph-based knowledge representation and reasoning formalism; fuzzy Conceptual Graphs (fCG) constitute an extension that enriches their expressiveness, exploiting the fuzzy set theory so as to relax their…

Graphs are structured data that models complex relations between real-world entities. Heterophilic graphs, where linked nodes are prone to be with different labels or dissimilar features, have recently attracted significant attention and…

Graphs are important data representations for describing objects and their relationships, which appear in a wide diversity of real-world scenarios. As one of a critical problem in this area, graph generation considers learning the…

The new concept of fuzzy interval matrices has been introduced in this book for the first time. The authors have not only introduced the notion of fuzzy interval matrices, interval neutrosophic matrices and fuzzy neutrosophic interval…

The need to measure bias encoded in tabular data that are used to solve pattern recognition problems is widely recognized by academia, legislators and enterprises alike. In previous work, we proposed a bias quantification measure, called…

This chapter explores neural networks, topological data analysis, and topological deep learning techniques, alongside statistical Bayesian methods, for processing images, time series, and graphs to maximize the potential of artificial…

Deep neural networks have enabled researchers to create powerful generalized frameworks, such as transformers, that can be used to solve well-studied problems in various application domains, such as text and image. However, such generalized…

The introduction of Fuzzy Relational Equations (FREs) has made problems that were unsolvable using algebraic linear equations into solvable ones. FREs have been applied to problemsin medicine, industry, transportation and all types of…

Computers and algorithms play an ever-increasing role in obtaining new results in graph theory. In this survey, we present a broad range of techniques used in computer-assisted graph theory, including the exhaustive generation of all…

Dynamic graph learning has gained significant attention as it offers a powerful means to model intricate interactions among entities across various real-world and scientific domains. Notably, graphs serve as effective representations for…

Graph Neural Networks (GNN) provide a powerful framework that elegantly integrates Graph theory with Machine learning for modeling and analysis of networked data. We consider the problem of quantifying the uncertainty in predictions of GNN…

Graph learning from data represents a canonical problem that has received substantial attention in the literature. However, insufficient work has been done in incorporating prior structural knowledge onto the learning of underlying…

Graph neural networks (GNNs) have excelled in various graph learning tasks, particularly node classification. However, their performance is often hampered by noisy measurements in real-world graphs, which can corrupt critical patterns in…

While uncertainty estimation for graphs recently gained traction, most methods rely on homophily and deteriorate in heterophilic settings. We address this by analyzing message passing neural networks from an information-theoretic…

We expand upon a graph theoretic set of uncertainty principles with tight bounds for difference estimators acting simultaneously in the graph domain and the frequency domain. We show that the eigenfunctions of a modified graph Laplacian and…

Graphs are ubiquitous in nature and can therefore serve as models for many practical but also theoretical problems. For this purpose, they can be defined as many different types which suitably reflect the individual contexts of the…

Classification of high dimensional data finds wide-ranging applications. In many of these applications equipping the resulting classification with a measure of uncertainty may be as important as the classification itself. In this paper we…

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…