A three-dimensional probabilistic fermatean neutrosophic hesitant green transportation system for the sustainable management of biomedical waste

Neutrosophic set (NS) is one of the extensive tools to handle unpredictability, vagueness and incompleteness that arise in real-world problems due to its miraculous characteristics. In this study, a generalization of NS, namely Probabilistic Fermatean Neutrosophic Hesitant Set (PFNHS) have been proposed to delineate the randomness and imprecision in a single framework. As a way of enhancing its pragmatic applicability in real-world problems, our set has been examined in terms of its fundamental operations, basic properties, score function, and accuracy function. Also, we have proposed Triangular Probabilistic Fermatean Neutrosophic Hesitant Number (Tr-PFNHN) along with its characteristics as a triangular form of PFNHS to depict the uncertainty by integrating probabilistic information in a fuzzy framework. On the other hand, to safeguard the wellbeing of community and environment from the hazardous impact of biomedical wastes (BMWs), the proper management of these wastes is extremely crucial. In this direction, a three-dimensional transportation model for the sustainable transportation of BMWs has been introduced with an aspiration to optimize the transportation cost, time, carbon emission and job opportunities in PFNH environment. Thereafter, fuzzy and non-fuzzy techniques namely fuzzy programming (FP) and global criterion method (GCM) have been utilized to deal with aforementioned model for the sustainable transportation of BMWs. Moreover, numerical computations, results, as well as the future objectives and restrictions are encompassed.