The multi-decision-making problem in the recruitment process using penta-partitioned neutrosophic distance measure

Document Type : Research Paper


1 Department of Mathematics, St. Jude’s College, Thoothoor, Kanyakumari-629 176, Tamil Nadu, India

2 PG and Research Department of Physics, Arul Anandar College, Karumathur, Madurai-625 514, Tamil Nadu, India

3 Department of Applied Sciences and Mathematics, Abu Dhabi University College of Arts and Sciences, P.O.Box.59911, Abu Dhabi, UAE

4 Department of Mathematics, Arunachala College of Arts and Science for Women, Vellichanthai, Kanyakumari-629203, Tamil Nadu, India



In this article, we introduce some different distance measures on penta-partitioned neutrosophic sets and some distance measures satisfy axioms of metric. We also formulate a new methodological approach to solve the multi-criteria decision-making problems, in which the suitable decision is by ranking the average of the proposed penta partitioned neutrosophic distance measure for the alternatives to the criteria under certain conditional criteria. Further, we apply these distance measures to a multi-criteria decision-making problem (MCDM) for the best employee selection to recruit for a post. The comparison is finally made between the proposed distance measures and the final decisions are the same in all penta-partitioned neutrosophic distance measures.


[1] M. Arockia Dasan and V.F. Little Flower, Some mappings in N-neutrosophic supra topological spaces, Neutrosophic Sets Syst. 50 (2022), 379–392.
[2] M. Arockia Dasan, E. Bementa, M. Aslam, and V.F. Little Flower, Multi-criteria decision-making problem in career determination using single-valued neutrosophic distance measure, Preprint,
[3] M. Arockia Dasan, E. Bementa, F. Smarandache, and X. Tubax, Neutrosophical Plant Hybridization in Decision-Making Problems, Neutrosophic Operational Research, Chapter 1, Springer, Cham, 2021, pp. 1–17.
[4] K. Atanassov, Intuitionistic fuzzy sets, Fuzzy Sets Syst. 20 (1986), 87–96.
[5] P. Biswas, S. Pramanik, and B.C. Giri, Cosine similarity measure based multi-criteria decision-making with trapezoidal fuzzy neutrosophic numbers, Neutrosophic Sets Syst. 8 (2015), 47–57.
[6] P. Biswas, S. Pramanik, and C. Giri, Some distance measures of single valued neutrosophic hesitant fuzzy sets and their applications to multiple criteria decision making, New Trends in Neutrosophic Theory and Applications, Brussels, Belgium, EU, Pons Editions, 2016, pp. 27–34.
[7] S. Broumi, S. Krishna Prabha, and V. Ulucay, Interval-valued Fermatean neutrosophic shortest path problem via score function, Neutrosophic Syst. Appl. 11 (2023), 1–10.
[8] S. Broumi, S. Mohanaselvi, T. Witczak, M. Talea, A. Bakali, and F. Smarandache, Complex Fermatean neutrosophic graph and application to decision making, Decis. Mak.: Appl. Manag. Engin. 6 (2023), no. 1, 474–501.
[9] S. Broumi and F. Smarandache, Several similarity measures of neutrosophic sets, Neutrosophic Sets Syst. 1(2013), no. 10, 54–62.
[10] S. Broumi, R. Sundareswaran, M. Shanmugapriya, A. Bakali, and M. Talea, Theory and applications of Fermatean neutrosophic graphs, Neutrosophic Sets Syst. 50 (2022), 248–286.
[11] S. Broumi, R. Sundareswaran, M. Shanmugapriya, P.K. Singh, M. Voskoglou, and M. Talea, Faculty performance evaluation through multi-criteria decision analysis using interval-valued Fermatean neutrosophic sets, Mathematics 11 (2023), no. 18, 3817.
[12] J.S. Chai, G. Selvachandran, F. Smarandache, Vassilis C. Gerogiannis, L. Hoang Son, Q.T. Bui, and B. Vo, New similarity measures for single valued neutrosophic sets with applications in pattern recognition and medical diagnosis problems, Complex Intell. Syst. 7 (2021), 703–723.
[13] P. Dutta, Medical diagnosis based on distance measures between picture fuzzy sets, Int. J. Fuzzy Syst. Appl. 7 (2018), no.4, 15–36.
[14] P. Dutta and S. Goala, Fuzzy decision making in medical diagnosis using an advanced distance measure on intuitionistic fuzzy sets, Open Cyber. Syst. J. 12 (2018), 136–149.
[15] G. Jayaparthasarathy, M. Arockia Dasan, V.F. Little Flower, and R. Ribin Christal, New open sets in Neutrosophic supra topological spaces, Neutrosophic Sets Syst. 31 (2020), 44–62.
[16] G. Jayaparthasarathy, V.F. Little Flower, and M. Arockia Dasan, Neutrosophic supra topological applications in data mining process, Neutrosophic Sets Syst. 27 (2019), 80–97.
[17] J.L. Kelley, General topology. Graduate Texts in Mathematics, Springer, vol. 27, 1975.
[18] P. Majumdar and S.K. Samanta, On similarity and entropy of neutrosophic sets, J. Intell. Fuzzy Syst. 26 (2014), no. 3, 1245–1252.
[19] R. Malick and S. Pramanik, Pentapartitioned neutrosophic set and its properties, Neutrosophic Sets Syst. 36 (2020), 184–192.
[20] K. Mondal and S. Pramanik, Neutrosophic similarity measure and its application to multi criteria decision making, Neutrosophic Sets Syst. 9 (2015), 80–86.
[21] C. P. Pappis and N.I. Karacapilidis, A comparative assessment of measures of similarity of fuzzy values, Fuzzy Sets Syst. 56 (1993), no. 2, 171–174.
[22] S. Pramanik and K. Mondal, Weighted fuzzy similarity measure based on tangent function and its application to medical diagnosis, Int. J. Innov. Res. Sci. Eng. Tech. 4 (2015), no. 2, 158–164.
[23] G. Shahzadi, M. Akram, and A.B. Saeid, An application of single-valued neutrosophic sets in medical diagnosis, Neutrosophic Sets Syst. 18 (2017), 80–87.
[24] F. Smarandache, Neutrosophic set, a generalization of the intuitionistic fuzzy sets, Int. J. Pure. Appl. Math. 24 (2005), 287–297.
[25] E. Szmidt and J. Kacprzyk, Distance between intuitionistic fuzzy sets, Fuzzy Sets Syst.  14 (2000), 505–518.
[26] E. Szmidt and J. Kacprzyk, Intuitionistic fuzzy set in some medical applications, Int. Conf. Comput. Intell., Berlin, Heidelberg: Springer Berlin Heidelberg, 2001.
[27] W. Voxman, Some remarks on distance between fuzzy numbers, Fuzzy Sets Syst. 119 (2001), 215–223.
[28] H. Wang, F. Smarandache, Y. Zhang, and R. Sunderraman, Single valued neutrosophic sets, Multi-space Multistructure 4 (2010), 410–413.
[29] J. Ye, Single valued neutrosophic cross-entropy for multi criteria decision making problems, Appl. Math. Model. 38 (2014), 1170–1175.
[30] J. Ye and Q. Zhang, Single valued neutrosophic similarity measures for multiple criteria decision-making, Neutrosophic Sets Syst. 2 (2014), 48–54.
[31] L. Zadeh, Fuzzy sets, Inf. Control 8 (1965), 338–353.

Articles in Press, Corrected Proof
Available Online from 03 May 2024
  • Receive Date: 20 December 2023
  • Revise Date: 29 February 2024
  • Accept Date: 01 March 2024