Table Of Content

Florentin marandache (author and editor) ollected apers (on Neutrosophics Theory and Applications) lobal nowledge 2022 Florentin Smarandache (author and editor) Collected Papers (on Neutrosophics Theory and Applications) Volume XII Peer-Reviewers: Saeid Jafari College of Vestsjaelland South, Slagelse, DENMARK [email protected] Ali Hussein Mahmood Al-Obaidi College of Education for Pure Science, University of Babylon, Hillah, IRAQ [email protected] S.Satham Hussain Jamal Mohamed College, Trichy, Tamil Nadu, INDIA [email protected] Le Hoang Son Vietnam National University, Hanoi, SR VIETNAM [email protected] Erick González-Caballero Technological University of Havana, Havana, CUBA [email protected] Muhammad Akram University of the Punjab, Lahore, PAKISTAN [email protected] Florentin Smarandache (author and editor) Collected Papers (on Neutrosophics Theory and Applications) Volume XII GLOBAL KNOWLEDGE Publishing House Miami, United States of America 2022 Editors: GLOBAL KNOWLEDGE - Publishing House 848 Brickell Ave Ste 950 Miami Florida 33131, United States https://egk.ccgecon.us [email protected] ADSUMUS – Scientific and Cultural Society 13, Dimitrie Cantemir St. 410473 Oradea City, Romania https://adsumus.wordpress.com/ [email protected] NSIA Publishing House Neutrosphic Science International Association https://www.publishing-nsia.com/ University of New Mexico, Gallup, United States Universidad Regional Autónoma de los Andes (UNIANDES), Babahoyo, Los Rios, Ecuador Publishing: Prof. Dan Florin Lazar [email protected] Prof. Dr. Maykel Yelandi Leyva Vazquez [email protected] ISBN 978-1-59973-741-6 Florentin Smarandache (author and editor) Collected Papers, XII Introductory Note This twelfth volume of Collected Papers includes 86 papers comprising 976 pages on Neutrosophic Theories and their Applications, published between 2013-2021 in the international book series about 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. Keywords Neutrosophy; Neutrosophic Logic; Neutrosophic Sets; Neutrosophic Crisp Set; Neutrosophic Topology; Neutrosophic Crisp Topology; Interval-Valued Neutrosophic Set; Interval-Valued Neutrosophic Subring; Interval-Valued Neutrosophic Normal Subring; Interval-Valued Neutrosophic Hypersoft Set; Neutrosophic Multiple Regression; Neutrosophic Regression; Neutrosophic Correlation; Neutrosophic Implication; Single Valued Neutrosophic Numbers; Neutrosophic Uninorm; Neutrosophic Implicatory; Neutrosophic Components; Neutrosophic Offset Components; Neutrosophic Distance; Similarity Measure; Bipolar Neutrosophic Sets; Neutrosophic Soft Rough Set; Single-Valued Neutrosophic Triplet Numbers; Single-Valued Neutrosophic Score Function; Single-Valued Neutrosophic Accuracy Function; Single-Valued Neutrosophic Certainty Function; Entropy Measure; Medical Diagnosis; Autoimmune Disease; Fuzzy Cognitive Maps; Neutrosophic Hypergraphs; Optimal Decision Making; Neutrosophic Cubic Translation; Neutrosophic Cubic Multiplication; Neutrosophic Cubic BF Ideal; Neutrosophic Cubic BF Subalgebra; Neutrosophic Cubic Magnified Translation; Quadratic Residues; Quadratic Nonresidues; Neutrosophic Quadratic Residues; Neutrosophic Quadratic Nonresidues; Neutrosophic Quadratic Residue Graph; Neutrosophic Quadratic Nonresidue Graph; Fuzzy Neutrosophic Soft Mapping; Coincidence Point; Fixed Point; Centroid Points; Neutrosophic Metric Space; Banach Contraction; Edelstein Contraction; Trapezoidal Fuzzy Neutrosophic Numbers; TriVariate Truth-Value; MultiVariate Truth-Value; UniVariate Truth-Value; Automata Theory; Box Function; Sociogram; Neutrosophic Sociogram; Neutrosociology; Group Analysis; Sociometry Analysis; Communication; Information; Extensics. 