N-Norm and N-conorm are extended in Neutrosophic Logic/Set.

In this volume, we present a set of research that was published in cooperation with a number of researchers and those interested in keeping pace with the great scientific development that our contemporary world is witnessing, and one of its products was neutrosophic science, which was founded by the American scientist and mathematical philosopher Florentin Smarandache in 1995. Through it, we present a new vision for some research methods. Operations research to the concepts of this science.

In this book, we introduce for the first time the notions of neutrosophic measure and neutrosophic integral, and we develop the 1995 notion of neutrosophic probability. We present many practical examples. It is possible to define the neutrosophic measure and consequently the neutrosophic integral and neutrosophic probability in many ways, because there are various types of indeterminacies, depending on the problem we need to solve. Neutrosophics study the indeterminacy. Indeterminacy is different from randomness. It can be caused by physical space materials and type of construction, by items involved in the space, etc.

“Neutrosophic Sets and Systems” has been created for publications on advanced studies in neutrosophy, neutrosophic set, neutrosophic logic, neutrosophic probability, neutrosophic statistics that started in 1995 and their applications in any field, such as the neutrosophic structures developed in algebra, geometry, topology, etc.

This is an eclectic tome of 100 papers in various fields of sciences, alphabetically listed, such as: astronomy, biology, calculus, chemistry, computer programming codification, economics and business and politics, education and administration, game theory, geometry, graph theory,information fusion, neutrosophic logic and set, non-Euclidean geometry, number theory, paradoxes, philosophy of science, psychology, quantum physics, scientific research methods, and statistics ¿ containing 800 pages.It was my preoccupation and collaboration as author, co-author, translator, or co-translator, and editor with many scientists from around the world for long time. Many ideas from this book are to be developed and expanded in future explorations.

This volume is a collection of thirteen papers, written by different authors and co-authors (listed in the order of the papers): J. J. Peng and J. Q. Wang, E. Marei, S. Kar, K. Basu, S. Mukherjee, I. M. Hezam, M. Abdel-Baset and F. Smarandache, K. Mondal, S. Pramanik, A. Ionescu, M. R. Praveen and P. Sekar, B. Teodorescu, D. Kour and K. Basu, P. P. Dey and B. C. Giri, A. A. A. Agboola. In first paper, the authors studied Multi-valued Neutrosophic Sets and its Application in Multi-criteria Decision-Making Problems. More on neutrosophic soft rough sets and its modification is discussed in the second paper. Solution of Multi-Criteria Assignment Problem using Neutrosophic Set Theory are studied in third paper. In fourth paper, Taylor Series Approximation to Solve Neutrosophic Multiobjective Programming Problem. Similarly in fifth paper, Decision Making Based on Some similarity Measures under Interval Rough Neutrosophic Environment is discussed. In paper six, Neutralité neutrosophique et expressivité dans le style journalistique is studied by the author. Neutrosophic Semilattices and Their Properties given in seventh paper. Liminality and Neutrosophy is proposed in the next paper. Application of Extended Fuzzy Program-ming Technique to a real life Transportation Problem in Neutrosophic environment in the next paper. Further, TOPSIS for Single Valued Neutrosophic Soft Expert Set Based Multi-attribute Decision Making Problems is discussed by the authors in the tenth paper. In eleventh paper, Neutrosophic Quadruple Numbers, Refined Neutrosophic Quadruple Numbers, Absorbance Law, and the Multiplication of Neutrosophic Quadruple Numbers have been studied by the author. In the next paper, On Refined Neutrosophic Algebraic Structures. At the end, Neutrosophic Actions, Prevalence Order, Refinement of Neutrosophic Entities, and Neutrosophic Literal Logical Operators are introduced by the authors.

This is the first volume of the Encyclopedia of Neutrosophic Researchers, edited from materials offered by the authors who responded to the editor’s invitation. The 78 authors are listed alphabetically. The introduction contains a short history of neutrosophics, together with links to the main papers and books. Neutrosophic set, neutrosophic logic, neutrosophic probability, neutrosophic statistics, neutrosophic measure, neutrosophic precalculus, neutrosophic calculus and so on are gaining significant attention in solving many real life problems that involve uncertainty, impreciseness, vagueness, incompleteness, inconsistent, and indeterminacy. In the past years the fields of neutrosophics have been extended and applied in various fields, such as: artificial intelligence, data mining, soft computing, decision making in incomplete / indeterminate / inconsistent information systems, image processing, computational modelling, robotics, medical diagnosis, biomedical engineering, investment problems, economic forecasting, social science, humanistic and practical achievements.