Neutrosophic set is a new mathematical tool for handling problems involving imprecise, indetermi nacy and inconsistent data. Pseudo-BCI algebra is a kind of non-classical logic algebra in close connection with various non-commutative fuzzy logics. Recently, we applied neutrosophic set theory to pseudo-BCI al gebras. In this paper, we study neutrosophic filters in pseudo-BCI algebras. The concepts of neutrosophic regular filter, neutrosophic closed filter and fuzzy regular filter in pseudo-BCI algebras are introduced, and some basic properties are discussed. Moreover, the relationships (...) among neutrosophic regular filter, fuzzy filters and anti-grouped neutrosophic filters are prese nted, and the results are proved: a neutrosophic filter (fuzzy filter) is a neutrosophic regular filter (fuzzy regular filter), if and only if it is both a neutrosophic closed filter (fuzzy closed filter) and an anti-grouped neutrosophic filter (fuzzy anti-grouped filter). (shrink)

In this paper, we presented antoher concept of neutrosophic open sets called neutrosophic semi-α-open sets and studied their fundamental poperties in neutrosophic topological spaces. We also present neutrospohic semi-α-interior and neutrosophic semi-α-closure and study some of their fundamental properties.

The concept of neutrosophic locally compact and neutrosophic compact open topology are introduced and some interesting propositions are discussed.

In this paper we present the concept of neutrosophic quadruple algebraic structures. Specially, we study neutrosophic quadruple rings and we present their elementary properties.

The notion of neutrosophic cubic set is originated from the hybridization of the concept of neutrosophic set and interval valued neutrosophic set. We define similarity measure for neutrosophic cubic sets and prove some of its basic properties. We present a new multi criteria group decision making method with linguistic variables in neutrosophic cubic set environment. Finally, we present a numerical example to demonstrate the usefulness and applicability of the proposed method.

In this paper, we introduce and investigate a new class of sets and functions between topological space called neutrosophic semi-supra open set and neutrosophic semi-supra open continuous functions respectively.

In this paper, we propose a new concept named the uniform single valued neutrosophic graph. An illustrative example and some properties are examined. Next, we develop an algorithmic approach for computing the complement of the single valued neutrosophic graph. A numerical example is demonstrated for computing the complement of single valued neutrosophic graphs and uniform single valued neutrosophic graph.

A hypergroup, as a generalization of the notion of a group, was introduced by F. Marty in 1934. The first book in hypergroup theory was published by Corsini. Nowadays, hypergroups have found applications to many subjects of pure and applied mathematics, for example, in geometry, topology, cryptography and coding theory, graphs and hypergraphs, probability theory, binary relations, theory of fuzzy and rough sets and automata theory, physics, and also in biological inheritance.

Today, soft computing is a field that is used a lot in solving real-world problems, such as problems in economics, finance, banking... With the aim to serve for solving the real problem, many new theories and/or tools which were proposed, improved to help soft computing used more efficiently. We can mention some theories as fuzzy sets theory (L. Zadeh, 1965), intuitionistic fuzzy set (K Atanasov, 1986), neutrosophic set (F. Smarandache 1999). In this paper, we introduce a new notion of (...) sup port-neutrosophic set (SNS), which is the combination a neutrosophic set with a fuzzy set. So, SNS set is a direct extension of fuzzy set and neutrosophic sets (F. Smarandache). Then, we define some operators on the support-neutrosophic sets, and investigate some properties of these operators. (shrink)

In this paper, we generalize the soft set to the hypersoft set by transforming the function F into a multi-attribute function. Then we introduce the hybrids of Crisp, Fuzzy, Intuitionistic Fuzzy, Neutrosophic, and Plithogenic Hypersoft Set.

This paper is an improvement of our paper “(t, i, f)-Neutrosophic Structures”, where we introduced for the first time a new type of structures, called (t, i, f)- Neutrosophic Structures, presented from a neutrosophic logic perspective, and we showed particular cases of such structures in geometry and in algebra.

