Covering-based general multigranulation intuitionistic fuzzy rough sets and corresponding applications to multi-attribute group decision-making.

This paper concerns the intuitionistic fuzzy (IF) decision-making method for solving uncertain or vague problems. This traditional method has imperfections in some particular circumstances. For this reason, we combine rough set theory and the IF decision-making approach in order to design a novel procedure for making decisions. Several types of covering-based general multigranulation IF rough set (CGMIFRS) models are proposed by using four types of IF neighborhoods. A related example to illustrate these models is given. Furthermore, the relationships among the eight kinds of CGMIFRS models are also investigated. By the recourse to the principle of the PROMETHEE II method, a multi-attribute group decision-making (MAGDM) approach with IF information based on CGMIFRS models is set forth. A comparative analysis shows that the optimal objects of our method based on two IF logical operators, the IF PROMETHEE method and the IF aggregation operators are consistent. We conclude that our novel method is more effective to deal with MAGDM problems with IF information than the existing MAGDM methods.