Neutrosophic Sets and Systems

Prof. Florentin Smarandache, PhD, Postdoc, Mathematics Department, University of New Mexico, Gallup, NM 87301, USA, Email:
Dr. Surapati Pramanik,
Nandalal Ghosh B.T. College, Panpur, Narayanpur, Dist-North 24 Parganas, West Bengal, India-743126, Email:

Associate Editors:
Said Broumi, University of Hassan II,  Casablanca, Morocco, Email:
Mohamed Abdel-Baset,
Faculty of Computers and Informatics, Zagazig University, Egypt, Email:
Prof. Le Hoang Son, VNU Univ. of Science, Vietnam National Univ. Hanoi, Vietnam, Email:

Huda E. Khalid, University of Telafer, College of Basic Education, Telafer - Mosul, Iraq, Email:
Prof. Xiaohong Zhang, Department of Mathematics, Shaanxi University of Science &Technology, Xian 710021, China, Email:
Dr. Mumtaz Ali, University of Southern Queensland, Australia, Email:

W. B. Vasantha Kandasamy, Indian Institute of Technology, Chennai, Tamil Nadu, India, Email:
A. A. Salama, Faculty of Science, Port Said University, Egypt, Email:
Young Bae Jun, Gyeongsang National University, South Korea, Email:
Vakkas Ulucay, Gaziantep University, Gaziantep, Turkey, Email:
Peide Liu, Shandong University of Finance and Economics, China, Email:
Pabitra Kumar Maji, Math Department, K. N. University, India, Email:
S. A. Albolwi, King Abdulaziz Univ., Jeddah, Saudi Arabia, Email:
Jun Ye, Shaoxing University, China, Email:

Madad Khan, Comsats Institute of Information Technology, Abbottabad, Pakistan, Email:
Dmitri Rabounski and Larissa Borissova, independent researchers, Email:, Email:
Selcuk Topal, Mathematics Department, Bitlis Eren University, Turkey, Email:
Ibrahim El-henawy, Faculty of Computers and Informatics, Zagazig University, Egypt, Email:
A. A. A. Agboola, Federal University of Agriculture, Abeokuta, Nigeria, Email:
Luu Quoc Dat, Univ. of Economics and Business, Vietnam National Univ., Hanoi, Vietnam, Email:
Maikel Leyva-Vazquez, Universidad de Guayaquil, Ecuador, Email:
Muhammad Akram, University of the Punjab, New Campus, Lahore, Pakistan, Email:
Irfan Deli, Muallim Rifat Faculty of Education, Kilis 7 Aralik University, Turkey, Email:
Ridvan Sahin, Department of Mathematics, Faculty of Science, Ataturk University, Erzurum 25240, Turkey, Email:
Ibrahim M. Hezam, Department of computer, Faculty of Education, Ibb University, Ibb City, Yemen, Email:
Pingping Chi, China-Asean International College, Dhurakij Pundit University, Bangkok 10210, Thailand, Email:

Ameirys Betancourt-Vázquez, 1 Instituto Superior Politécnico de Tecnologias e Ciências (ISPTEC), Luanda, Angola, E-mail:
Karina Pérez-Teruel, Universidad Abierta para Adultos (UAPA), Santiago de los Caballeros, República Dominicana, E-mail:
Neilys González Benítez, Centro Meteorológico Pinar del Río, Cuba, E-mail:

B. Davvaz, Department of Mathematics, Yazd University, Iran, Email:
Victor Christianto, Malang Institute of Agriculture (IPM), Malang, Indonesia, Email:

Wadei Al-Omeri,
Department of Mathematics, Al-Balqa Applied University, Salt 19117, Jordan, Email:
Ganeshsree Selvachandran, UCSI University, Jalan Menara Gading, Kuala Lumpur, Malaysia, Email

Arun Kumar Sangaiah, VIT University, Vellore, India, Email:
Kul Hur, Wonkwang University, Iksan, Jeollabukdo, South Korea, Email:
Kemale Veliyeva & Sadi Bayramov, Department of Algebra and Geometry, Baku State University, 23 Z. Khalilov Str., AZ1148, Baku, Azerbaijan, Email:, Email:
Inayatur Rehman, College of Arts and Applied Sciences, Dhofar University Salalah, Oman, Email:
Riad K. Al-Hamido, Math Departent, College of Science, Al-Baath University, Homs, Syria, Email: riad-  

Faruk Karaaslan, Çankırı Karatekin University, Çankırı, Turkey, e-mail:
Suriana Alias, Universiti Teknologi MARA (UiTM) Kelantan, Campus Machang, 18500 Machang, Kelantan, Malaysia, Email:
Angelo de Oliveira, Ciencia da Computacao, Universidade Federal de Rondonia, Porto Velho - Rondonia, Brasil, Email:
Valeri Kroumov, Okayama University of Science, Japan, Email:

E. K. Zavadskas, Vilnius Gediminas Technical University, Vilnius, Lithuania, Email:

Darjan Karabasevic, University Business Academy, Novi Sad, Serbia, Email:

Dragisa Stanujkic, Technical Faculty in Bor, University of Belgrade, Bor,
Serbia, Email:
Luige Vladareanu, Romanian Academy, Bucharest, Romania, Email:

Stefan Vladutescu, University of Craiova, Romania, Email:

