In this paper one generalizes the classical probability and imprecise probability to the notion of “neutrosophic probability” in order to be able to model Heisenberg’s Uncertainty Principle of a particle’s behavior, Schrödinger’s Cat Theory, and the state of bosons which do not obey Pauli’s Exclusion Principle (in quantum physics).

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.

This volume contains 45 papers, written by the author alone or in collaboration with the following co-authors: Mumtaz Ali, Said Broumi, Sukanto Bhattacharya, Mamoni Dhar, Irfan Deli, Mincong Deng, Alexandru Gal, Valeri Kroumov, Pabitra Kumar Maji, Maikel Leyva-Vazquez, Feng Liu, Pinaki Majumdar, Munazza Naz, Karina Perez-Teruel, Rıdvan Sahin, A. A. Salama, Muhammad Shabir, Rajshekhar Sunderraman, Luige Vladareanu, Magdalena Vladila, Stefan Vladutescu, Haibin Wang, Hongnian Yu, Yan-Qing Zhang.

This volume is a collection of ten papers, written by different authors and co-authors (listed in the order of the papers): F. Smarandache, Jun Ye, M. Shabir, M. Ali, M. Naz, F. Yuhua, A. A. Salama, S. Vladutescu, Y. Guo, A. Sengur, S. Broumi, P. Chi, and P. Liu. In first paper, the author proposed Neutrosophic Measure and neutrosophic Integral. Another Form of Correlation Coefficient between Single Valued Neutrosophic Sets and Multiple Attribute Decision-Making Method is proposed in the second paper. Soft Neutrosophic Group is studied in third paper. In fourth paper Neutrosophic Example in Physics is discussed. Similarly in fifth paper Filters via Neutrosophic Crisp Sets are discussed. In paper six, Commnication vs. Information, an Axiomatic Neutrosophic Solution is presented by the authors. A Novel Image Segmentation Algorithm Based on Neutrosophic Filtering and Level Set is given in seventh paper. Paper eight is about to Neutrosophic Crisp Points and Neutrosophic Crisp Ideals. In the next paper Several Similarity Measures of Neutrosophic Sets are discussed. The authors introduced An Extended TOPSIS Method for the Multiple Attribute Decision Making Problems Based on Interval Neutrosophic Sets in the last paper.

“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.

“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 volume is a collection of seventeen papers, written by different authors and co-authors (listed in the order of the papers): F. Smarandache, K. Bhutani, M. Kumar, G. Garg, S. Aggarwal, P. Biswas, S. Pramanik, B. C. Giri, J. Ye, A. Mukherjee, M. Datta, S. Sarkar, N. Shah, M. K. EL Gayyar, S. K. Patro, B. C. Cuong, P. H. Phong, A. A. Salama, I. M. Hanafy, H. Elghawalby and M. S. Dabash, R. Roy, P. Das, D. Mandal, Santhi R., Udhayarani N., F. Yuhua, S. A. Akinleye, A.A.A. Agboola, and J. Chen.

This book is a collection of articles, notes, reviews, blogs and abstracts on Physics. Some are published for the first time here, some were previously published in journals, and revised here. We approach a novel form of plasma, Unmatter Plasma. The electron-positron beam plasma was generated in the laboratory in the beginning of 2015. This experimental fact shows that unmatter, a new form of matter that is formed by matter and antimatter bind together (mathematically predicted a decade ago) really exists. Further, we generalize the Lorentz Contraction Factor for the case when the lengths are moving at an oblique angle with respect to the motion direction, and show that the angles of the moving relativistic objects are distorted. Then, using the Oblique-Length Contraction Factor, we show several trigonometric relations between distorted and original angles of moving object lengths in the Special Theory of Relativity. We also discuss some paradoxes which we call “neutrosophic” since they are based on indeterminacy (or neutrality, i.e. neither true nor false), which is the third component in neutrosophic logic. We generalize the Venn diagram to a Neutrosophic Diagram, which deals with vague, inexact, ambiguous, ill-defined ideas, statements, notions, entities with unclear borders. We define the neutrosophic truth table, then we introduce two neutrosophic operators (neuterization and antonymization operators), and give many classes of neutrosophic paradoxes. Other topics addressed in this book are: neutrosophic physics as a new field of research, neutrosophic numbers in physics, neutrosophic degree of paradoxicity, unparticle and unmatter, multispace and multistructure, nucleon clusters, and others.

