A new multi-objective optimization ratio analysis plus full multiplication form method for the selection of an appropriate mining method based on 2-tuple spherical fuzzy linguistic sets

The selection of an appropriate mining method is considered as an important tool in the mining design process. The adoption of a mining method can be regarded as a complex multi-attribute group decision-making (MAGDM) problem as it may contain uncertainty and vagueness. The main goal of this paper is to propose an extended multi-objective optimization ratio analysis plus full multiplication form (MULTIMOORA) method that is based on a 2-tuple spherical fuzzy linguistic set (2TSFLS). The MULTIMOORA method under 2TSFL conditinos has been developled as a novel approach to deal with uncertainty in decision-making problems. The proposed work shows that 2TSFLSs contain collaborated features of spherical fuzzy sets (SFSs) and 2-tuple linguistic term sets (2TLTSs) and, hence, can be considered as a rapid and efficient tool to represent the experts' judgments. Thus, the broader structure of SFSs, the ability of 2TLTSs to represent linguistic assessments, and the efficiency of the MULTIMOORA approach have motivated us to present this work. To attain our desired results, we built a normalized Hamming distance measure and score function for 2TSFLSs. We demonstrate the applicability and realism of the proposed method with the help of a numerical example, that is, the selection of a suitable mining method for the Kaiyang phosphate mine. Then, the results of the proposed work are compared with the results of existing methods to better reflect the strength and effectiveness of the proposed work. Finally, we conclude that the proposed MULTIMOORA method within a 2TSFLS framework is quite efficient and comprehensive to deal with the arising MAGDM problems.