Jump to ContentJump to Main Navigation
Show Summary Details
More options …

Journal of Artificial Intelligence and Soft Computing Research

The Journal of Polish Neural Network Society, the University of Social Sciences in Lodz & Czestochowa University of Technology

4 Issues per year

Open Access
See all formats and pricing
More options …

n-Valued Refined Neutrosophic Soft Sets and their Applications in Decision Making Problems and Medical Diagnosis

Shawkat Alkhazaleh / Ayman A. Hazaymeh
  • Department of Mathematics, Faculty of Science and Information Technology, Jadara University, Jordan
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
Published Online: 2017-11-01 | DOI: https://doi.org/10.1515/jaiscr-2018-0005


In this work we use the concept of a ‘n’-valued refined neutrosophic soft sets and its properties to solve decision making problems, Also a similarity measure between two ‘n’-valued refined neutrosophic soft sets are proposed. A medical diagnosis (MD) method is established for ‘n’-valued refined neutrosophic soft set setting using similarity measures. Lastly a numerical example is given to demonstrate the possible application of similarity measures in medical diagnosis (MD).

Keywords: neutrosophic set; neutrosophic soft set; ‘n’-valued refined neutrosophic set; ‘n’-valued refined neutrosophic soft set; similarity measures; decision making; medical diagnosis


  • [1] A. A. A. Agboola, On refined neutrosophic algebraic structures, Neutrosophic Sets and Systems, 10:99–101, 2015.Google Scholar

  • [2] S. Alkhazaleh, ‘n’-valued refined neutrosophic soft set theory, Journal of Intelligent & Fuzzy Systems 32 (6), pp. 4311-4318.CrossrefWeb of ScienceGoogle Scholar

  • [3] S. Alkhazaleh, Time-neutrosophic soft set and its applications, Journal of Intelligent & Fuzzy Systems, 30(2):1087–1098, 2016.Web of ScienceCrossrefGoogle Scholar

  • [4] S. Alkhazaleh and A. R. Salleh, Possibility fuzzy soft set, Advances in Decision Sciences, page 18, 2011.Google Scholar

  • [5] S. Broumi and I. Deli, Correlation measure for neutrosophic refined sets and its application in medical diagnosis, Palestine Journal of Mathematics, 5(1):135–143, 2016.Google Scholar

  • [6] S. Broumi, I. Deli, and F. Smarandache, Critical Review, volume X, chapter ‘n’-valued Interval Neutrosophic Sets and Their Application in Medical Diagnosis, pages 45–69, Center for Mathematics of Uncertainty, Creighton University, USA, 2015.Google Scholar

  • [7] S. Broumi and F. Smarandache, Intuitionistic neutrosophic soft set, Journal of Information and Computing Science, 8(2):130–140, 2013.Google Scholar

  • [8] S. Broumi and F. Smarandache, Neutrosophic refined similarity measure based on cosine function, Neutrosophic Sets and Systems, 6:42–48, 2014.Google Scholar

  • [9] S. Broumi and F. Smarandache, Extended hausdorff distance and similarity measures for neutrosophic refined sets and their application in medical diagnosis, Journal of New Theory, 7:64–78, 2015.Google Scholar

  • [10] M. Şahin, S. Alkhazaleh, and V. Uluçay, Neutrosophic soft expert sets, Applied Mathematics, 6:116–127, 2015.Google Scholar

  • [11] Y. Jun, Single-valued neutrosophic similarity measures based on cotangent function and their application in the fault diagnosis of steam turbine, Soft Computing, pages 1–9, 2015.Google Scholar

  • [12] F. Karaaslan, Correlation coefficients of single-valued neutrosophic refined soft sets and their applications in clustering analysis, Neural Computing and Applications, 2016:1–13, 2016.Google Scholar

  • [13] P. Maji, Neutrosophic soft set, Annals of Fuzzy Mathematics and Informatics, 5(1):157–168, 2013.Google Scholar

  • [14] P. Maji, A. Roy, and R. Biswas, Soft set theory, Computers and Mathematics with Applications, 45:555–562, 2003.Google Scholar

  • [15] D. Molodtsov, Soft set theory-first results, Computers and Mathematics with Applications, 37:19–31, 1999.Google Scholar

  • [16] A. Mukherjee and S. Sarkar, A new method of measuring similarity between two neutrosophic soft sets and its application in pattern recognition problems, Neutrosophic Sets and Systems, 8:63–68, 2015.Google Scholar

  • [17] F. Smarandache, Neutrosophic logic and set, mss, 1995.Google Scholar

  • [18] F. Smarandache, Neutrosophy, Neutrosophic Probability, Set, and Logic, Amer. Res. Press, Rehoboth, USA, 1998.Google Scholar

  • [19] F. Smarandache, A Unifying Field in Logics, Neutrosophy: Neutrosophic Probability, Set and Logic, Amer. Res. Press, Rehoboth, USA, 1999.Google Scholar

  • [20] F. Smarandache, Neutrosophic set, a generalization of the intuitionistic fuzzy sets, International Journal of Pure and Applied Mathematics, 24:287–297, 20055.Google Scholar

  • [21] F. Smarandache, ‘n’-valued refined neutrosophic logic and its applications in physics, Progress in Physics, 4:143–146, 2013.Google Scholar

  • [22] F. Smarandache, Refined literal indeterminacy and the multiplication law of subindeterminacies, Neutrosophic Sets and Systems, 9:1–7, 2015.Google Scholar

  • [23] F. Smarandache, (t,i,f)-neutrosophic structures and i neutrosophic structures, Neutrosophic Sets and Systems, 8:3–10, 2015.Google Scholar

About the article

Received: 2017-01-03

Accepted: 2017-03-22

Published Online: 2017-11-01

Published in Print: 2018-01-01

Citation Information: Journal of Artificial Intelligence and Soft Computing Research, Volume 8, Issue 1, Pages 79–86, ISSN (Online) 2083-2567, DOI: https://doi.org/10.1515/jaiscr-2018-0005.

Export Citation

© 2018 Shawkat Alkhazaleh et al., published by De Gruyter Open. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License. BY-NC-ND 4.0

Comments (0)

Please log in or register to comment.
Log in