Florentin Smarandache

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

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.