Contributing to the fast-growing new field of neutrosophy, this book provides a significant collection of inedited articles covering the latest ongoing research area. Neutrosopy is above all a new view on modelling, tailored to effectively address the uncertainties inherent to 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 and inconsistent. Development of neutrosophy, since its conception by Smarandache in 1988, has grown exponentially by conceptual extensions to logics, measure, sets, graphs, as well as practical applications in namely all fields. It can be thought of as a generalization of fuzzy logic and its variants like intuitionistic fuzzy logic. Registered in a 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 extends the already numerous books of him and other researchers on the subject. This book starts by describing in an application major step for product acceptance determination using similarity measure index by applying neutrosophic statistics. In one of the latest major mathematics branches, 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 system of linear equations in neutrosophic representation. We also go to the opposite end of the theory, down to the practical details of implementation of topology using the C# language. Neutrosophic probability is another big new research field. Here we give a study on the advantages of using neutrosophic variables. Other disciplines such as algebraic structures, topological spaces, and decision-making as well as problems in logistics and transport are covered by the remaining articles. Last but not least, a major paper is given, that concludes this short presentation of our book, " When Neutrosophic Theory Meets Three-Way Decisions ".
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