A new method for ranking q-rung ortho-pair fuzzy numbers and application.

The effectiveness of the q-rung ortho-pair fuzzy multi-attribute decision-making method is primarily influenced by the q-rung ortho-pair fuzzy number ranking method. This paper conducts an in-depth analysis of the shortcomings of eight existing q-rung ortho-pair fuzzy number ranking methods. A refined approach to ranking q-rung ortho-pair fuzzy numbers is proposed, wherein the method synthesizes the effects of the q-power transformation applied to both membership and non-membership degrees, alongside an exponential adjustment component. This formulation ensures greater discrimination power and robustness in uncertain environments. This method addresses the issues of poor robustness and the inability to achieve a complete ranking in existing approaches. Finally, the proposed ranking approach is incorporated into a q-rung orthopair fuzzy multi-attribute decision-making framework and is subsequently employed to address a practical case involving the selection of an optimal warehouse location for an e-commerce enterprise.