Selection of third-party logistics provider based on extended multimoora technique under double hierarchy linguistic single-valued neutrosophic set

The demand for third-party logistics (3PL) providers becomes an increasingly important issue for corporations seeking improved customer service and cost reduction. Currently, there is no way to select the appropriate method for selecting 3PL. Therefore, this paper develops a new extended multi-objective optimization ratio analysis plus full multiplicative form (MULTIMOORA) method under double hierarchy linguistic single-valued neutrosophic sets (DHLSVNSs). For this, we first develop a new mathematical tool, i.e., DHLSVNSs, by studying single-valued neutrosophic set (SVN) and double hierarchy linguistic term set (DHLTSs), which is very effective for solving uncertainty in decision-making problems. A list of Einstein aggregation operators and their fundamental aspects for DHLSVNSs are presented based on Einstein's norms, as aggregation operators play an essential role in decision-making. A step-by-step algorithm of the Extended DHLSVN-MULTIMOORA approach is designed to tackle ambiguous and uncertain data during decision-making problems. The algorithm developed for the suggested technique is illustrated with a numerical example relevant to 3PL. A comparison of the proposed methods with various existing methodologies is carried out to demonstrate the superiority of the suggested algorithms.