Hesitant q-rung orthopair fuzzy aggregation operators with their applications in multi-criteria decision making

Document Type : Research Paper


1 Department of Mathematics and Statistics Faculty of Basic and Applied Sciences International Islamic University Islamabad Pakistan,

2 Department of Mathematics, Islamabad Model College for Girls F-6/2, Islamabad, Pakistan


The aim of this manuscript is to present a new concept of hesitant q-rung orthopair fuzzy sets (Hq-ROFSs) by combining the concept of the q-ROFSs as well as Hesitant fuzzy sets. The proposed concept is the generalization of the fuzzy sets, intuitionistic fuzzy sets, hesitant fuzzy sets, and Pythagorean fuzzy sets as well as intuitionistic hesitant fuzzy sets (IHFSs) and hesitant Pythagorean fuzzy sets (HPFSs).Furthermore some basic operational laws of hesitant q-rung orthopair fuzzy have been investigated. The score and accuracy functions are defined which play a vital role in decision making process for making comparison between the hesitant q-rung orthopair fuzzy numbers (Hq-ROFNs). Under the Hq-ROF environment, Hq-ROF weighted averaging (Hq-ROFWA) and Hq-ROF weighted geometric (Hq-ROFWG) operators are introduced and various properties of these aggregation operators are studied. Additionaly, a numerical application shows that how the proposed operators are utilized to solve multi-criteria decision making (MCDM) problems in which experts added their optimistic and pessimistic preferences. Finally the analysis of proposed method with other methods is presented which show that the method presented in this paper is more flexible and superior than existing methods.