Optimal granulation selection for similarity measure-based multigranulation intuitionistic fuzzy decision-theoretic rough sets

Similarity measure is an important uncertainty measurement in intuitionistic fuzzy set (IFS) theory. In this study, a novel similarity measure is presented by the combination of the information carried by hesitancy degree and the endpoint distance of membership and nonmembership, respectively. Moreover, a numerical example is used to verify the reasonable of the proposed similarity measure. After that, the similarity measure is applied to construct the IF decision-theoretic rough set (IF-DTRS) model and multigranulation IF decision-theoretic rough set (MG-IF-DTRS) model. Some properties of IF-DTRS and MG-IF-DTRS are also investigated. Thirdly, based on granular significance, a novel approach of optimal granulation selection is formulated. Finally, a heuristic algorithm is designed and the effectiveness of this algorithm is demonstrated by an illustrative example.