This eighth volume of Collected Papers includes 75 papers comprising 973 pages on (theoretic and applied) neutrosophics, written between 2010-2022 by the author alone or in collaboration with the following 102 co-authors (alphabetically ordered) from 24 countries: Mohamed Abdel-Basset, Abduallah Gamal, Firoz Ahmad, Ahmad Yusuf Adhami, Ahmed B. Al-Nafee, Ali Hassan, Mumtaz Ali, Akbar Rezaei, Assia Bakali, Ayoub Bahnasse, Azeddine Elhassouny, Durga Banerjee, Romualdas Bausys, Mircea Boșcoianu, Traian Alexandru Buda, Bui Cong Cuong, Emilia Calefariu, Ahmet Çevik, Chang Su Kim, Victor Christianto, Dae Wan Kim, Daud Ahmad, Arindam Dey, Partha Pratim Dey, Mamouni Dhar, H. A. Elagamy, Ahmed K. Essa, Sudipta Gayen, Bibhas C. Giri, Daniela Gîfu, Noel Batista Hernández, Hojjatollah Farahani, Huda E. Khalid, Irfan Deli, Saeid Jafari, Tèmítópé Gbóláhàn Jaíyéolá, Sripati Jha, Sudan Jha, Ilanthenral Kandasamy, W.B. Vasantha Kandasamy, Darjan Karabašević, M. Karthika, Kawther F. Alhasan, Giruta Kazakeviciute-Januskeviciene, Qaisar Khan, Kishore Kumar P K, Prem Kumar Singh, Ranjan Kumar, Maikel Leyva-Vázquez, Mahmoud Ismail, Tahir Mahmood, Hafsa Masood Malik, Mohammad Abobala, Mai Mohamed, Gunasekaran Manogaran, Seema Mehra, Kalyan Mondal, Mohamed Talea, Mullai Murugappan, Muhammad Akram, Muhammad Aslam Malik, Muhammad Khalid Mahmood, Nivetha Martin, Durga Nagarajan, Nguyen Van Dinh, Nguyen Xuan Thao, Lewis Nkenyereya, Jagan M. Obbineni, M. Parimala, S. K. Patro, Peide Liu, Pham Hong Phong, Surapati Pramanik, Gyanendra Prasad Joshi, Quek Shio Gai, R. Radha, A.A. Salama, S. Satham Hussain, Mehmet Șahin, Said Broumi, Ganeshsree Selvachandran, Selvaraj Ganesan, Shahbaz Ali, Shouzhen Zeng, Manjeet Singh, A. Stanis Arul Mary, Dragiša Stanujkić, Yusuf Șubaș, Rui-Pu Tan, Mirela Teodorescu, Selçuk Topal, Zenonas Turskis, Vakkas Uluçay, Norberto Valcárcel Izquierdo, V. Venkateswara Rao, Volkan Duran, Ying Li, Young Bae Jun, Wadei F. Al-Omeri, Jian-qiang Wang, Lihshing Leigh Wang, Edmundas Kazimieras Zavadskas.

This special issue reflects the impact of neutrosophic theory in Latin America, especially after creating the Latin American Association of Neutrosophic Sciences. Among the areas of publication most addressed in the region are found in the interrelation of social sciences and neutrosophy, presenting outstanding results in these research areas. The main objective of this special issue is to divulge the impact publication related to the Neutrosophic theory and explore new areas of research and application in the region. The SI reflects the influence of the neutrosophic publications in Latin America by opening new research areas mainly related to Neutrosophic Statistics, Plithogeny, and NeutroAlgebra. Furthermore, it is worth mentioning the incorporation of authors from new countries in the region, such as Paraguay, Uruguay, and Panama, to have authors in total from 15 countries, 12 of them from the Latin American region.