软集理论及其扩展的动态综述（第二版）

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Abstract:Soft set theory provides a systematic framework for parameterized decision-making by associating each parameter with a subset of a given universe, thereby enabling structured representations of uncertainty [1, 2]. Over the past decades, the theory has evolved into a broad range of extensions, including hypersoft sets, superhypersoft sets, TreeSoft sets, bipolar soft sets, and dynamic soft sets, while also establishing connections with various mathematical disciplines, particularly topology and matroid theory. This book presents a comprehensive survey of soft set theory and its principal extensions, with particular emphasis on parameter spaces, value spaces, representative mathematical constructions, and the underlying assumptions necessary for rigorous comparisons among different frameworks. It carefully distinguishes established definitions from the literature from exploratory formulations and critically examines the limitations of selected claims concerning representation and reduction. Building upon the first edition, this second edition introduces additional concepts and illustrative examples, addresses previously identified mathematical inconsistencies and typographical errors, and refines the overall structure and presentation to enhance mathematical rigor, clarity, and readability.

Comments:	Book. Publisher: Neutrosophic Science International Association (NSIA) Publishing House. ISBN: 978-1-972502-68-6
Subjects:	Artificial Intelligence (cs.AI); Combinatorics (math.CO)
MSC classes:	03E72, 03E75
Cite as:	arXiv:2602.21268 [cs.AI]
	(or arXiv:2602.21268v2 [cs.AI] for this version)
	https://doi.org/10.48550/arXiv.2602.21268 arXiv-issued DOI via DataCite

Submission history

From: Takaaki Fujita [view email]
[v1] Tue, 24 Feb 2026 11:58:45 UTC (1,648 KB)
[v2] Tue, 10 Nov 2026 11:40:30 UTC (1,543 KB)