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Full Length Article
International Journal of Neutrosophic Science
Volume 13 , Issue 1, PP: 52-60 , 2021 | Cite this article as | XML |PDF


PROMTHEE Plithogenic Pythagorean Hypergraphic Approach in Smart Materials Selection

Authors Names :   Nivetha Martin   1     Florentin Smarandache   2     Said Broumi   3  

1  Affiliation :  Department of Mathematics, Arul Anandar College (Autonomous), Karumathur

    Email :  nivetha.martin710@gmail.com

2  Affiliation :  Department of Mathematics, University of New Mexico, Gallup, NM 87301, USA

    Email :  smarand@unm.edu

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

    Email :  broumisaid78@gmail.com

Doi   :   https://doi.org/10.54216/IJNS.130105

Received:Septembre 17, 2020 Accepted: January 08, 2021

Abstract :


The production sectors are optimizing its profit with the employment of smart materials at recent times and one of the challenges faced is the selection of smart materials. This article proposes a new decision-making method based on the approach of PROMTHEE plithogenic Pythagorean hypergraph. The efficiency of the proposed method is determined in the selection of smart materials that are significantly utilized in the production processes by the production sectors. In this research work, the decision making on smart material selection environment is characterized by four major influencing factors such as production processes, operational necessities, fiscal constraints and external effects with eighteen sub-factors. The main objective of this research work is to determine the core sub-factors persuading the selection of smart materials based on the five-point scale of expert’s opinion represented as Pythagorean neutrosophic number. Out of eighteen sub-factors four significant factors belonging to each of the major factors were identified by this method.  The plithogenic hypergraphs with Pythagorean representation are the extension of plithogenic hypergraphs and the novel decision - making method with the integration of PROMTHEE developed in this article will certainly benefit the decision makers on smart material selection. Comparative analysis on the criteria is also made based on Pythagorean neutrosophic sets & neutrosophic sets.


Keywords :

Plithogenic sets , Pythagorean Neutrosophic number , Hypergraph , PROMTHEE , Smart materials

References :


[1]  Smarandache,  F.  Plithogeny,  Plithogenic  Set,  Logic,  Probability,  and  Statistics.  2018,arXiv  preprint arXiv:1808.03948


[2]  Abdel-Basset M, El-Hoseny M, Gamal A, Smarandache F. "A novel model for evaluation Hospital medical care systems based on plithogenic sets",Artif Intell Med, Vol.1, 2019


[3]  Grida., Mohamed., Rehab Mohamed.,Abdelnaser H. Zaid. "A Novel Plithogenic MCDM Framework for Evaluating the Performance of IoT Based Supply Chain." Neutrosophic Sets and Systems, Vol.33, 1, pp-323-341,2020.


[4]  Quek, S.G., Selvachandran, G., Smarandache, F.,Vimala, J.,Le, S.H., Bui, Q.-T., Gerogiannis, V.C. "Entropy Measures for Plithogenic Sets and Applications in Multi-Attribute Decision Making",Mathematics ,Vol.8, pp-1-17,2020.


[5]  Abdel-Basset. M., Mohamed. R., Zaied, A. E. N. H.,Smarandache, F. "A hybrid plithogenic decision-making approach  with  quality  function  deployment  for  selecting  supply  chain  sustainability metrics",Symmetry,Vol.11,No.7,pp-1-21,2019.


[6]  Mohamed Abdel-Basset & Weiping Ding & Rehab Mohamed & Noura Metawa,"An Integrated Plithogenic MCDM approach for financial performance evaluation of manufacturing industries," Risk Management, Palgrave Macmillan, Vol. 22, No.3, pp-192-218,2020


[7]  Smarandache, F. "Extension of Soft set to Hypersoft Set and then to Plithogenic Hypersoft Set", Neutrosophic set and Systems, Vol.22, pp-68-70,2018.


[8]  Muhammad Rayees Ahmad., Muhammad Saeed; Usman Afzal., Miin-Shen Yang, "A Novel MCDM Method Based on Plithogenic Hypersoft Sets under Fuzzy Neutrosophic Environment", Symmetry , Vol.12.No.11.pp-1-23,2020.


