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Successfully organizing the transport of hazardous materials and handling them correctly is a very important logistical task that affects both the overall flow of transport and the environment. Safety advisors for the transport of hazardous materials have a very important role to play in the proper and safe development of the transport flow for these materials; their task is primarily to use their knowledge and effort to prevent potential accidents from happening. In this research, a total of 21 safety advisors for the transport of hazardous materials in Serbia are assessed using a new model that integrates Linguistic Neutrosophic Numbers (LNN) and the WASPAS (Weighted Aggregated Sum Product Assessment) method. In this way, two important contributions are made, namely a completely new methodology for assessing the work of advisors and the new LNN WASPAS model, which enriches the field of multi-criteria decision making. The advisors are assessed by seven experts on the basis of nine criteria. After performing a sensitivity analysis on the results, validation of the model is carried out. The results obtained by the LNN WASPAS model are validated by comparing them with the results obtained by LNN extensions of the TOPSIS (Technique for Order Performance by Similarity to Ideal Solution), LNN CODAS (COmbinative Distance-based ASsessment), LNN VIKOR (Multi-criteria Optimization and Compromise Solution) and LNN MABAC (Multi-Attributive Border Approximation area Comparison) models. The LNN CODAS, LNN VIKOR and LNN MABAC are also further developed in this study, which is an additional contribution made by the paper. After the sensitivity analysis, the SCC (Spearman Correlation Coefficient) is calculated which confirms the stability of the previously obtained results. © 2019, Springer-Verlag London Ltd., part of Springer Nature.