Study represents an application of the neutrosophic method, for solving the contradiction between communication and information. In addition, it recourse to an appropriate method of approaching the contradictions: Extensics, as the method and the science of solving the contradictions. The research core is the reality that the scientific research of communication-information relationship has reached a dead end. The bivalent relationship communicationinformation, information-communication has come to be contradictory, and the two concepts to block each other. After the critical examination of conflicting (...) positions expressed by many experts in the field, the extensic and inclusive hypothesis is issued that information is a form of communication. The object of communication is the sending of a message. The message may consist of thoughts, ideas, opinions, feelings, beliefs, facts, information, intelligence or other significational elements. When the message content is primarily informational, communication will become information or intelligence. The arguments of supporting the hypothesis are: a) linguistic (the most important being that there is "communication of information" but not "information of communication"; also, it is clarified and reinforced the over situated referent, that of the communication as a process), b) systemic-procedural (in the communication system is developing an information system; the informing actant is a type of communicator, the information process is a communication process), c) practical (the delimitation eliminates the efforts of disparate and inconsistent understanding of the two concepts), d) epistemological arguments (the possibility of intersubjective thinking of reality is created), linguistic arguments, e) logical and realistic arguments (it is noted the situation that allows to think coherently in a system of concepts - derivative series or integrative groups) f) and arguments from historical experience (the concept of communication has temporal priority, it appears 13 times in Julius Caesar’s writings ). In an axiomatic conclusion, the main arguments are summarized in four axioms: three are based on the pertinent observations of specialists, and the fourth is a relevant application of Florentin Smarandache’s neutrosophic theory. (shrink)

This paper is an extension of “(t, i, f)-Neutrosophic Structures” applicability , where were introduced for the first time a new type of structures, called (t, i, f)- Neutrosophic Structures, presented from a neutrosophic logic perspective.

In this paper, we introduce for the first time the neutrosophic quadruple numbers (of the form a + bT + cI + dF) and the refined neutrosophic quadruple numbers. Then we define an absorbance law, based on a prevalence order, both of them in order to multiply the neutrosophic components T, I, F, or their sub-components tJ, Ik, Fl and thus to construct the multiplication of neutrosophic quadruple numbers.

In this paper, we define for the first time three neutrosophic actions and their properties. We then introduce the prevalence order on {T, I, F} with respect to a given neutrosophic operator “o”, which may be subjective - as defined by the neutrosophic experts; and the refinement of neutrosophic entities <A>, <neutA>, and <antiA> . Then we extend the classical logical operators to neutrosophic literal logical operators and to refined literal logical operators, and we define the refinement neutrosophic literal space.

This eleventh volume of Collected Papers includes 90 papers comprising 988 pages on Physics, Artificial Intelligence, Health Issues, Decision Making, Economics, Statistics, written between 2001-2022 by the author alone or in collaboration with the following 84 co-authors (alphabetically ordered) from 19 countries: Abhijit Saha, Abu Sufian, Jack Allen, Shahbaz Ali, Ali Safaa Sadiq, Aliya Fahmi, Atiqa Fakhar, Atiqa Firdous, Sukanto Bhattacharya, Robert N. Boyd, Victor Chang, Victor Christianto, V. Christy, Dao The Son, Debjit Dutta, Azeddine Elhassouny, Fazal Ghani, Fazli Amin, (...) Anirudha Ghosha, Nasruddin Hassan, Hoang Viet Long, Jhulaneswar Baidya, Jin Kim, Jun Ye, Darjan Karabašević, Vasilios N. Katsikis, Ieva Meidutė-Kavaliauskienė, F. Kaymarm, Nour Eldeen M. Khalifa, Madad Khan, Qaisar Khan, M. Khoshnevisan, Kifayat Ullah,, Volodymyr Krasnoholovets, Mukesh Kumar, Le Hoang Son, Luong Thi Hong Lan, Tahir Mahmood, Mahmoud Ismail, Mohamed Abdel-Basset, Siti Nurul Fitriah Mohamad, Mohamed Loey, Mai Mohamed, K. Mohana, Kalyan Mondal, Muhammad Gulfam, Muhammad Khalid Mahmood, Muhammad Jamil, Muhammad Yaqub Khan, Muhammad Riaz, Nguyen Dinh Hoa, Cu Nguyen Giap, Nguyen Tho Thong, Peide Liu, Pham Huy Thong, Gabrijela Popović‬‬‬‬‬‬‬‬‬‬, Surapati Pramanik, Dmitri Rabounski, Roslan Hasni, Rumi Roy, Tapan Kumar Roy, Said Broumi, Saleem Abdullah, Muzafer Saračević, Ganeshsree Selvachandran, Shariful Alam, Shyamal Dalapati, Housila P. Singh, R. Singh, Rajesh Singh, Predrag S. Stanimirović, Kasan Susilo, Dragiša Stanujkić, Alexandra Şandru, Ovidiu Ilie Şandru, Zenonas Turskis, Yunita Umniyati, Alptekin Ulutaș, Maikel Yelandi Leyva Vázquez, Binyamin Yusoff, Edmundas Kazimieras Zavadskas, Zhao Loon Wang.‬‬‬‬. (shrink)

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.‬‬. (shrink)

