将模糊、粗糙等不确定数学工具与图论结合，构建更强大的组合分析框架。
Advancing Uncertain Combinatorics through Graphization, Hyperization, and Uncertainization: Fuzzy, Neutrosophic, Soft, Rough, and Beyond
- 用中立度、真值、假值三元组扩展图结构，支持不确定性建模
- 提出超图与高阶结构的不确定化模型，涵盖新集合概念
- 适合研究不确定系统建模的学者，可作理论参考
组合学研究离散对象在特定规则下的计数、排列与组合。针对现实数据与决策中的不确定性，现代集合论形式如模糊集、中性集、粗糙集、软集及多值集被提出。其中，中性集通过为每个元素赋予真值、不确定性与假值来刻画不确定性。与此同时，这些不确定框架正被拓展至图化与超图化形式，广义图模型涵盖经典图、超图及更高阶的“超超图”结构；相关超图与超超图概念亦延伸至图论之外。本书（第2版）综述并整合了组合学、不确定集、不确定图及超/超超图框架的最新进展，引入若干新图与集概念。代表性成果包括通过中性超集、中性欠集、中性偏移集及非标准实数集扩展图论概念。第二版新增概念、修正排版错误，并重新审视数学一致性，旨在成为紧凑参考书与进一步研究的灵感来源。
原文摘要 · Abstract (English)
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.
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