Contributing to the fast growing new field of neutrosophy, this book provides a significant collection of unedited articles covering the latest ongoing research area. Neutrosopy is above all a new view on modelling, tailored to effectively address the uncertainties inherent of the real world. In short, Neutrosophy supersedes in logics the binary approach of true or false by introducing a third state: neutral, which can be also interpreted as indeterminate, uncertain, inconsistent …. Development of neutrosophy since its conception by Smarandache in 1988 exponentially grows by conceptual extensions of logics, measure, sets, graphs, as well as practical applications in namely all fields. It can be think as generalization of fuzzy logic and its variants like intuitionistic fuzzy logic. Registered in wide collection of books on this promising field, here we deliver to researchers, lecturers and postgraduate students pursuing research on neutrosophic a set of eighteen unreleased articles on state of the art theoretical developments, applications and understanding of neutrosophy. This volume complements the reference works of the founder and extend the already numerous books of this editor on the subject. This book starts by describing a major application of neutrosophy: product acceptance determination using a similarity measure index by applying neutrosophic statistics. In one the latest leading mathematics branch: Graph theory, we provide an article on neutrosophic extension of graphs that we can call a neutrosophic graph. A reflection is given on the true nature of neutrosophy by exploring its link with learning such as by Artificial Neural Networks, including Deep Learning. Again, in Mathematics a discussion is made on the solving of systems of linear equations in neutrosophic representation. We also go to the opposite of theory, down to the practical details of implementation for topology using the C# language. Neutrosophic probability is another big new research field. Here, we present a study on the advantages of using neutrosophic variables. Other discipline such as algebra, topology, decision making as well as problem as in logistics and transport are concerned by the remaining articles. Last but not least, we would like to finally mention a major paper to conclude this short presentation of our book titled When Neutrosophic Theory Meets Three-Way Decisions.
