Handbook of Rough Set Extensions and Uncertainty Models
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866908989036429312 |
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| author | Fujita, Takaaki Smarandache, Florentin |
| author_facet | Fujita, Takaaki Smarandache, Florentin |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_19794 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Handbook of Rough Set Extensions and Uncertainty Models Fujita, Takaaki Smarandache, Florentin Artificial Intelligence Computational Engineering, Finance, and Science Machine Learning 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. |
| title | Handbook of Rough Set Extensions and Uncertainty Models |
| topic | Artificial Intelligence Computational Engineering, Finance, and Science Machine Learning |
| url | https://arxiv.org/abs/2604.19794 |