5 Florentin Smarandache (author and editor) Collected Papers, XII Florentin Smarandache is an emeritus prof. dr. of mathematics at the University of New Mexico, United States. He got his MSc in Mathematics and Computer Science from the University of Craiova, Romania, PhD in Mathematics from the State University of Kishinev, and Postdoctoral in Applied Mathematics from Okayama University of Sciences, Japan, and The Guangdong University of Technology, Guangzhou, China. He is the founder of neutrosophy (generalization of dialectics), neutrosophic set, logic, probability and statistics since 1995 and has published hundreds of papers and books on neutrosophic physics, superluminal and instantaneous physics, unmatter, quantum paradoxes, absolute theory of relativity, redshift and blueshift due to the medium gradient and refraction index besides the Doppler effect, paradoxism, outerart, neutrosophy as a new branch of philosophy, Law of Included Multiple-Middle, multispace and multistructure, hypersoft set, IndetermSoft Set and IndetermHyperSoft Set, SuperHyperGraph, SuperHyperTopology, SuperHyperAlgebra, Neutrosophic SuperHyperAlgebra, degree of dependence and independence between neutrosophic components, refined neutrosophic set, neutrosophic over-under-off-set, plithogenic set / logic / probability / statistics, neutrosophic triplet and duplet structures, quadruple neutrosophic structures, extension of algebraic structures to NeutroAlgebra and AntiAlgebra, NeutroGeometry & AntiGeometry, Dezert-Smarandache Theory and so on to many peer-reviewed international journals and many books and he presented papers and plenary lectures to many international conferences around the world. In addition, he published many books of poetry, dramas, children’ stories, translations, essays, a novel, folklore collections, traveling memories, and art albums [ http://fs.unm.edu/FlorentinSmarandache.htm ]. 6 Florentin Smarandache (author and editor) Collected Papers, XII Contents Florentin Smarandache Neutrosophic Measure and Neutrosophic Integral / 29 Muhammad Shabir, Mumtaz Ali, Munazza Naz, and Florentin Smarandache Soft Neutrosophic Group / 34 A.A. Salama. Florentin Smarandache Filters via Neutrosophic Crisp Sets / 47 Florentin Smarandache, Ştefan Vlăduțescu Communication vs. Information, an Axiomatic Neutrosophic Solution / 51 Said Broumi, Florentin Smarandache Several Similarity Measures of Neutrosophic Sets / 59 Said Broumi, Florentin Smarandache On Neutrosophic Implications / 68 A.A. Salama, Florentin Smarandache, Valeri Kroumov Neutrosophic Crisp Sets & Neutrosophic Crisp Topological Spaces / 77 Vasantha Kandasamy, Florentin Smarandache Neutrosophic Lattices / 83 Mumtaz Ali, Florentin Smarandache, Muhammad Shabir, Munazza Naz Soft Neutrosophic Bigroup and Soft Neutrosophic N-Group / 89 A.A. Salama, Florentin Smarandache, S.A. Alblowi The Characteristic Function of a Neutrosophic Set / 116 Mamouni Dhar, Said Broumi, Florentin Smarandache A Note on Square Neutrosophic Fuzzy Matrices / 120 A.A. Salama, Haitham A. El-Ghareeb, Ayman M. Manie, Florentin Smarandache Introduction to Develop Some Software Programs for Dealing with Neutrosophic Sets / 125 Mumtaz Ali, Florentin Smarandache, Muhammad Shabir, Munazza Naz Soft Neutrosophic Ring and Soft Neutrosophic Field / 127 A.A. Salama, Florentin Smarandache, S.A. Alblowi New Neutrosophic Crisp Topological Concepts / 134 Mumtaz Ali, Christopher Dyer, Muhammad Shabir, Florentin Smarandache Soft Neutrosophic Loops and Their Generalization / 139 Mumtaz Ali, Florentin Smarandache, Muhammad Shabir, Luige Vladareanu Generalization of Neutrosophic Rings and Neutrosophic Fields / 160 7 Florentin Smarandache (author and editor) Collected Papers, XII Said Broumi, Florentin