We present a study of linear models using the concepts of neutrosophic science, the science that was built on the basis that there is no absolute truth, there is no confirmed data, issues cannot be limited to right and wrong only. There is a third state between error and right, an indeterminate, undetermined, uncertain state. It is indeterminacy. Neutrosophic science gave each issue three dimensions, namely (T, I, F), correctness in degrees, indeterminacy in degrees, and error in degrees. It was (...) founded by the American philosopher and mathematician Florentin Smarandache, in 1995 and came as a generalization of fuzzy logic that was founded by the scientist Lotfi. A. Zadeh, in 1965. (shrink)

This fourteenth volume of Collected Papers is an eclectic tome of 87 papers in Neutrosophics and other fields, such as mathematics, fuzzy sets, intuitionistic fuzzy sets, picture fuzzy sets, information fusion, robotics, statistics, or extenics, comprising 936 pages, published between 2008-2022 in different scientific journals or currently in press, by the author alone or in collaboration with the following 99 co-authors (alphabetically ordered) from 26 countries: Ahmed B. Al-Nafee, Adesina Abdul Akeem Agboola, Akbar Rezaei, Shariful Alam, Marina Alonso, Fran Andujar, (...) Toshinori Asai, Assia Bakali, Azmat Hussain, Daniela Baran, Bijan Davvaz, Bilal Hadjadji, Carlos Díaz Bohorquez, Robert N. Boyd, M. Caldas, Cenap Özel, Pankaj Chauhan, Victor Christianto, Salvador Coll, Shyamal Dalapati, Irfan Deli, Balasubramanian Elavarasan, Fahad Alsharari, Yonfei Feng, Daniela Gîfu, Rafael Rojas Gualdrón, Haipeng Wang, Hemant Kumar Gianey, Noel Batista Hernández, Abdel-Nasser Hussein, Ibrahim M. Hezam, Ilanthenral Kandasamy, W.B. Vasantha Kandasamy, Muthusamy Karthika, Nour Eldeen M. Khalifa, Madad Khan, Kifayat Ullah, Valeri Kroumov, Tapan Kumar Roy, Deepesh Kunwar, Le Thi Nhung, Pedro López, Mai Mohamed, Manh Van Vu, Miguel A. Quiroz-Martínez, Marcel Migdalovici, Kritika Mishra, Mohamed Abdel-Basset, Mohamed Talea, Mohammad Hamidi, Mohammed Alshumrani, Mohamed Loey, Muhammad Akram, Muhammad Shabir, Mumtaz Ali, Nassim Abbas, Munazza Naz, Ngan Thi Roan, Nguyen Xuan Thao, Rishwanth Mani Parimala, Ion Pătrașcu, Surapati Pramanik, Quek Shio Gai, Qiang Guo, Rajab Ali Borzooei, Nimitha Rajesh, Jesús Estupiñan Ricardo, Juan Miguel Martínez Rubio, Saeed Mirvakili, Arsham Borumand Saeid, Saeid Jafari, Said Broumi, Ahmed A. Salama, Nirmala Sawan, Gheorghe Săvoiu, Ganeshsree Selvachandran, Seok-Zun Song, Shahzaib Ashraf, Jayant Singh, Rajesh Singh, Son Hoang Le, Tahir Mahmood, Kenta Takaya, Mirela Teodorescu, Ramalingam Udhayakumar, Maikel Y. Leyva Vázquez, V. Venkateswara Rao, Luige Vlădăreanu, Victor Vlădăreanu, Gabriela Vlădeanu, Michael Voskoglou, Yaser Saber, Yong Deng, You He, Youcef Chibani, Young Bae Jun, Wadei F. Al-Omeri, Hongbo Wang, Zayen Azzouz Omar. (shrink)

