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Takaaki Fujita

Publications and source records attributed to Takaaki Fujita.

14 recordsLinked to original sources
arXiv2026

Representing Higher-Order Networks: A Survey of Graph-Based Frameworks

Many real-world phenomena can be naturally represented using graphs and networks. Classical graph models, however, are generally restricted to pairwise interactions and may therefore be insufficient for capturing the richer structural relationships encountered in practical systems. Higher-order graph formalisms extend the classical framework by incorporating multiway, hierarchical, temporal, multilayer, recursive, and tensor-based interactions, thereby enabling more expressive representations of complex systems. This book provides a comprehensive overview of mathematical concepts and frameworks for modeling higher-order networks. It surveys foundational notions, extended frameworks, and newly introduced formalisms, with particular emphasis on their underlying structural principles, interrelationships, and respective modeling roles. Its primary objective is to offer a unified perspective that enables readers to compare diverse higher-order network models and to identify suitable mathematical tools for both theoretical investigation and practical application. Now in its fourth edition, this volume presents an expanded, revised, and corrected treatment of foundational concepts, established extensions, and recently introduced structures, while maintaining a unifying focus on the relationships among these models. It is intended to serve as a reference for researchers and students studying and comparing higher-order network models in combinatorics, topology, applied mathematics, and related fields.

cs.SI↗
arXiv2026

Fuzzy, Neutrosophic, and Uncertain Graph Theory: Properties and Applications

This book presents a comprehensive and systematic survey of graph theory under uncertainty, with particular emphasis on the unifying role of the uncertain graph framework. It reviews fundamental concepts, structural properties, graph classes, and graph parameters within fuzzy, neutrosophic, and related models, while also introducing a wide range of extensions such as uncertain digraphs, hypergraphs, superhypergraphs, and dynamic graphs. In addition to theoretical developments, the book explores practical applications, including uncertain molecular graphs, decision-making systems, graph neural networks, knowledge graphs, and cognitive maps. By organizing diverse uncertainty-aware graph models within a common perspective, this work provides a coherent framework for understanding their relationships, capabilities, and applications in complex systems.

cs.AI↗
arXiv2026

Various Properties of Various Ultrafilters, Various Graph Width Parameters, and Various Connectivity Systems (with Survey)

This book studies ultrafilters on connectivity systems, that is, on pairs \((X,f)\) where \(X\) is a finite set and \(f:2^{X}\to \mathbb{N}\) is a symmetric submodular function. Ultrafilters, which play a fundamental role in topology and set theory, are considered here in this broader setting, with particular emphasis on their connections to graph width parameters and to the structural analysis of graph complexity. We develop several results on ultrafilters on connectivity systems and examine related notions such as prefilters, ultra-prefilters, and filter subbases. We also discuss additional width-, length-, and depth-type parameters that naturally arise in this framework, thereby broadening the perspective from which graph structure may be studied. In addition, the book compares a wide range of graph width parameters and related concepts, with the aim of providing a unified viewpoint and a useful point of departure for further research in graph theory and computational complexity. More broadly, the book highlights connections with several neighboring areas of mathematics, including set theory, lattice theory, and matroid theory. It also contains survey-style material intended to clarify the current landscape of graph width theory and to stimulate further developments in the subject.

math.CO↗
arXiv2026

Handbook of Rough Set Extensions and Uncertainty Models

Rough set theory models uncertainty by approximating target concepts through lower and upper sets induced by indiscernibility, or more generally, by granulation relations in data tables. This perspective captures vagueness caused by limited observational resolution and supports set-theoretic reasoning about what can be determined with certainty and what remains only possible. This book is written as a map of models. Rather than developing a single algorithmic pipeline in depth, it provides a systematic survey of the main rough set paradigms and their extension routes. More specifically, representative variants are organized according to (i) the underlying granulation mechanism, such as equivalence-based, tolerance-based, covering-based, neighborhood-based, and probabilistic approximations, and (ii) the uncertainty semantics attached to data and relations, such as crisp, fuzzy, intuitionistic fuzzy, neutrosophic, and plithogenic settings. The book also explains how each choice changes the form of approximations and the interpretation of boundary regions. Throughout the book, small illustrative examples are used to clarify modeling intent and typical use cases in classification and decision support. Finally, an important clarification of scope should be noted. Since the main purpose of this book is to provide a map of models, the Abstract and Introduction should not lead readers to expect that feature reduction and rule induction are primary objectives. Although these topics are central in the rough set literature, they are treated here mainly as motivating applications and as entry points to the broader research landscape. The principal aim of the book is to survey and position rough set models and their extensions in a systematic and coherent manner.

