134 127
Full Length Article
International Journal of Neutrosophic Science
Volume 17 , Issue 2, PP: 127 - 143 , 2021 | Cite this article as | XML | Html |PDF

Title

Multi Criteria Decision Making Algorithm Via Complex Neutrosophic Nano Topological Spaces

Authors Names :   Mani Parimala   1 *     Muthusamy Karthika   2     Sivaraman Murali   3     Florentin Smarandache   4     Muhammad Riaz   5     Saeid Jafari   6  

1  Affiliation :  Department of Mathematics, Bannari Amman Institute of Technology, Sathyamangalam-638401, Tamil Nadu, India.

    Email :  rishwanthpari@gmail.com


2  Affiliation :  Department of Mathematics, Bannari Amman Institute of Technology, Sathyamangalam-638401, Tamil Nadu, India.

    Email :  karthikamuthusamy1991@gmail.com


3  Affiliation :  Department of Mathematics, Coimbatore Institute of Technology, Coimbatore, Tamil Nadu, India.

    Email :  muralisvino@gmail.com


4  Affiliation :  Mathematics & Science Department, University of New Mexico, 705 Gurley Ave., Gallup, NM 87301, USA

    Email :  fsmarandache@gmail.com


5  Affiliation :  Department of Mathematics, University of the Punjab Lahore, Pakistan

    Email :  mriaz.math@pu.edu.pk


6  Affiliation :  jafaripersia@gmail.com

    Email :  College of Vestsjaelland South, Herrestraede 11, 4200 Slagelse, Denmark



Doi   :   https://doi.org/10.54216/IJNS.170204

Received: June 19, 2021 Accepted: December 27, 2021

Abstract :

The scope of this manuscript is to instigate the present-day perception of complex neutrosophic nano topological spaces and delve into a few of its spectacles. We also illustrate the spectacles with numerical quantities. Decision making plays an important role to diagnose a diseases in medical field. So a method is developed to achieve this under complex neutrosophic nano topological spaces (CNNTSs). A comparative assessment is provided to demonstrate the distinction between the unique concept and the existing approaches.

Keywords :

complex neutrosophic topology , complex neutrosophic nano topological spaces , complex neutrosophic nano-closed sets , complex neutrosophic interior and closure

References :

[1]       M. Ali, F. Smarandache. Complex neutrosophic set. Neural Computing and Applications, 12, 2015. DOI:10.1007/s00521-015-2154-y.

[2]       I. Arokiarani, R. Dhavaseelan, S. Jafari, M. Parimala. On some new notions and functions in neutrosophic topological spaces, Neutrosophic Sets Syst., 16, pp. 16-19, 2017.

[3]       K. T. Atanassov. Intuitionstic fuzzy sets, Fuzzy sets and systems, 20, pp. 87-96, 1986.

[4]       D. Coker. An introduction to fuzzy topological spaces, Fuzzy sets and systems, 88, pp. 81-89, 1997.

[5]       K. Kuratowski.Topology Vol. II (transl.), Academic Press, New York, 1966.

[6]       M. Karthika, M. Parimala, S. Jafari, F. Smarandache, Mohammad Alshumrani, Cenap Ozel, R. Udhayakumar. Neutrosophic complex αψ connectedness in neutrosophic complex topological spaces. Neutrosophic sets and systems, 29, pp. 158-164, 2019.

[7]       M. Lellis Thivagar, S. Jafari, V. Sutha Devi,V. Antonysamy, A novel approach to nano topology via neutrosophic sets, Neutrosophic sets and systems, 20, pp. 86-94, 2018.

[8]       M. Parimala, S. Jafari, and S. Murali, Nano Ideal Generalized Closed Sets in Nano Ideal Topological Spaces,

Annales Univ. Sci. Budapest., 60, pp. 3-11, 2017.

[9]       M. Parimala, R. Jeevitha, S. Jafari, F. Smarandache and R. Udhayakumar. Neutrosophic αψ-Homeomorphism in

Neutrosophic Topological Spaces, Information,9, 187, pp. 1-10, 2018. doi:10.3390/info9080187.