This sixth volume of Collected Papers includes 74 papers comprising 974 pages on (theoretic and applied) neutrosophics, written between 2015-2021 by the author alone or in collaboration with the following 121 co-authors from 19 countries: Mohamed Abdel-Basset, Abdel Nasser H. Zaied, Abduallah Gamal, Amir Abdullah, Firoz Ahmad, Nadeem Ahmad, Ahmad Yusuf Adhami, Ahmed Aboelfetouh, Ahmed Mostafa Khalil, Shariful Alam, W. Alharbi, Ali Hassan, Mumtaz Ali, Amira S. Ashour, Asmaa Atef, Assia Bakali, Ayoub Bahnasse, A. A. Azzam, Willem K.M. Brauers, Bui (...) Cong Cuong, Fausto Cavallaro, Ahmet Çevik, Robby I. Chandra, Kalaivani Chandran, Victor Chang, Chang Su Kim, Jyotir Moy Chatterjee, Victor Christianto, Chunxin Bo, Mihaela Colhon, Shyamal Dalapati, Arindam Dey, Dunqian Cao, Fahad Alsharari, Faruk Karaaslan, Aleksandra Fedajev, Daniela Gîfu, Hina Gulzar, Haitham A. El-Ghareeb, Masooma Raza Hashmi, Hewayda El-Ghawalby, Hoang Viet Long, Le Hoang Son, F. Nirmala Irudayam, Branislav Ivanov, S. Jafari, Jeong Gon Lee, Milena Jevtić, Sudan Jha, Junhui Kim, Ilanthenral Kandasamy, W.B. Vasantha Kandasamy, Darjan Karabašević, Songül Karabatak, Abdullah Kargın, M. Karthika, Ieva Meidute-Kavaliauskiene, Madad Khan, Majid Khan, Manju Khari, Kifayat Ullah, K. Kishore, Kul Hur, Santanu Kumar Patro, Prem Kumar Singh, Raghvendra Kumar, Tapan Kumar Roy, Malayalan Lathamaheswari, Luu Quoc Dat, T. Madhumathi, Tahir Mahmood, Mladjan Maksimovic, Gunasekaran Manogaran, Nivetha Martin, M. Kasi Mayan, Mai Mohamed, Mohamed Talea, Muhammad Akram, Muhammad Gulistan, Raja Muhammad Hashim, Muhammad Riaz, Muhammad Saeed, Rana Muhammad Zulqarnain, Nada A. Nabeeh, Deivanayagampillai Nagarajan, Xenia Negrea, Nguyen Xuan Thao, Jagan M. Obbineni, Angelo de Oliveira, M. Parimala, Gabrijela Popovic, Ishaani Priyadarshini, Yaser Saber, Mehmet Șahin, Said Broumi, A. A. Salama, M. Saleh, Ganeshsree Selvachandran, Dönüș Șengür, Shio Gai Quek, Songtao Shao, Dragiša Stanujkić, Surapati Pramanik, Swathi Sundari Sundaramoorthy, Mirela Teodorescu, Selçuk Topal, Muhammed Turhan, Alptekin Ulutaș, Luige Vlădăreanu, Victor Vlădăreanu, Ştefan Vlăduţescu, Dan Valeriu Voinea, Volkan Duran, Navneet Yadav, Yanhui Guo, Naveed Yaqoob, Yongquan Zhou, Young Bae Jun, Xiaohong Zhang, Xiao Long Xin, Edmundas Kazimieras Zavadskas. (shrink)

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. (shrink)

This twelfth volume of Collected Papers includes 86 papers comprising 976 pages on Neutrosophics Theory and Applications, published between 2013-2021 in the international journal and book series “Neutrosophic Sets and Systems” by the author alone or in collaboration with the following 112 co-authors (alphabetically ordered) from 21 countries: Abdel Nasser H. Zaied, Muhammad Akram, Bobin Albert, S. A. Alblowi, S. Anitha, Guennoun Asmae, Assia Bakali, Ayman M. Manie, Abdul Sami Awan, Azeddine Elhassouny, Erick González-Caballero, D. Dafik, Mithun Datta, Arindam Dey, (...) Mamouni Dhar, Christopher Dyer, Nur Ain Ebas, Mohamed Eisa, Ahmed K. Essa, Faruk Karaaslan, João Alcione Sganderla Figueiredo, Jorge Fernando Goyes García, N. Ramila Gandhi, Sudipta Gayen, Gustavo Alvarez Gómez, Sharon Dinarza Álvarez Gómez, Haitham A. El-Ghareeb, Hamiden Abd El-Wahed Khalifa, Masooma Raza Hashmi, Ibrahim M. Hezam, German Acurio Hidalgo, Le Hoang Son, R. Jahir Hussain, S. Satham Hussain, Ali Hussein Mahmood Al-Obaidi, Hays Hatem Imran, Nabeela Ishfaq, Saeid Jafari, R. Jansi, V. Jeyanthi, M. Jeyaraman, Sripati Jha, Jun Ye, W.B. Vasantha Kandasamy, Abdullah Kargın, J. Kavikumar, Kawther Fawzi Hamza Alhasan, Huda E. Khalid, Neha Andalleb Khalid, Mohsin Khalid, Madad Khan, D. Koley, Valeri Kroumov, Manoranjan Kumar Singh, Pavan Kumar, Prem Kumar Singh, Ranjan Kumar, Malayalan Lathamaheswari, A.N. Mangayarkkarasi, Carlos Rosero Martínez, Marvelio Alfaro Matos, Mai Mohamed, Nivetha Martin, Mohamed Abdel-Basset, Mohamed Talea, K. Mohana, Muhammad Irfan Ahamad, Rana Muhammad Zulqarnain, Muhammad Riaz, Muhammad Saeed, Muhammad Saqlain, Muhammad Shabir, Muhammad Zeeshan, Anjan Mukherjee, Mumtaz Ali, Deivanayagampillai Nagarajan, Iqra Nawaz, Munazza Naz, Roan Thi Ngan, Necati Olgun, Rodolfo González Ortega, P. Pandiammal, I. Pradeepa, R. Princy, Marcos David Oviedo Rodríguez, Jesús Estupiñán Ricardo, A. Rohini, Sabu Sebastian, Abhijit Saha, Mehmet Șahin, Said Broumi, Saima Anis, A.A. Salama, Ganeshsree Selvachandran, Seyed Ahmad Edalatpanah, Sajana Shaik, Soufiane Idbrahim, S. Sowndrarajan, Mohamed Talea, Ruipu Tan, Chalapathi Tekuri, Selçuk Topal, S. P. Tiwari, Vakkas Uluçay, Maikel Leyva Vázquez, Chinnadurai Veerappan, M. Venkatachalam, Luige Vlădăreanu, Ştefan Vlăduţescu, Young Bae Jun, Wadei F. Al-Omeri, Xiao Long Xin.‬‬‬‬‬‬. (shrink)

