Three-way decisions with dual hesitant fuzzy covering-based rough set and their applications in medical diagnosis.

As an extension of partition, fuzzy β -covering can provide a more realistic and accurate description of incomplete information. In this paper, we mainly integrate the idea of fuzzy β -covering with dual hesitant fuzzy (DHF) information and construct some novel three-way decision (3WD) models with DHF covering-based rough set. Firstly, we propose the notions of DHF β -covering, DHF β -minimal description and DHF β -maximal description, and then construct three types of DHF neighborhood operators. Meanwhile, we introduce DHF conditional probability by using DHF neighborhood operator. Secondly, in terms of DHF conditional probability, DHF covering-based probabilistic rough set, DHF covering-based decision-theoretic rough set and their 3WD models are established. In light of DHF neighborhood operator, we propose two pairs of optimistic and pessimistic DHF decision evaluation functions and build two 3WD models through them. Lastly, a numerical example is employed to elaborate the application of the above models, which is effective and credible to medicine screening for Alzheimer's disease. • Proposed neighborhood operators in dual hesitant fuzzy environment. • Three-way decision based on dual hesitant fuzzy probabilistic rough sets. • Three-way decision based on dual hesitant fuzzy decision-theoretic rough sets. • Three-way decision based on dual hesitant fuzzy decision evaluation functions. • Experiment on medication screening of Alzheimer's disease are given. [ABSTRACT FROM AUTHOR]