Attribute reduction in incomplete ordered information systems with fuzzy decision

Rough set theory has been applied extensively to attribute reduction. Classical rough sets provide a theoretical framework for attribute reduction based on complete data with regular attributes where the domains are not ordered by preference. However, their scope does not include incomplete data with fuzzy decisions under a preference-ordered domain, which are common in real real-world applications. Therefore, in this study, a general framework is proposed for attribute reduction from incomplete ordered information systems with fuzzy decisions by combining dominance-based rough sets with α-cut sets, where α is the fuzzy decision attribute value. First, the judgement theorems and discernibility functions are established by applying Boolean reasoning techniques to attribute reduction in consistent and inconsistent incomplete ordered information systems with fuzzy decision. In addition, forward and backward attribute reduction algorithms are designed for consistent and inconsistent systems, respectively, to find near-optimal attribute reducts. Finally, the experimental results based on different datasets, demonstrate that the proposed algorithms are more effective for attribute reduction in most cases than other reduction algorithms.