Handbook of Rough Set Extensions and Uncertainty Models
Summary: arXiv:2604.19794v1 Announce Type: new
Abstract
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.
Overview
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:
- The underlying granulation mechanism:
- Equivalence-based
- Tolerance-based
- Covering-based
- Neighborhood-based
- Probabilistic approximations
- The uncertainty semantics attached to data and relations:
- Crisp
- Fuzzy
- Intuitionistic fuzzy
- Neutrosophic
- Plithogenic settings
Modeling Intent and Use Cases
The book 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. These examples help to bridge theory and practical applications, showcasing how rough set models can be employed in real-world scenarios.
Scope Clarification
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.
Conclusion
The principal aim of the book is to survey and position rough set models and their extensions in a systematic and coherent manner. By providing a comprehensive overview, the authors hope to inspire further research and exploration in the field of rough set theory and its applications, fostering a deeper understanding of uncertainty modeling.