This book is inspired by a German theoretical physicist, Sabine Hossenfelder’s publication: “Lost in Mathematics”. Her book seems to question highly mathematical and a lot of abstraction in the development of physics and cosmology studies nowadays. There is clear tendency that in recent decades, the physics science has been predominated by such an advanced mathematics, which at times sounding more like acrobatics approach to a reality. Through books by senior mathematical-physicists like Unzicker and Peter Woit, we know that the answer (...) of TOE is not in superstring theories or other variations of such 26 dimensional bosonic string theory, of which none of those theories survived experimental test, but perhaps in low dimensional physics. As Alexander Unzicker suggests, perhaps it is more advisable to consider rotation in 3D space (known as SO3), or a kind of superfluid vortices version of gravitation theory. We can also reconsider proposition by the late Prof F. Winterberg (formerly professor at Univ. Nevada, Reno), that it is most likely that superfluid phonon roton theory in 3D can replace the entire superstring theories. While we don’t explore yet implications of his model to particle physics, we discuss here some published papers at several journals in the past few years. (shrink)

In this paper, we introduce the integer programming in neutrosophic environment, by considering coffecients of problem as a triangulare neutrosophic numbers. The degrees of acceptance, indeterminacy and rejection of objectives are simultaneously considered. The Neutrosophic Integer Programming Problem (NIP) is transformed into a crisp programming model, using truth membership (T), indeterminacy membership (I), and falsity membership (F) functions as well as single valued triangular neutrosophic numbers. To measure the efficiency of the model, we solved several numerical examples.

We use a neutrosophic set, instead of an intuitionistic fuzzy because the neutrosophic set is more general, and it allows for independent and partial independent components, while in an intuitionistic fuzzy set, all components are totally dependent. In this article, we present and demonstrate the concept of neutrosophic invariant subgroups. We delve into the exploration of this notion to establish and study the neutrosophic quotient group. Further, we give the concept of a neutrosophic normal subgroup as a novel concept.

Cloud computing (ClC) has become a more popular computer paradigm in the preceding few years. Quality of Service (QoS) is becoming a crucial issue in service alteration because of the rapid growth in the number of cloud services. When evaluating cloud service functioning using several performance measures, the issue becomes more complex and non-trivial. It is therefore quite difficult and crucial for consumers to choose the best cloud service. The user's choices are provided in a quantifiable manner in the current (...) methods for choosing cloud services. Hence, this study attempts to achieve this objective through construction. decision-making framework so-called cloud services evaluator (CSsEv). The main indicator and its sub-indicators are formed as nodes at levels(n) in tree soft sets (TSSs). Thereafter Single Value Neutrosophic Sets (SVNSs) as branch of neutrosophic sets which conjunction with the Multi-Criteria Decision Making (MCDM) technique to facilitate analysis and evaluation process for the available Cloud services providers. Hence, entropy is employed to obtain indicators and sub_indicators weights and Complex Proportional Assessment utilizes these weights to facilitate the decision process of selecting optimal ClSPs. (shrink)

This paper introduces a refined single-valued neutrosophic set (RSVNS) and presents a similarity measure of RSVNSs. Then a multicriteria decision-making method with RSVNS information is developed based on the similarity measure of RSVNSs. By the similarity measure between each alternative and the ideal solution (ideal alternative), all the alternatives can be ranked and the best one can be selected as well. Finally, an actual example on the selecting problems of construction projects demonstrates the application and effectiveness of the proposed method.

