Journal of Intelligent & Fuzzy Systems xx (20xx) x–xx DOI:10.3233/JIFS-181476 IOS Press 1 Multigranulation hesitant Pythagorean fuzzy rough sets and its application in multi-attribute decision making Jia-Jia Zhou and Hai-Long Yang ∗ College of Mathematics and Information Science, Shaanxi Normal University, P.R. China Abstract. Hesitant Pythagorean fuzzy set (HPFS) is a generalization of fuzzy set (FS). By integrating HPFS with rough set (RS), the notion of single granulation hesitant Pythagorean fuzzy rough sets (SGHPFRSs) is firstly put forward. Then, in view of the multigranulation framework, two types of multigranulation hesitant Pythagorean fuzzy rough sets (MGHPFRSs) are proposed, which are called the optimistic multigranulation hesitant Pythagorean fuzzy rough sets (OMGHPFRSs) and pessimistic multigranulation hesitant Pythagorean fuzzy rough sets (PMGHPFRSs). The connections between serial hesi- tant Pythagorean fuzzy relations and hesitant Pythagorean fuzzy approximation operators are established. The relationship between the MGHPFRSs and SGHPFRSs will be explored. Moreover, the relationship between the OMGHPFRSs and PMGHPFRSs will be established subsequently. Ultimately, an illustrative example will be given to expound the availability about the MGHPFRSs in multi-attribute decision making. Keywords: Rough sets, SGHPFRSs, MGHPFRSs, multi-attribute decision making 1. Introduction RS originated by Pawlak [20, 21] is an appeal- ing tool to handle uncertainty. However, it treats the partition of the universe as the original notion to construct the approximation operators. Aimed at this issue, many researchers exert themselves to remedy the rigidness of the condition in Pawlak’s RS, such as the equivalence relation are relaxed with fuzzy relation [7], similarity relation [26] and other gen- eralizations of RS can be found in [2, 4, 5, 12, 14, 43, 45–47, 50, 59]. Furthermore, Zhang et al. [57, 60] groped the uncertainty of probabilistic rough set. Yager originated the notion of Pythagorean fuzzy set (PFS) [39–41], which is a loose form of intu- itionistic fuzzy set (IFS) [1]. Speaking of PFS, an ∗ Corresponding author. Hai-Long Yang, E-mail: yanghailong @snnu.edu.cn. appealing feature is that the condition is loosened in Pythagorean fuzzy environment. Since the origi- nation of PFS, it unlocks new avenues of study in handling uncertainty issues. In [8], Garg explored the correlation coefficient between Pythagorean fuzzy sets (PFSs). Gao et al. [9] make an exploration of Pythagorean fuzzy interaction aggregation operators. Liang and Xu [16] groped the three-way decisions using ideal TOPSIS solutions under Pythagorean fuzzy information. In [22–24], Peng et al. stud- ied some results of PFSs, Pythagorean fuzzy soft set, and the fundamental properties of Pythagorean fuzzy aggregation operators. Zhang [54] groped a novel approach based on similarity measure for Pythagorean fuzzy multiple criteria group decision making. Hesitant fuzzy sets (HFSs) [27, 28] originated by Torra have been paid great attentions in recent years. Hesitant Pythagorean fuzzy sets (HPFSs) [15] is put 1064-1246/19/$35.00 © 2019 – IOS Press and the authors. All rights reserved Corrected Proof