[10]    M.Parimala, R.Jeevitha, A.Selvakumar. A New Type of Weakly Closed Set in Ideal Topological Spaces, International Journal of Mathematics and its Applications, 5(4-C), pp. 301-312, 2017.

[11]    M. Parimala, M. Karthika, R. Dhavaseelan, S. Jafari. On neutrosophic supra pre-continuous functions in neutrosophic topological spaces, New Trends in Neutrosophic Theory and Applications , 2, pp. 371-383, 2018.

[12]    M. Parimala, M. Karthika, S. Jafari, F. Smarandache , R. Udhayakumar. Neutrosophic nano ideal topological structures, Neutrosophic sets and systems, 24, pp. 70-77, 2019.

[13]    M. Parimala, M. Karthika, S. Jafari, F. Smarandache, R. Udhayakumar. Decision-Making via Neutrosophic

Support Soft Topological Spaces. Symmetry, 10, pp. 1-10, 2018. doi:10.3390/sym10060217

[14]    M. Parimala and R. Perumal, Weaker form of open sets in nano ideal topological spaces, Global Journal of Pure and Applied Mathematics, 12(1), pp. 302-305,2016.

[15]    M. Parimala, F. Smarandache, S. Jafari, R. Udhayakumar, On Neutrosophic αψ -Closed Sets, Information, 9,

103, pp. 1-7, 2018.

[16]    M. Riaz, F. Smarandache, F. Karaaslan, M. R. Hashmi, I. Nawaz. Neutrosophic Soft Topology and its Applications to Multi-Criteria Decision Making. Neutrosophic sets and systems,35, pp. 198-219, 2020.

[17]    M. Riaz, Naeem, K.; Zareef, I. Afzal, D. Neutrosophic N-Soft Sets with TOPSIS method for Multiple Attribute

Decision Making. Neutrosophic sets and systems, 32, pp. 1-24, 2020.

[18]    M. Riaz, B. Davvaz, A. Fakhar, A. Firdous. Hesitant fuzzy soft topology and its applications to multi-attribute group decision-making. Soft Computing, pp. 1-21, 2020. https://doi.org/10.1007/s00500-020-04938-0.

[19]    M. Riaz, S.T. Tehrim. Cubic bipolar fuzzy set with application to multi-criteria group decision making using geometric aggregation operators. Soft Computing, 2020, https://doi.org/10.1007/s00500-020-04927-3.

[20]    A. A. Salama, S. A. Alblowi. Neutrosophic Set and Neutrosophic Topological Spaces, IOSR J. Math., 3, pp. 31-35, 2012.

[21]    A. A. Salama. Florentin Smarandache, Valeri Kromov. Neutrosophic Closed Set and Neutrosophic Continuous

Functions, Neutrosophic Sets and Systems, 4, pp. 4-8, 2014.

[22]    F. Smarandache. Neutrosophy and Neutrosophic Logic, First International Conference on Neutrosophy, Neutrosophic Logic Set, Probability and Statistics; University of New Mexico, Gallup, NM, USA, 2002.

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

Probability, American Research Press, Rehoboth, NM, USA, 1999.

[24]    F. Smarandache. Extension of HyperGraph to n-SuperHyperGraph and to Plithogenic n-SuperHyperGraph, and

Extension of HyperAlgebra to n-ary (Classical-/Neutro-/Anti-) HyperAlgebra, Neutrosophic Sets and Systems, 33, pp. 290-296, 2020.

[25]    L. A. Zadeh. Fuzzy Sets, Information and Control, 18, pp. 338-353, 1965.

[26]    F. Zafer, M. Akram, A novel decision-making method based on rough fuzzy information. Int. J. Fuzzy Syst.

 

2017. doi:10.1007/s40815-017-0368-0.


Cite this Article as :
Mani Parimala , Muthusamy Karthika , Sivaraman Murali , Florentin Smarandache , Muhammad Riaz , Saeid Jafari, Multi Criteria Decision Making Algorithm Via Complex Neutrosophic Nano Topological Spaces, International Journal of Neutrosophic Science, Vol. 17 , No. 2 , (2021) : 127 - 143 (Doi   :  https://doi.org/10.54216/IJNS.170204)