The purpose of this study is to propose new similarity measures namely rough variational coefficient similarity measure under the rough neutrosophic environment. The weighted rough variational coefficient similarity measure has been also defined. The weighted rough variational coefficient similarity measures between the rough ideal alternative and each alternative are xxxxx calculated to find the best alternative. The ranking order of all the alternatives can be determined by using the numerical values of similarity measures. Finally, an illustrative example has been provided (...) to show the effectiveness and validity of the proposed approach. Comparisons of decision results of existing rough similarity measures have been provided. (shrink)

This paper is devoted to present Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) method for multi-attribute group decision making under rough neutrosophic environment. The concept of rough neutrosophic set is a powerful mathematical tool to deal with uncertainty, indeterminacy and inconsistency. In this paper, a new approach for multi-attribute group decision making problems is proposed by extending the TOPSIS method under rough neutrosophic environment. Rough neutrosophic set is characterized by the upper and lower approximation operators and the (...) pair of neutrosophic sets that are characterized by truth-membership degree, indeterminacy membership degree, and falsity membership degree. In the decision situation, ratings of alternatives with respect to each attribute are characterized by rough neutrosophic sets that reflect the decision makers’ opinion. Rough neutrosophic weighted averaging operator has been used to aggregate the individual decision maker’s opinion into group opinion for rating the importance of attributes and alternatives. Finally, a numerical example has been provided to demonstrate the applicability and effectiveness of the proposed approach. (shrink)

In this study, we propose a new approach based on fuzzy TODIM (Portuguese acronym for interactive and multicriteria decision-making) for decision-making problems in uncertain environments. Our method incorporates group utility and individual regret, which are often ignored in traditional multicriteria decision-making (MCDM) methods. To enhance the analysis and application of fuzzy sets in decision-making processes, we introduce novel entropy and distance measures for q-rung picture fuzzy sets. These measures include an entropy measure based on the sine function and a distance (...) measure derived from the Jensen-Shannon divergence. In our methodology, incorporating the sine function into the entropy measure stands out as a distinctive decision, grounded in a profound understanding of the inherent characteristics of fuzzy sets. Utilizing the sine function proves especially advantageous when handling fuzzy sets that exhibit cyclical variations or fluctuations in their membership degrees. We effectively weight the criteria for an improved evaluation by using this new entropy measure. The introduced distance measure finds application in the TODIM approach, allowing the execution of TODIM method steps within a fuzzy environment until the determination of one alternative’s dominance over another—an advancement beyond traditional approaches. We apply our enhanced fuzzy TODIM method to a real-life construction project management problem from the literature and compare the results with those in the literature and obtained from other MCDM methods. Our proposed measures are robust, as demonstrated by the sensitivity analysis that varied the weights of group utility and individual regret, with the results visualized in a 3D sensitivity plot. The findings demonstrate the superiority of our method in providing a more comprehensive evaluation of alternatives, making it a useful tool for decision-makers facing complex and uncertain decision-making problems. (shrink)

Characterizations of an (∈, ∈)-neutrosophic ideal are considered. Any ideal in a BCK/BCI-algebra will be realized as level neutrosophic ideals of some (∈, ∈)-neutrosophic ideal. The relation between (∈, ∈)-neutrosophic ideal and (∈, ∈)-neutrosophic subalgebra in a BCK-algebra is discussed. Conditions for an (∈, ∈)-neutrosophic subalgebra to be a (∈, ∈)-neutrosophic ideal are provided. Using a collection of ideals in a BCK/BCI-algebra, an (∈, ∈)-neutrosophic ideal is established. Equivalence relations on the family of all (∈, ∈)-neutrosophic ideals are introduced, and (...) related properties are investigated. (shrink)

We introduce Pura Vida Neutrosophic Algebra, an algebraic structure consisting of neutrosophic numbers equipped with two binary operations namely addition and multiplication. The addition can be calculated sometimes with the function min and other times with the max function. The multiplication operation is the usual sum between numbers. Pura Vida Neutrosophic Algebra is an extension of both Tropical Algebra (also known as Min-Plus, or Min-Algebra) and Max-Plus Algebra (also known as Max-algebra). Tropical and Max-Plus algebras are algebraic structures included in (...) semirings and their operations can be used in matrices and vectors. Pura Vida Neutrosophic Algebra is included in Neutrosophic semirings and can be used in Neutrosophic matrices and vectors. (shrink)