cs.AI↗
arXiv2026

Survey of Various Fuzzy and Uncertain Decision-Making Methods

Decision-making in real applications is often affected by vagueness, incomplete information, heterogeneous data, and conflicting expert opinions. This survey reviews uncertainty-aware multi-criteria decision-making (MCDM) and organizes the field into a concise, task-oriented taxonomy. We summarize problem-level settings (discrete, group/consensus, dynamic, multi-stage, multi-level, multiagent, and multi-scenario), weight elicitation (subjective and objective schemes under fuzzy/linguistic inputs), and inter-criteria structure and causality modelling. For solution procedures, we contrast compensatory scoring methods, distance-to-reference and compromise approaches, and non-compensatory outranking frameworks for ranking or sorting. We also outline rule/evidence-based and sequential decision models that produce interpretable rules or policies. The survey highlights typical inputs, core computational steps, and primary outputs, and provides guidance on choosing methods according to robustness, interpretability, and data availability. It concludes with open directions on explainable uncertainty integration, stability, and scalability in large-scale and dynamic decision environments.

cs.AI↗
arXiv2026

A Dynamic Survey of Fuzzy, Intuitionistic Fuzzy, Neutrosophic, Plithogenic, and Extensional Sets

Real-world phenomena often exhibit vagueness, partial truth, and incomplete information. To model such uncertainty in a mathematically rigorous way, many generalized set-theoretic frameworks have been introduced, including Fuzzy Sets [1], Intuitionistic Fuzzy Sets [2], Neutrosophic Sets [3,4], Vague Sets [5], Hesitant Fuzzy Sets [6], Picture Fuzzy Sets [7], Quadripartitioned Neutrosophic Sets [8], Penta-Partitioned Neutrosophic Sets [9], Plithogenic Sets [10], HyperFuzzy Sets [11], and HyperNeutrosophic Sets [12]. Within these frameworks, a wide range of notions has been proposed and studied, particularly in the settings of fuzzy, intuitionistic fuzzy, neutrosophic, and plithogenic set theories. This extensive literature underscores both the significance of these theories and the breadth of their application areas. As a result, many ideas, constructions, and structural patterns recur across these four major families of uncertainty-oriented models. In this book, we provide a comprehensive, large-scale survey of Fuzzy, Intuitionistic Fuzzy, Neutrosophic, and Plithogenic Sets. Our goal is to give readers a systematic overview of existing developments and, through a unified exposition, to stimulate new insights, further conceptual extensions, and additional applications across a wide range of disciplines.

cs.AI↗
arXiv2026

Theoretical Foundations of Superhypergraph and Plithogenic Graph Neural Networks

Hypergraphs generalize classical graphs by allowing a single edge to connect multiple vertices, providing a natural language for modeling higher-order interactions. Superhypergraphs extend this paradigm further by accommodating nested, set-valued entities and relations, enabling the representation of hierarchical, multi-level structures beyond the expressive reach of ordinary graphs or hypergraphs. In parallel, neural networks-especially Graph Neural Networks (GNNs)-have become a standard tool for learning from relational data, and recent years have seen rapid progress on Hypergraph Neural Networks (HGNNs) and their theoretical properties. To model uncertainty and multi-aspect attributes in complex networks, several graded and multi-valued graph frameworks have been developed, including fuzzy graphs and neutrosophic graphs. The plithogenic graph framework unifies and refines these approaches by incorporating multi-valued attributes together with membership and contradiction mechanisms, offering a flexible representation for heterogeneous and partially inconsistent information. This book develops the theoretical foundations of SuperHyperGraph Neural Networks (SHGNNs) and Plithogenic Graph Neural Networks, with the goal of extending message-passing principles to these advanced higher-order structures. We provide rigorous definitions, establish fundamental structural properties, and prove well-definedness results for key constructions, with particular emphasis on strengthened formulations of Soft Graph Neural Networks and Rough Graph Neural Networks.