[9]  Shazia  Rana  .,  Madiha  Qayyum.,Muhammad  Saeed.,  Florentin  Smarandache  .,  Bakhtawar  Ali Khan., "Plithogenic Fuzzy Whole Hypersoft Set, Construction of Operators and their Application in Frequency Matrix Multi Attribute Decision Making Technique", Neutrosophic Sets and Systems, Vol 28, pp.34-50,2019.


[10]                  Nivetha Martin., Florentin Smarandache, Introduction to Combined Plithogenic Hypersoft sets,  Neutrosophic Sets and Systems, Vol 35, pp.503-510,2020.


[11]                  Martin,  Nivetha  and  Florentin  Smarandache.  "Concentric  Plithogenic  Hypergraph  based  on  Plithogenic Hypersoft sets – A Novel Outlook." Neutrosophic Sets and Systems Vol.33, pp-78-91,2020.


[12]                  Smarandache,  Florentin.,  "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, Vol 33, pp.290-296,2020


[13]                  Florentin Smarandache., Nivetha Martin., "Plithogenic n- Super Hypergraph in Novel Multi – Attribute Decision Making", International Journal of Neutrosophic Science, Vol.7,pp-8-30,2020.


[14]                  Jansi.R, Mohana.K., Florentin Smarandache, "Correlation Measure for Pythagorean Neutrosophic Fuzzy Sets with T and F as Dependent Neutrosophic Components", Neutrosophic Sets and Systems Vol.30, pp-202-212,2019.


[15]                  Yager., "Pythagorean Fuzzy Subsets",In:Proc Joint IFSA World Congress and NAFIPS Annual Meeting,Edmonton,Canada, pp-57-61,2013.


[16]                  Lazim Abdullah.,Pinxin Goh., Decision making method based on Pythagorean fuzzy sets and its application to solid waste management, Complex & Intelligent Systems, vol. 1,pp- 1-7,2019.


[17]                  Carlos Granados.,"Pythagorean Neutrosophic Pre-Open Sets". MathLAB Journal, 6, 65-74,2020




[18]                  Ajay, D., and Chellamani, P., "Pythagorean Neutrosophic Fuzzy Graphs", International Journal of Neutrosophic Science, 11(2), 108–114,2020.




[19]                  Jansi, R and Mohana, K.,"Pythagorean neutrosophic Subring of a ring", Journal of Computational Mathematica, 4(2), 1-9,2020.




[20]                 Solairaju and    Shajahan, "Transforming Neutrosophic Fuzzy Set into Fuzzy Set by Imprecision Method", Journal of ComputerandMathematicalSciences,Vol.9,No.10,pp-1392-1399,2018.


[21]                  Lazim Abdullah.,Waimun Chan.,Alireza Afshari, "Application of PROMETHEE method for green supplier selection: a comparative result based on preference functions", Journal of Industrial Engineering International,Vol.15, pp-271–285,2018.


[22]                  Huchang Liao, "Multi-criteria decision making with intuitionistic fuzzy PROMETHEE", Journal of Intelligent and Fuzzy Systems ,Vol.27,No.4,pp-1703-1717,2014.


[23]                  Feng Feng.,Feng Feng.,Zeshui Xu.,Zeshui Xu.,Hamido., FujitaHamido., FujitaMeiqi Liang., "Enhancing PROMETHEE method with intuitionistic fuzzy soft sets", International Journal of Intelligent Systems,Vol. 35,No.2,pp- 1071-1104, 2020.


[24]                  Fatma Altun.,Rıdvan Şahin.,Rıdvan Şahin.,Coşkun Güler., "Multi-criteria decision making approach based on PROMETHEE with probabilistic simplified neutrosophic sets", Soft Computing, Vol.24,No.1,pp- 4899–4915,2020.


Cite this Article as :
Nivetha Martin , Florentin Smarandache , Said Broumi, PROMTHEE Plithogenic Pythagorean Hypergraphic Approach in Smart Materials Selection, International Journal of Neutrosophic Science, Vol. 13 , No. 1 , (2021) : 52-60 (Doi   :  https://doi.org/10.54216/IJNS.130105)