**7. Conclusions**

A multi *Q*-hesitant fuzzy soft multi-granulation rough set is a new hybrid model, which is a combination of powerful topics: multi *Q*-hesitant fuzzy soft sets and multi-granulation rough sets. We have defined *MkQHFS* rough approximation operators in terms of *MkQHFS* relations and *MkQHFS* multi-granulation rough approximation operators in terms of *MkQHFS* relations. We have investigated the properties of lower and upper *MkQHFS* rough approximation operators and lower and upper *MkQHFS* multi-granulation rough approximation operators. Finally, we have developed a general framework for dealing with uncertainty decision-making by using the multi *Q*-hesitant fuzzy soft multi-granulation rough sets. We have used the photovoltaic systems fault detection to indicate the principle steps of the decision methodology. In the future, we will mainly focus on investigating uncertain measures and knowledge reductions of the *MkQHFS* rough sets.

**Author Contributions:** K.M.A., N.O.A. and M.A. conceived of the presented idea. K.M.A. and N.O.A. developed the theory and performed the computations. K.M.A. and M.A. wrote the paper.

**Funding:** The authors received no specific funding for this work.

**Conflicts of Interest:** The authors declare that there is no conflict of interests regarding the publication of this paper.
