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.

翻译：组合数学研究离散对象在特定规则下的计数、排列与组合方式。受现实世界数据与决策中不确定性的驱动，模糊集、中智集、粗糙集、软集及泛生集等现代集合论形式体系得以发展。其中，中智集通过为每个元素分配真度、不确定度与假度来建模不确定性。与此同时，这些不确定性框架正日益以图化与超化形式被研究，其中广义图模型涵盖了经典图、超图及更高阶的“超超”结构；相关的超与超超概念也出现在图论之外的领域。本书（第二版）综述并整合了组合数学、不确定集合、不确定图及超/超超框架交叉领域的最新进展，同时引入了若干新的图与集合概念。作为代表性贡献，我们通过中智超集、中智亚集、中智偏集及非标准实数集扩展了图论概念。第二版新增了近期提出的概念，修正了排版问题，并重新审视了数学一致性，旨在成为一本简洁的参考书并为后续研究提供灵感来源。