Smarandache Cosine Similarity Measure of Interval Valued Neutrosophic Sets / 166 A.A. Salama, Florentin Smarandache Neutrosophic Crisp Set Theory / 172 A.A. Salama, Florentin Smarandache, Mohamed Eisa Introduction to Image Processing via Neutrosophic Techniques / 181 Anjan Mukherjee, Mithun Datta, Florentin Smarandache Interval Valued Neutrosophic Soft Topological Spaces / 187 Mumtaz Ali, Florentin Smarandache, Luige Vlădăreanu, Muhammad Shabir Generalization of Soft Neutrosophic Rings and Soft Neutrosophic Fields / 197 Said Broumi, Florentin Smarandache Neutrosophic Refined Similarity Measure Based on Cosine Function / 204 Mumtaz Ali, Florentin Smarandache, Muhammad Shabir Soft Neutrosophic Groupoids and Their Generalization / 211 Said Broumi, Florentin Smarandache Interval Neutrosophic Rough Set / 231 Mumtaz Ali, Florentin Smarandache, Said Broumi, Muhammad Shabir A New Approach to Multi-spaces Through the Application of Soft Sets / 240 Said Broumi, Florentin Smarandache Soft Interval-Valued Neutrosophic Rough Sets / 246 Said Broumi, Florentin Smarandache An Extended TOPSIS Method for Multiple Attribute Decision Making based on Interval Neutrosophic Uncertain Linguistic Variables / 258 Florentin Smarandache Thesis-Antithesis-Neutrothesis, and Neutrosynthesis / 268 Florentin Smarandache Refined Literal Indeterminacy and the Multiplication Law of Sub-Indeterminacies / 270 Ibrahim M. Hezam, Mohamed Abdel-Baset, Florentin Smarandache Taylor Series Approximation to Solve Neutrosophic Multiobjective Programming Problem / 276 Florentin Smarandache Neutrosophic Quadruple Numbers, Refined Neutrosophic Quadruple Numbers, Absorbance Law, and the Multiplication of Neutrosophic Quadruple Numbers / 283 8 Florentin Smarandache (author and editor) Collected Papers, XII Said Broumi, Assia Bakali, Mohamed Talea, Florentin Smarandache Isolated Single Valued Neutrosophic Graphs / 286 Florentin Smarandache Degree of Dependence and Independence of the (Sub)Components of Fuzzy Set and Neutrosophic Set / 290 Florentin Smarandache Degrees of Membership > 1 and < 0 of the Elements with Respect to a Neutrosophic OffSet / 293 Huda E. Khalid, Florentin Smarandache, Ahmed K. Essa A Neutrosophic Binomial Factorial Theorem with their Refrains / 299 Mai Mohamed, Mohamed Abdel-Basset, Abdel Nasser H. Zaied, Florentin Smarandache Neutrosophic Integer Programming Problem / 304 Florentin Smarandache Neutrosophic Modal Logic / 309 S. Broumi, A. Dey, A. Bakali, M. Talea, F. Smarandache, L. H. Son, D. Koley Uniform Single Valued Neutrosophic Graphs / 316 Sabu Sebastian, Florentin Smarandache Extension of Crisp Functions on Neutrosophic Sets / 324 Said Broumi, Le Hoang Son, Assia Bakali, Mohamed Talea, Florentin Smarandache, Ganeshsree Selvachandran Computing Operational Matrices in Neutrosophic Envioraments: A MATLAB Toolbox / 329 Huda E. Khalid, Florentin Smarandache, Ahmed K. Essa The Basic Notions for (over, off, under) Neutrosophic Geometric Programming Problems / 338 Said Broumi, Mohamed Talea, Assia Bakali, Prem Kumar Singh, Florentin Smarandache Energy and Spectrum Analysis of Interval Valued Neutrosophic Graph using MATLAB / 351 Rodolfo González Ortega, Marcos David Oviedo Rodríguez, Maikel Leyva Vázquez, Jesús Estupiñán Ricardo, João Alcione Sganderla Figueiredo, Florentin Smarandache Pestel analysis based on neutrosophic cognitive maps and neutrosophic numbers for the sinos river basin management / 366 J. Kavikumar, D. Nagarajan, Said Broumi, F. Smarandache, M. Lathamaheswari, Nur Ain Ebas Neutrosophic General Finite Automata / 375 S. Broumi, D. Nagarajan, A. Bakali, M. Talea, F. Smarandache, M. Lathamaheswari, J. Kavikumar Implementation of Neutrosophic Function Memberships Using MATLAB Program / 395 9