Logical Disjunction Double-Quantitative Fuzzy Rough Sets

The variable precision rough set model mainly utilizes a controlled degree of misclassiffication between the concept and equivalence classes namely relative quantitative information to approximate a concept. And the graded rough set approximates a concept through internal and external inclusion degrees between the concept and equivalence classes namely absolute quantitative information. Both variable precision and graded rough sets can be used to handle databases with misclassiffication. However, these two models could not effectively handle the real-valued datasets because discretizing will lead to information loss. Therefore, we study the rough set theory by bidirectional quantization under fuzzy relations. Firstly, a logical disjunction double-quantitative fuzzy rough set model is proposed based on the bidirectional quantization. Secondly, we analyze relationships between approximations and different rough regions in the new model. Meanwhile, several important theorems are given to deepen understanding of related concepts. Finally, a medical data case is used to illustrate the importance of the study.