Some power Heronian mean operators in multiple attribute decision-making based on q-rung orthopair hesitant fuzzy environment

Abstract

ABSTRACT As the generalisation of intuitionistic fuzzy sets (IFSs) and Pythagorean fuzzy set (PFS), the q-rung orthopair fuzzy set (q-ROFS) is more useful to express fuzzy and ambiguous information. Meanwhile, to consider human’s hesitance, the concept of q-rung orthopair hesitant fuzzy set (q-ROHFS) is presented, which can be more valid for handling real multiple attribute decision-making (MADM) problems. To fuse the information in q-ROHFS more effectively, in this article, based on power average (PA) operator and generalised Heronian mean (GHM) operator, some q-rung orthopair hesitant fuzzy power generalised Heronian mean (q-ROHFPGHM) operators which can consider the relationships between being fused arguments are defined and studied. Evidently, the new proposed operators can obtain more exact results than other existing methods. In addition, some precious properties of these operators are discussed. Afterwards, the defined aggregation operators are used to MADM with q-rung orthopair hesitant fuzzy numbers (q-ROHFNs) and the MADM decision-making model is developed. In accordance with the defined operators and built model, the q-rung orthopair hesitant fuzzy weighted power generalised Heronian mean (q-ROHFWPGHM) operator and the q-rung orthopair hesitant fuzzy weighted power generalised geometric Heronian mean (q-ROHFWPGGHM) operator are applied to deal with green supplier selection in supply chain management, and the availability and superiority of the proposed operators are analysed by comparing with some existing approaches. The method presented in this paper can effectually solve the MADM problems which the decision-making information is expressed by q-ROHFNs and the attributes are interactive.