Multi-Attribute Decision-Making for Road Slope Treatment Selection Based on Spherical Single-Valued Neutrosophic Value Triangular Aggregation Operators

Areas in the East China Sea are often affected by bad weather such as typhoons and rainy seasons, so geological disasters such as road slope landslides and avalanches often occur in these areas. To prevent the geological disasters, it is necessary to perform comprehensive treatments of road slopes to ensure their stability and safety. Due to the uncertainty and vagueness of decision makers’ judgements and cognitions in the evaluation process of slope treatment schemes, there is a Single-Valued Neutrosophic Value (SvNV) uncertainty in a neutrosophic decision scenario. To effectively express the hybrid information of a crisp SvNV and its uncertain space (sphere with a radius), we need to develop a Spherical Single-Valued Neutrosophic Set/Value (S-SvNS/S-SvNV) and its Multi-Attribute Decision Making (MADM) technique. Therefore, this study requires the following new content to address the current gaps in neutrosophic research. First, we propose an S-SvNS and the basic relations, trigonometric operation laws, and score and accuracy formulae of S-SvNVs. Second, the S-SvNV trigonometric weighted averaging and geometric aggregation operators are established for the aggregation of S-SvNVs. Third, a MADM technique based on the established two aggregation operators and the score and accuracy formulae of S-SvNVs is developed for solving MADM problems with unknown attribute weights and periodicity in the scenario of S-SvNSs. Fourth, the developed technique is applied to an actual selection example of road slope treatment schemes and then its efficiency is verified by sensitivity analysis and comparison with the existing MADM techniques under the scenarios of SvNSs and S-SvNSs.