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

#### **Kholood Mohammad Alsager 1, Noura Omair Alshehri 2 and Muhammad Akram 3,***∗*


Received: 20 October 2018; Accepted: 14 November 2018; Published: 4 December 2018

**Abstract:** 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.

**Keywords:** *Q*-hesitant fuzzy soft set; multi *Q*-hesitant fuzzy soft rough set; photovoltaic systems fault detection approach; decision-making method
