This volume is a collection of seven papers, written by different authors and co-authors (listed in the order of the papers): A. A. Salama, F. Smarandache, Valeri Kroumov, A. A. A. Agboola, S. A. Akinleye, M. Ali, M. Shabir, M. Naz, I. Deli, Y. Toktas, S. Broumi, Z. Zhang, C. Wu, S. A. Alblowi, C. Dyer. In first paper, the authors proposed Neutrosophic Closed Set and Neutrosophic Continuous Function. Neutrosophic Vector spaces are proposed in the second paper. Neutrosophic Bi-LA-Semigroup and Neutrosophic N-LA-Semigroup is studied in third paper. In fourth paper Neutrosophic Parameterized Soft Relations and Their Applications are introduced. Similarly in fifth paper A novel method for single valued neutrosophic multi-criteria decision making with incomplete weight information are discussed. In paper six, New Neutrosophic Crisp Topological Concept is presented by the authors. Soft Neutrosophic Loops and Their Generalization is given in seventh 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.

This volume is a collection of ten papers by contributors F. Smarandache, F. Yuhua, K. Mondal, S. Pramanik, S. Broumi, J. Ye, A. A. Salama,, N. Easa, S. A. Elhafez, M. M. Lotfy, L. Kong, Y. Wu, P. Biswas, B. C. Giri, A. Mukkerjee, and S. Sarkar, focusing on a new kind of algebraic structures called (T, I, F)- Neutrosophic Structures; Expanding Uncertainty Principle to Certainty-Uncertainty Principles with Neutrosophy and Quad-stage Methods; Rough Neutrosophic Multi-Attribute Decision-Making Based on Rough Accuracy Score Function; an Extended TOPSIS Method for Multiple Attribute Decision Making based on Interval Neutrosophic Uncertain Linguistic Variable; Review of Recommender Systems Algorithms Utilized in Social Networks based e-Learning Systems & Neutrosophic System; Fault Diagnosis Method of Gasoline Engines Using the Cosine Similarity Measure of Neutrosophic Numbers; Cosine Similarity Measure Based Multi-attribute Decision-making with Trapezoidal Fuzzy Neutrosophic Numbers; Thesis-Antithesis-Neutrothesis, and Neutrosynthesis; Negating Four Color Theorem with Neutrosophy and Quadstage Method; and A new method of measuring similarity between two neutrosophic soft sets and its application in pattern recognition problems.

Twelve papers on soft interval-valued neutrosophic rough sets, fuzzy neutosophic relation equations with geometric programming, rough neutrosophic multi-attribute decision-making, classes of neutrosophic crisp nearly open sets and possible application to GIS topology, neutrosophic probability in physics, and similar topics. Contributors: H. E. Khalid, K. Mondal, S. Pramanik, A. A. Salama, S. Broumi, F. Smarandache, F. Yuhua, M. Ali, M. Shabir, V. Patrascu, S. Ye, J. Fu, J. Ye, A. Hussain, and L. Vladareanu.

“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.

Papers on neutrosophic statistics, neutrosophic probability, plithogenic set, paradoxism, neutrosophic set, NeutroAlgebra, etc. and their applications.