Multigranulation hesitant Pythagorean fuzzy rough sets and its application in multi-attribute decision making

Article type: Research Article

Authors: Zhou, Jia-Jia | Yang, Hai-Long^{; *}

Affiliations: College of Mathematics and Information Science, Shaanxi Normal University, P.R. China

Correspondence: [*] Corresponding author. Hai-Long Yang, E-mail: yanghailong@snnu.edu.cn.

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 hesitant 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

DOI: 10.3233/JIFS-181476

Journal: Journal of Intelligent & Fuzzy Systems, vol. 36, no. 6, pp. 5631-5644, 2019