Multigranulation single valued neutrosophic covering-based rough sets and their applications to multi-criteria group decision making

In this paper, three types of (philosophical, optimistic and pessimistic) multigranulation single valued neutrosophic (SVN) covering-based rough set models are presented, and these three models are applied to the problem of multi-criteria group decision making (MCGDM). Firstly, a type of SVN covering-based rough set model is proposed. Based on this rough set model, three types of multigranulation SVN covering-based rough set models under the concept of multigranulation SVN $eta$-covering approximation space are proposed, where $eta$ is a SVN number. Moreover, the connections among these four models are investigated. Secondly, some conditions under which different multigranulation SVN $eta$-covering approximation spaces induced the same multigranulation SVN covering approximation operators are presented. Finally, three novel methods are presented to MCGDM problems under the multigranulation SVN covering-based rough set models. Furthermore, the proposed MCGDM methods are compared with other methods through a problem about paper defect diagnosis.