The concept of a hypersoft membership function is introduced in the extension of a soft set known as a hypersoft set, permitting it to handle complicated and uncertain information in a more powerful and flexible manner. Many academics have already become fascinated with this new area of study, leading to the development of a number of hybrid structures. This chapter develops some new hybrid hypersoft set structures by taking into account multiple fuzzy set-like settings and possibility degree-based settings collectively. Additionally, (...) numerical examples are included to clarify the concept of these structures. Researchers can utilize this work to better understand and apply a variety of mathematical ideas. (shrink)

In this chapter, a new type Hyper groups are defined, corresponding basic properties and examples for new type Hyper groups are given and proved. Moreover, new type Hypergroups groups and are compared to hyper groups and groups. New type Hyper groups are shown to have a more general structure according to Hyper groups and groups. Also, new type SuperHyper groups are defined, corresponding basic properties and examples for new type SuperHyper are given and proved. Furthermore, we defined neutro-new type SuperHyper (...) groups. (shrink)

This paper introduces the novel concept of Neutro-BCK-algebra. In Neutro-BCK-algebra, the outcome of any given two elements under an underlying operation (neutro-sophication procedure) has three cases, such as: appurtenance, non-appurtenance, or indeterminate.

Because anticipated and retrospective regret play important roles in practical deliberation and motivation, better understanding them can illuminate the contours of human agency. However, the possibility of self-ignorance and the fact that we change over time can make regret—especially anticipatory regret—not only a poor predictor of where the agent will be in the future but also an unreliable indicator of where the agent stands. Granting these, this paper examines the way in which prospective and, particularly, retrospective regret can nevertheless yield (...) important insight into the sorts of creatures we are, both generally and individually. The experience of retrospective regret can show a person she values something in a way she did not know or that she is (or was) a different person than she had thought, insights which can factor into forward-looking, or prospective, deliberation. Such instances of revelatory regret reveal something to the agent about herself as agent. I examine two cases of agential self-ignorance. In the first, the experience of regret reveals what the agent values, not only to others but even to the agent himself. In the second, the agent anticipates experiencing regret for an action but does not experience the regret, suggesting that the agent did not value the rejected alternative in the way she thought. Anticipatory regret is forward-looking and can play an important role in practical deliberation. But insofar as anticipatory regret flows from one’s imperfect judgment and prospection about oneself, retrospective regret can be an important corrective in helping the agent understand her own standpoint. (shrink)

In this paper we introduce the concept of interval valued neutrosophic soft topological space together with interval valued neutrosophic soft finer and interval valued neutrosophic soft coarser topology. We also define interval valued neutrosophic interior and closer of an interval valued neutrosophic soft set. Some theorems and examples are cites. Interval valued neutrosophic soft subspace topology are studied. Some examples and theorems regarding this concept are presented.

In this article, we first provide a modified definition of SuperHyperGraphs (SHG) and we call it Restricted SuperHyperGraphs (R-SHG). We then generalize the R-SHG to the neutrosophic graphs and then define the corresponding trees. In the following, we examine the Helly property for subtrees of SuperHyperGraphs.

Both neutrosophic sets theory and rough sets theory are emerging as powerful tool for managing uncertainty, indeterminate, incomplete and imprecise information .In this paper we develop an hybrid structure called “ rough neutrosophic sets” and studied their properties.

لأننا نعيش في عالم يكتنفه الغموض من كل جانب؛ عالم تتسم معرفتنا لأحداثه ووقائعه بالتناقض واللاتحديد، وتُفصح قضايانا اللغوية الواصفة له عن الصدق تارة وعن الكذب تارة أخرى، فنحن في حاجة إلى فلسفة جديدة تعكس حقيقة رؤيتنا النسبية لهذا العالم وقصور معرفتنا به؛ ونحن في حاجة إلى نسقٍِ منطقي يُلائم معطياته غير المكتملة ويُشبع معالجاتنا لها، سواء على مستوى ممارسات الحياة اليومية أو على مستوى الممارسة العلمية بمختلف أشكالها. والفلسفة التي يقترحها هذا الكتاب هي «النيوتروسوفيا»؛ تلك النظرية التي قدمها الفيلسوف (...) والرياضي الأمريكي «فلورنتن سمارانداكه» العام 1995 كتعميم للنزعة الجدلية، والتي تكشف بأسلوب جديد عن تناقضات الفكر وحركته الدائبة والمتصلة بين الصدق والكذب، وتُعيد لملكة السلب هيبتها المفقودة لدى العقل القانع بوهم الثبات المطلق. ومن هذه النظرية ينبثق المنطق النيوتروسوفي كتعميم لأنساق المنطق المعاصر متعدد القيم، لاسيما المنطق الحدسي الغائم. ورغم حداثة النظرية والنسق، وتعدد مجالات تطبيقهما في الفكر الغربي المعاصر، وبصفة خاصة مجالات العلم التقني، إلا أن ثمة استخدامات أخرى لهما لدى مفكري العرب والإسلام إبان مرحلة ازدهار الحضارة الإسلامية، وهو ما يكشف عنه الكتاب من خلال دراسة منطقية مقارنة، تميط اللثام عن أصالة وخصوبة الفكر العربي، فضلاً عن تحرره وتسامحه وجمعه بين الرأي والرأي الآخر، في وقت يوسم فيه من قبل الغرب بالانغلاقية، والتشدد، والتحجر، ورفض الآخر، وخصومة الحوار الجدلي. (shrink)

