A linguistic intuitionistic multi-criteria decision-making method based on the Frank Heronian mean operator and its application in evaluating coal mine safety

Coal mine safety has been a pressing issue for many years, and it is a constant and non-negligible problem that must be addressed during any coal mining process. This paper focuses on developing an innovative multi-criteria decision-making (MCDM) method to address coal mine safety evaluation problems. Because lots of uncertain and fuzzy information exists in the process of evaluating coal mine safety, linguistic intuitionistic fuzzy numbers (LIFNs) are introduced to depict the evaluation information necessary to the process. Furthermore, the handling of qualitative information requires the effective support of quantitative tools, and the linguistic scale function (LSF) is therefore employed to deal with linguistic intuitionistic information. First, the distance, a valid ranking method, and Frank operations are proposed for LIFNs. Subsequently, the linguistic intuitionistic fuzzy Frank improved weighted Heronian mean (LIFFIWHM) operator is developed. Then, a linguistic intuitionistic MCDM method for coal mine safety evaluation is constructed based on the developed operator. Finally, an illustrative example is provided to demonstrate the proposed method, and its feasibility and validity are further verified by a sensitivity analysis and comparison with other existing methods.