287 191
Full Length Article
International Journal of Neutrosophic Science
Volume 18 , Issue 4, PP: 301-312 , 2022 | Cite this article as | XML | Html |PDF


MCDM Problem using Generalized Dodecagonal Neutrosophic Number using Max – Min and Min – Max Principle

Authors Names :   L.Jeromia Anthvanet   1     A. Rajkumar   2     D.Nagarajan   3 *     Broumi Said   4  

1  Affiliation :  Hindustan Institute of Technology and Science, Chennai, India.

    Email :  janthvanet@gmail.com

2  Affiliation :  Hindustan Institute of Technology and Science, Chennai, India.

    Email :  arajkumar@hindustanuniv.ac.in

3  Affiliation :  Department of Mathematics, Rajalakshmi Institute of Technology, Chennai, India.

    Email :  dnrmsu2002@yahoo.com

4  Affiliation :  Laboratory of Information Processing, Faculty of Science Ben M’Sik, University of Hassan II, Casablanca, Morocco

    Email :  broumisaid78@gmail.com

Doi   :   https://doi.org/10.54216/IJNS.180425

Received: March 27, 2022 Accepted: July 09, 2022

Abstract :

Deciding is the most vital part in any situation or problem that we face in our real time atmosphere. It is the situation where we must decide on the available choices. We have introduced Dodecagonal Neutrosophic Number and its properties. The concept of max-min and min-max principle is applied to the problem that is taken. The concept of heavy ordered weighted averaging operator by assigning equal weights to the attributes and a solution is found for a MCDM problem.

Keywords :

Multi-criteria decision making; Neutrosophic Number; Dodecagonal Neutrosophic Number; Max – min principle; Min – max principle; heavy ordered weighted averaging operator.

References :

[1] F. Smarandache, “Neutrosophy and Neutrosophic Logic, First International Conference on

Neutrosophy, Neutrosophic Logic Set, Probability & Statistics”, University of New Mexico, Gallup,

NM 87301, USA (2002).

[2] F. Smarandache, “Neutrosophic Set, a generalization of Intuitionistic Fuzzy Sets”, International

Journal of Pure and Applied Mathematics, 24, 287 – 297, (2005).

[3] H. J. Zimmermann, Fuzzy Set Theory and Its Applications, Kluwer-Nijhoff, Boston, Mass, USA, 2nd

edition, 1991.

[4] J. Q. Wang, Z. Zhang, “Aggregation operators on intuitionistic trapezoidal fuzzy number and its

application to multi-criteria decision-making problems”, Journal of Systems Engineering and

Electronics, 20 (2009) 321-326.

[5] K. Selvakumari, S. Lavanya, “Solving Fuzzy Game Problem in Octagonal Neutrosophic

Numbers using Heavy OWA Operator”, International Journal of Engineering and Technology, 7

(4.39), 497 – 499, 2018.

[6] R. R. Yager, “On Ordered Weighted Averaging Aggregation Operators in Multi- Criteria Decision

Making”. IEEE Transactions on Systems, Man and Cybernetics, 1988, 18: 183-190.

[7] R. R. Yager, “Heavy OWA operators,” Fuzzy Optimization and decision making, vol.1, no.4, pp.379-


[8] T. Maeda, “On Characterization of equilibrium strategy of two-person zero sum games with fuzzy

payoffs”, Fuzzy Sets and Systems, 139(2), 2004, 283 – 296.

[9] V. Vijay, S. Chandra, C.R. Bector, “Matrix games with fuzzy goals and fuzzy payoffs”, Omega,33(5)

(2005), 425-429.

[10] Zadeh L. A. “Fuzzy Sets”. Information and control, 1965, 8(3): 338-353.

[11] Atanassov, K., Intuitionistic fuzzy sets. In V. Sgurev, ed., ITKRS Session, Sofia, June 1983,

Central Sci. and Techn. Library, Bulg. Academy of Sciences, 1984.

[12] Smarandache, F., Neutrosophy and Neutrosophic Logic, First International Conference on

Neutrosophy, Neutrosophic Logic, Set, Probability, and Statistics University of New Mexico,

Gallup, NM 87301, USA,2002.

[13] Smarandache, F. A Unifying Field in Logics: Neutrosophic Logic. Neutrosophy, Neutrosophic

Set, Neutrosophic Probability. American Research Press, Rehoboth, NM, 1999.

[14] Smarandache, F., Neutrosophic set a generalization of the intuitionistic fuzzy sets. Inter. J. Pure

Appl. Math., 24, 287 – 297, 2005.

[15] Salama, A. A., Smarandache, F., & Kroumov, V., Neutrosophic crisp Sets & Neutrosophic crisp

Topological Spaces. Sets and Systems, 2(1), 25-30, 2014.

[16] Smarandache, F. & Pramanik, S. (Eds). (2016). New trends in neutrosophic theory and

applications. Brussels: Pons Editions.

[17] Salama, A. A., Smarandache, F., Neutrosophic Crisp Set Theory, Educational. Education

Publishing 1313 Chesapeake, Avenue, Columbus, Ohio 43212, (2015).

[18] Salama, A. A., & Smarandache, F. Neutrosophic crisp probability theory & decision-making

process, Critical Review: A Publication of Society for Mathematics of Uncertainty, vol. 12, p.

34-48, 2016.

Cite this Article as :
L.Jeromia Anthvanet , A. Rajkumar , D.Nagarajan , Broumi Said, MCDM Problem using Generalized Dodecagonal Neutrosophic Number using Max – Min and Min – Max Principle, International Journal of Neutrosophic Science, Vol. 18 , No. 4 , (2022) : 301-312 (Doi   :  https://doi.org/10.54216/IJNS.180425)