In this article, we shall define the addition and multiplication of two neutrosophic fuzzy matrices. Thereafter, some properties of addition and multiplication of these matrices are also put forward.

In this paper , the authors explore neutrosophic statistics, that was initiated by Florentin Smarandache in 1998 and developed in 2014, by presenting various examples of several statistical distributions, from the work [1]. The paper is presented with more case studies, by means of which this neutrosophic version of statistical distribution becomes more pronounced.

Smarandache (1995) defined the notion of neutrosophic sets, which is a generalization of Zadeh's fuzzy set and Atanassov's intuitionistic fuzzy set. In this paper, we first develop some similarity measures of neutrosophic sets. We will present a method to calculate the distance between neutrosophic sets (NS) on the basis of the Hausdorff distance. Then we will use this distance to generate a new similarity measure to calculate the degree of similarity between NS. Finally we will prove some properties of (...) the proposed similarity measures. (shrink)

The Vehicle Routing Problem (VRP) has been extensively studied by different researchers from all over the world in recent years. Multiple solutions have been proposed for different variations of the problem, such as Capacitive Vehicle Routing Problem (CVRP), Vehicle Routing Problem with Time Windows (VRP-TW), Vehicle Routing Problem with Pickup and Delivery (VRPPD), among others, all of them with deterministic times. In the last years, researchers have been interested in including in their different models the variations that travel times may (...) experience when exposed to all kind of phenomena, mainly vehicle traffic. This article addresses the VRP from this perspective, proposing the design and implementation of a genetic algorithm based on neutrosophic theory for calculating the fitness function of each route, considering the variability and uncertainty present in travel times. A deterministic genetic algorithm is also implemented with the average travel times to compare it with the neutrosophic algorithm using simulation. As conclusion, a deterministic algorithm does not necessarily generate the best solution in the real world, full of uncertainty. Also, the quantification of uncertainty using neutrosophic theory can be used in route planning, opening a broad and interesting field of research for future investigations. (shrink)

The neutrosophic automorphisms of a neutrosophic groups G (I) , denoted by Aut(G (I)) is a neu-trosophic group under the usual mapping composition. It is a permutation of G (I) which is also a neutrosophic homomorphism. Moreover, suppose that X1 = X(G (I)) is the neutrosophic group of inner neutrosophic auto-morphisms of a neutrosophic group G (I) and Xn the neutrosophic group of inner neutrosophic automorphisms of Xn-1. In this paper, we show that if any neutrosophic group of the sequence (...) G (I), X1, X2, … is the identity, then G (I) is nilpotent. (shrink)

In this paper, we generalize the definition of Neutrosophic sets and present a method for extending crisp functions on Neutrosophic sets and study some properties of such extended functions.

In this paper we have defined neutrosophic ideals, neutrosophic interior ideals, netrosophic quasi-ideals and neutrosophic bi-ideals (neutrosophic generalized bi-ideals) and proved some results related to them. Furthermore, we have done some characterization of a neutrosophic LA-semigroup by the properties of its neutrosophic ideals. It has been proved that in a neutrosophic intra-regular LA-semigroup neutrosophic left, right, two-sided, interior, bi-ideal, generalized bi-ideal and quasi-ideals coincide and we have also proved that the set of neutrosophic ideals of a neutrosophic intra-regular LA-semigroup forms (...) a semilattice structure. (shrink)

In this paper, we first propose the concept of divergence measure on neutrosophic sets. We also provide some formulas for the divergence measure for neutrosophic sets. After that, we investigate the properties of proposed neutrosophic divergence measure. Finally, we also apply these formulas in medical problem and the classification problem.

This Paper combines interval- valued neutrouphic sets and rough sets. It studies roughness in interval- valued neutrosophic sets and some of its properties. Finally we propose a Hamming distance between lower and upper approximations of interval valued neutrosophic sets.