cs.AI↗
arXiv2026

Reconsideration of Tangle and Ultrafilter using Separation and Partition

Tangle is a concept in graph theory that has a dual relationship with branch-width which is well-known graph width parameter. Ultrafilter, a fundamental notion in mathematics, is similarly known to have a dual relationship with branch-width when extended to a connectivity system (X, f). We will reconsider these concepts using separation and partition.

math.CO↗
arXiv2026

Matroid, Ideal, Ultrafilter, Tangle, and so on: Reconsideration of Obstruction to linear decomposition

The investigation of width parameters in both graph and algebraic contexts has attracted considerable interest. Among these parameters, the linear branch width has emerged as a crucial measure. In this concise paper, we explore the concept of linear decomposition, specifically focusing on the single filter in a connectivity system. Additionally, we examine the relevance of matroids, antimatroids, and greedoids in the context of connectivity systems. Our primary objective in this study is to shed light on the impediments to linear decomposition from multiple perspectives.

math.CO↗
arXiv2026

Revitalizing education through ict: a short overview of japan's current landscape

The domain of Information and Communication Technology (ICT) education has garnered significant consideration in recent times. However, several challenges are inherent to this area of study, including monetary expense, temporal factors, pedagogical environment, teacher training programs, incentive, syllabus design, and health-related concerns. This paper presents an analysis of the difficulties encountered in the realm of ICT education in Japan, taking into account ten different perspectives. A peer-reviewed article of this Preprint also exists "Fujita, T. (2023). REVITALIZING EDUCATION THROUGH ICT: A SHORT OVERVIEW OF JAPAN'S CURRENT LANDSCAPE. European Journal of Social Sciences Studies, 8(5)."

cs.CY↗
arXiv2026

A Dynamic Survey of Soft Set Theory and Its Extensions

Soft set theory provides a direct framework for parameterized decision modeling by assigning to each attribute (parameter) a subset of a given universe, thereby representing uncertainty in a structured way [1, 2]. Over the past decades, the theory has expanded into numerous variants-including hypersoft sets, superhypersoft sets, TreeSoft sets, bipolar soft sets, and dynamic soft sets-and has been connected to diverse areas such as topology and matroid theory. In this book, we present a survey-style overview of soft sets and their major extensions, highlighting core definitions, representative constructions, and key directions of current development.

cs.AI↗
arXiv2026

Advancing Uncertain Combinatorics through Graphization, Hyperization, and Uncertainization: Fuzzy, Neutrosophic, Soft, Rough, and Beyond

Combinatorics studies how discrete objects can be counted, arranged, and combined under specified rules. Motivated by uncertainty in real-world data and decisions, modern set-theoretic formalisms such as fuzzy sets, neutrosophic sets, rough sets, soft sets, and plithogenic sets have been developed. In particular, neutrosophic sets model uncertainty by assigning to each element degrees of truth, indeterminacy, and falsity. In parallel, these uncertainty frameworks are increasingly investigated in graphized and hyperized forms, where generalized graph models encompass classical graphs, hypergraphs, and higher-order "superhyper" structures; related hyper- and superhyper-concepts also arise beyond graph theory. This book (Edition 2.0) surveys and consolidates recent developments at the intersection of combinatorics, uncertain sets, uncertain graphs, and hyper/superhyper frameworks, while introducing several new graph and set concepts. As representative contributions, we extend graph-theoretic notions via Neutrosophic Oversets, Neutrosophic Undersets, Neutrosophic Offsets, and the Nonstandard Real Set. The second edition adds newly introduced concepts, corrects typographical issues, and re-examines mathematical consistency, aiming to serve as a compact reference and a source of inspiration for further research.

cs.AI↗
arXiv2023

Exploring two concepts: branch decomposition and weak ultrafilter on connectivity system

This paper explores two fundamental concepts: branch width and weak ultrafilter. Branch width is a significant graph width parameter that measures the degree of connectivity in a graph using a branch decomposition and a symmetric submodular function. Weak ultrafilter, introduced as a weakened definition of an ultrafilter, plays a vital role in interpreting defaults in logic. We introduce the concept of Weak Ultrafilter on the connectivity system (X, f) and demonstrate its duality with branch decomposition. This study enhances our understanding of these concepts in graph combinatorial and logical contexts.

math.CO↗