A two-stage multi-criteria decision-making method with interval-valued q-Rung Orthopair fuzzy technology for selecting bike-sharing recycling supplier

Abstract

Bike-Sharing has rapidly attracted worldwide attention for its benefits, such as easing traffic congestion and reducing greenhouse gases. However, the waste of resources and environmental pollution caused by discarded bike-sharing should not be underestimated. To tackle this severe problem by selecting the bike-sharing recycling supplier, this paper proposes a two-stage multi-criteria decision-making (MCDM) method using interval-valued q-Rung Orthopair fuzzy (IVq-ROF) technique. In the first stage, based on the Einstein operations, IVq-ROF Einstein operators are defined to aggregate the evaluation information of bike-sharing recycling suppliers. Specifically, IVq-ROF Einstein weighted averaging (IVq-ROFEWA) operator, IVq-ROF Einstein order weighted averaging (IVq-ROFEOWA) operator, IVq-ROF Einstein weighted geometric (IVq-ROFEWG) operator, and IVq-ROF Einstein order weighted geometric (IVq-ROFEOWG) operator are constructed and proved, respectively. In addition, the properties of the proposed operators, including consistency, boundedness and monotonicity, are given and proved. In the second stage, based on the IVq-ROFEWA operator, a MCDM method utilizing Technique for Order Preference by Similarity to an Ideal Solution (TOPSIS) in the IVq-ROF environment is presented to select the best bike-sharing recycling supplier. Subsequently, a case study is conducted on the selection of the optimal bike-sharing recycling supplier by exploiting the proposed two-stage MCDM method, which reflects the practicality and availability of the proposed method. Finally, the validity and superiority of the proposed method are verified by comparison and sensitivity analysis.