This chapter reviews three formulations of rough set theory, i. e., element-based definition, granule-based definition, and subsystem-based definition. These formulations are adopted to generalize rough sets from three directions. The first direction is to use an arbitrary binary relation to generalize the equivalence relation in the element-based definition. The second is to use a covering to generalize the partition in the granule-based definition, and the third to use a subsystem to generalize the Boolean algebra in the subsystem-based definition. In addition, we provide some insights into the theoretical aspects of these generalizations, mainly with respect to relations with non-classical logic and topology theory.
Yao, J., Ciucci, D., Zhang, Y. (2015). Generalized rough sets. In J. Kacprzyk, W. Pedrycz (a cura di), Springer Handbook of Computational Intelligence (pp. 413-424). Springer Berlin Heidelberg [10.1007/978-3-662-43505-2_25].
Generalized rough sets
CIUCCI, DAVIDE ELIOSecondo
;
2015
Abstract
This chapter reviews three formulations of rough set theory, i. e., element-based definition, granule-based definition, and subsystem-based definition. These formulations are adopted to generalize rough sets from three directions. The first direction is to use an arbitrary binary relation to generalize the equivalence relation in the element-based definition. The second is to use a covering to generalize the partition in the granule-based definition, and the third to use a subsystem to generalize the Boolean algebra in the subsystem-based definition. In addition, we provide some insights into the theoretical aspects of these generalizations, mainly with respect to relations with non-classical logic and topology theory.
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