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In this paper, we propose a new hybrid model, multi Q-hesitant fuzzy soft multi-granulation rough set model, by combining a multi Q-hesitant fuzzy soft set and multi-granulation rough set. We demonstrate some useful properties of these multi Q-hesitant fuzzy soft multi-granulation rough sets. Furthermore, we define multi Q-hesitant fuzzy soft (MkQHFS) rough approximation operators in terms of MkQHFS relations and MkQHFS multi-granulation rough approximation operators in terms of MkQHFS relations. We study the main properties of lower and upper MkQHFS rough approximation operators and lower and upper MkQHFS multi-granulation rough approximation operators. Moreover, we develop a general framework for dealing with uncertainty in decision-making by using the multi Q-hesitant fuzzy soft multi-granulation rough sets. We analyze the photovoltaic systems fault detection to show the proposed decision methodology.

A Decision-Making Approach Based on a Multi Q-Hesitant Fuzzy Soft Multi-Granulation Rough Model