The aim of this paper is to introduce a new types of neutrosophic crisp relations as a generalization to intuitionistic relations due to Indira et al.[9], and study some of its properties. Finally, the concepts of the star and retract neutrosophic relations are introduces and studied and some properties of these concepts will be investigated.

We introduce the category NCSet consisting of neutrosophic crisp sets and morphisms between them. And we study NCSet in the sense of a topological universe and prove that it is Cartesian closed over Set, where Set denotes the category consisting of ordinary sets and ordinary mappings between them.

In this paper, we introduce the new notion of intuitionistic neutrosophic crisp sets as a tool for approximating undefinable or complex concepts in real world. First, we deal with some of its algebraic structures. Next, we define an intuitionistic neutrosophic crisp topology, base (subbase) and interior (closure), respectively and investigate some of each properties, and give some examples. Finally, we discussed various intuitionistic neutrosophic crisp continuities.

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.

“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 tenth volume of Collected Papers includes 86 papers in English and Spanish languages comprising 972 pages, written between 2014-2022 by the author alone or in collaboration with the following 105 co-authors (alphabetically ordered) from 26 countries: Abu Sufian, Ali Hassan, Ali Safaa Sadiq, Anirudha Ghosh, Assia Bakali, Atiqe Ur Rahman, Laura Bogdan, Willem K.M. Brauers, Erick González Caballero, Fausto Cavallaro, Gavrilă Calefariu, T. Chalapathi, Victor Christianto, Mihaela Colhon, Sergiu Boris Cononovici, Mamoni Dhar, Irfan Deli, Rebeca Escobar-Jara, Alexandru Gal, N. Gandotra, Sudipta Gayen, Vassilis C. Gerogiannis, Noel Batista Hernández, Hongnian Yu, Hongbo Wang, Mihaiela Iliescu, F. Nirmala Irudayam, Sripati Jha, Darjan Karabašević, T. Katican, Bakhtawar Ali Khan, Hina Khan, Volodymyr Krasnoholovets, R. Kiran Kumar, Manoranjan Kumar Singh, Ranjan Kumar, M. Lathamaheswari, Yasar Mahmood, Nivetha Martin, Adrian Mărgean, Octavian Melinte, Mingcong Deng, Marcel Migdalovici, Monika Moga, Sana Moin, Mohamed Abdel-Basset, Mohamed Elhoseny, Rehab Mohamed, Mohamed Talea, Kalyan Mondal, Muhammad Aslam, Muhammad Aslam Malik, Muhammad Ihsan, Muhammad Naveed Jafar, Muhammad Rayees Ahmad, Muhammad Saeed, Muhammad Saqlain, Muhammad Shabir, Mujahid Abbas, Mumtaz Ali, Radu I. Munteanu, Ghulam Murtaza, Munazza Naz, Tahsin Oner, ‪Gabrijela Popović, Surapati Pramanik, R. Priya, S.P. Priyadharshini, Midha Qayyum, Quang-Thinh Bui, Shazia Rana, Akbara Rezaei, Jesús Estupiñán Ricardo, Rıdvan Sahin, Saeeda Mirvakili, Said Broumi, A. A. Salama, Flavius Aurelian Sârbu, Ganeshsree Selvachandran, Javid Shabbir, Shio Gai Quek, Son Hoang Le, Florentin Smarandache, Dragiša Stanujkić, S. Sudha, Taha Yasin Ozturk, Zaigham Tahir, The Houw Iong, Ayse Topal, Alptekin Ulutaș, Maikel Yelandi Leyva Vázquez, Rizha Vitania, Luige Vlădăreanu, Victor Vlădăreanu, Ștefan Vlăduțescu, J. Vimala, Dan Valeriu Voinea, Adem Yolcu, Yongfei Feng, Abd El-Nasser H. Zaied, Edmundas Kazimieras Zavadskas.