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Full Length Article
Volume 7 , Issue 1, PP: 08-30 , 2020


Plithogenic n-Super Hypergraph in Novel Multi-Attribute Decision Making

Authors Names :   Florentin Smarandache   1 *     Nivetha Martin   2  

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

    Email :  smarand@unm.edu

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

    Email :  nivetha.martin710@gmail.com

Doi   :  10.5281/zenodo.3876206

Abstract :

An optimal decision-making environment demands feasible Multi-Attribute Decision-Making methods. Plithogenic n – Super Hypergraph introduced by Smarandache is a novel concept and it involves many attributes. This article aims to bridge the concept of Plithogenic n-Super Hypergraph in the vicinity of optimal decision making. This research work introduces the novel concepts of enveloping vertex, super enveloping vertex, dominant enveloping vertex, classification of the dominant enveloping vertex (input, intervene, output dominant enveloping vertices), plithogenic connectors. An application of Plithogenic n-super hypergraph in making optimum decisions is discussed under various decision-making scenarios. Several insights are drawn from this research work and will certainly benefit the decision-makers to overcome the challenges in building decisions.

Keywords :

Plithogenic n-super hypergraph , decision making , attributes , dominant enveloping vertex.

References :

[1]  Ishizaka, A., Labib, A.. "Review of the main developments in the analytic hierarchy process", Expert Systems with Applications, Vol 38, pp.14336-14345, 2011.

[2]  Saaty, T. L., "A scaling method for priorities in hierarchical structures",Journal of Mathematical Psychology. Elsevier: Amsterdam, Vol 15, pp.234-281, 1977.

[3]  Tzeng, G.H.; Huang, J.J. "Multiple Attribute Decision Making: Methods and Applications"; CRC Press: Boca Raton, FL, USA, 2011.

[4]  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 .

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

[6]  Gayathri.N., Helen.M., Mounika.P., "Utilization of Jaccard  Index Measures on Multiple Attribute Group Decision Making under Neutrosophic Environment", International Journal of Neutrosophic Science,Vol. 3, pp.67-77, 2020.

[7]  Muhammad Naveed Jafar.,Muhammad Saqlain., Ahmad Raza Shafiq., Muhammad Khalid., Hamza Akbar., Aamir Naveed., " New Technology in Agriculture Using Neutrosophic Soft Matrices with the Help of Score Function ", International Journal of Neutrosophic Science,Vol. 3,pp.78-88, 2020.

[8]  Ajay.D.,Aldring.J.,Abirami.S.,Jeni Seles Martina.D., " A SVTrN-number approach of multi-objective optimization on the basis of simple ratio analysis based on MCDM method ", International Journal of Neutrosophic Science ,Vol. 5, pp.16-28, 2020.

[9]  Luis Andrés Crespo Berti.,"Application of the neutrosophic system to tax havens with a criminal approach",International Journal of Neutrosophic Science ,Vol. 5, pp.91-106, 2020.

[10]                 Abdel-Basset, M., Manogaran, G., Mohamed, M., Chilamkurti, N., "Three-way decisions based on neutrosophic sets and AHP-QFD framework for supplier selection problem". Future Gener. Comput. Syst. Vol 89, pp.19–30,2018.

[11]                 Abdel-Basset, M., Mohamed, M., Smarandache, F., "A hybrid neutrosophic group ANP-TOPSIS framework for supplier selection problems". Symmetry Vol 10, pp.226, 2018.

[12]                 Abdel-Basset, M., El-hoseny, M., Gamal, A., & Smarandache, F., "A novel model for evaluation Hospital medical care systems based on plithogenic sets". Artificial intelligence in medicine, 100, 101710,2019

[13]                 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 11,903,2019.

[14]                 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.