Philippe Schweizer, Independant Researcher, Av. de Lonay 11, 1110 Morges, Switzerland, Email:
Saeid Jafari, College of Vestsjaelland South, Slagelse, Denmark, Email:
Willem K. M. Brauers, Faculty of Applied Economics, University of Antwerp, Antwerp, Belgium, Email:
M. Ganster, Graz University of Technology, Graz, Austria, Email:
Umberto Rivieccio,
Department of Philosophy, University of Genoa, Italy, Email:
F. Gallego Lupiaňez, Universidad Complutense, Madrid, Spain, Email:
Francisco Chiclana, School of Computer Science and Informatics, De Montfort University, The Gateway, Leicester, LE1 9BH, United Kingdom, E-mail:

Yanhui Guo,
University of Illinois at Springfield, One University Plaza, Springfield, IL 62703, United States, Email:

Neutrosophic Sets and Systems
An International Journal in Information Science and Engineering

Information for Authors and Subscribers:
Neutrosophic Sets and Systems (NSS) is an academic journal, published quarterly online and on paper, that has been created for publications of advanced studies in neutrosophy, neutrosophic set, neutrosophic logic, neutrosophic probability, neutrosophic statistics etc. and their applications in any field.
All submitted papers should be professional, in good English, containing a brief review of a problem and obtained results.

Papers are checked for plagiarism and self-plagiarism with an automated computer program.

Read the Information for Authors.
All submissions should be designed in these formats: MS Word template, or Latex template. References should be in APA style.
To submit a paper, e-mail the file to the editors. To order printed issues, contact the editors. This journal is open-access, non-commercial, academic edition. No publication fees.

University of New Mexico's website on neutrosophic theories and applications is:

University of New Mexico's Logo

The NSS international journal is funded by the University of New Mexico and Neutrosophic Science International Association (NSIA). Its official website is:

Neutrosophic Sets and Systems's Logo

Publication Ethics and Malpractice Statement
Neutrosophic Sets and Systems international journal is committed to ensuring ethics in publication and quality of articles. The journal aims to publish only original scientific papers that contribute in the area of neutrosophic theories & their applications and related topics. Accordance to standards of ethical behavior it is therefore expected from all parties involved: Authors, Editors, Reviewers, and the Publishers.

Our Publication Ethics and Malpractice statement is based on Committee on Publication Ethics (COPE) Best Practice Guidelines for Journal Editors.

Reviewer's Report
The reviewing process is the following: several members of the Reviewing Committee choose at least three reviewers from around the world. Each reviewer sends a report and a recommendation: accept, reject, or accept after minor or major corrections. Fill in the Reviewer Report.

Copyright Transfer Agreement
The authors should sign and return the Copyright Transfer Agreement.

Open Access Statement
Users are freely allowed to read, download, copy, distribute, link to, or print the full texts of the articles in this journal without asking for prior permission from the publishers or the authors. This is in accordance with the BOAI definition of open access.

Best Neutrosophic Paper Award
Annually the Award Committee accords Neutrosophic Diplomas to the authors for the best published neutrosophic papers.

Download issues of the NSS international journal:
Issues of Neutrosophic Sets and Systems are accessible, in PDF format, through the direct links from below.

Vol. 21, 2018; Vol. 20, 2018; Vol. 19, 2018;
Vol. 18, 2017 Vol. 17;  Vol. 16, 2017Vol. 15, 2017;

Vol. 14, 2016 Vol. 13, 2016;  Vol. 12, 2016;  Vol. 11, 2016;

Vol. 10, 2015 Vol. 9, 2015;  Vol. 8, 2015Vol. 7, 2015;     

Vol. 6, 2014;  Vol. 5,  2014;  Vol. 4, 2014 Vol. 3, 2014;  

Vol. 2, 2013 Vol. 1, 2013.

Download separate NSS articles with DOI numbers


Visit our open-source Digital Science Library

The authors of neutrosophic papers are included in
Encyclopedia of Neutrosophic Researchers
Vol. 1, Vol. 2

Neutrosophic Science International Association (NSIA)
with branches in 40 countries around the world.

Postal Address
Neutrosophic Sets and Systems, University of New Mexico, Mathematics & Science Department, 705 Gurley Ave., Gallup, NM 87301, U.S.A.

Copyright @ Neutrosophic Sets and Systems 
This is an open access journal distributed under the Creative Commons Attribution License that permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. 

ISSN (print): 2331-6055, ISSN (online): 2331-608X

Impact Factor: 1.739

NSS has been accepted by SCOPUS. Starting with Vol. 19, 2018, all NSS articles are indexed in Scopus.

NSS is also indexed by Google Scholar, Google Plus, Google Books, EBSCO, Cengage Thompson Gale (USA), Cengage Learning, ProQuest, Amazon Kindle, DOAJ (Sweden), University Grants Commission (UGC) - India, International Society for Research Activity (ISRA), Scientific Index Services (SIS), Academic Research Index (ResearchBib), Index Copernicus (European Union),CNKI (Tongfang Knowledge Network Technology Co., Beijing, China), Baidu Scholar (China) etc.

Google Dictionary has translated the neologisms "neutrosophy" (1) and "neutrosophic" (2), coined in 1995 for the first time, into about 100 languages.

FOLDOC Dictionary of Computing (1, 2), Webster Dictionary (1, 2), Wordnik (1),, The Free Dictionary (1), Wiktionary (2), YourDictionary (1, 2), OneLook Dictionary (1, 2), Dictionary / Thesaurus (1), Online Medical Dictionary (1, 2), and Encyclopedia (1, 2) have included these scientific neologisms.


DOI numbers are assigned to all published articles.


Registered by the Library of Congress, Washington DC, United States,