Algebraic Structures of Neutrosophic Triplets, Neutrosophic Duplets, or Neutrosophic Multisets

Neutrosophy (1995) is a new branch of philosophy that studies triads of the form (, , ), where is an entity {i.e. element, concept, idea, theory, logical proposition, etc.}, is the opposite of , while is the neutral (or indeterminate) between them, i.e., neither nor .Based on neutrosophy, the neutrosophic triplets were founded, which have a similar form (x, neut(x), anti(x)), that satisfy several axioms, for each element x in a given set.This collective book presents original research papers by many neutrosophic researchers from around the world, that report on the state-of-the-art and recent advancements of neutrosophic triplets, neutrosophic duplets, neutrosophic multisets and their algebraic structures – that have been defined recently in 2016 but have gained interest from world researchers. Connections between classical algebraic structures and neutrosophic triplet / duplet / multiset structures are also studied. And numerous neutrosophic applications in various fields, such as: multi-criteria decision making, image segmentation, medical diagnosis, fault diagnosis, clustering data, neutrosophic probability, human resource management, strategic planning, forecasting model, multi-granulation, supplier selection problems, typhoon disaster evaluation, skin lesson detection, mining algorithm for big data analysis, etc

Dual Generalized Nonnegative Normal Neutrosophic Bonferroni Mean Operators and Their Application in Multiple Attribute Decision Making

For multiple attribute decision making, ranking and information aggregation problems are increasingly receiving attention. In a normal neutrosophic number, the ranking method does not satisfy the ranking principle

A NOVEL RISK EVALUATION APPROACH FOR FREQUENTLY ENCOUNTERED RISKS IN SHIP ENGINE ROOMS

The purpose of this study is to evaluate risks which are frequently encountered in the engine room on-board. In this context, twenty common risks are assessed using the neutrosophic analytic hierarchy process (N-AHP) and trapezoidal fuzzy technique for order preference by similarity to ideal solution (TrF-TOPSIS). In maritime risk evaluation, since it is frequently required the linguistic assessment of decision-makers to achieve a robust risk assessment tool, neutrosophic sets and fuzzy sets are used together in this study. Neutrosophic sets represent real-world problems effectively by considering all aspects of decision-making situations, (i.e. truthiness, indeterminacy, and falsity). Therefore, AHP is integrated with neutrosophic sets to assign weights of risk parameters initially. Then, the encountered risks are prioritized by TrF-TOPSIS. Finally, preventative actions for the risks have been discussed. In conclusion of the study, it is shown that skin exposure to the fuels/oils, exposure to chemicals and exposure to high pressure and temperature liquids are the most important risks through the engine room on-board. This study both emphasizes the importance of preventing damage to crew in the risk assessment of ship engine rooms and aims to increase the level of safety control and minimize the potential environmental impacts of a ship\u27s damage