(Inverse) Neutrosophic special n-domination in neutrosophic graphs with application in decision making

Document Type : Research Paper


1 Researcher, Department of Cognitive Modeling and Simulation, Faculty of Artificial Intelligence and Cognitive Sciences, Imam Hossein University, Tehran, Iran

2 Department of Mathematics, Shahid Beheshti University, Tehran, Iran


In this paper the meanings of neutrosophic special $n$-dominating set,  neutrosophic special $n$-domination number, inverse neutrosophic special domination set (number) and  inverse neutrosophic special $n$-domination number are introduced and some of related results are investigated. Finally, an application of inverse neutrosophic special dominating set in decision making under ashy clauses between certainty and uncertainty is provided. In fact, we present a decision-making problem in real-world applied example which discusses the factors influencing a companys efficiency. The presented model is, in fact, a factor-based model wherein the impact score of each factor is divided into two types of direct and indirect influences.


Main Subjects

[1] Akram, M. Single-Valued Neutrosophic Graphs. Infosys Science Foundation Series in Mathematical Sciences, Springer, 2018, 213-237.
[2] Akram, M.; Shahzadi, S. Neutrosophic soft graphs with application. Journal of Intelligent & Fuzzy Systems. 2017, 32(1), 841-858, 2017.
[3] Akram, M.; Shahzadi, G. Operations on single-valued neutrosophic graphs, Journal of Uncertain Systems. 2017, 11(1), 1-26
[4] Atanassov, K. Intuitionistic fuzzy sets. Fuzzy Sets Syst. 1986, 20, 87-96.
[5] Atanassov, K.; Gargov, G. Interval valued intuitionistic fuzzy sets. Fuzzy Sets Syst. 1989, 31, 343-349.
[6] Banitalebi, S. Irregular vague graphs. J. algebr. hyperstrucres log. algebr. 2021, 2, 73-90.
[7] Banitalebi, S.; Ahn, S. S.; Jun, Y. B.; Borzooei, R. A. Normal m-domination and inverse m-domination in Pythagorean fuzzy graphs with application in decision making. J. Intell. Fuzzy Syst. (2022), 1-10.
[8] Banitalebi, S.; Borzooei, R. A. Domination in Pythagorean fuzzy graphs. Granul. Comput. 2023, 1-8.
[9] Banitalebi, S.; Borzooei, R. A. Domination of vague graphs by using of strong arcs. J. Math. Ext. 2022, 16(3), 1-22.
[10] Banitalebi, S.; Borzooei, R. A. 2-Domination in vague graphs. J. Algebr. Struct. their Appl. 2021, 8, 203-222.
[11] Banitalebi, S.; Borzooei, R. A. Neutrosophic special dominating set in neutrosophic graphs, NSS. 2021, 45, 26-39.
[12] Broumi, S.; Talea, M.; Bakali, A.; Smarandache, F. Single valued neutrosophic graphs. J. New Theory. 2016, 10, 861-101.
[13] Deng, J.; Zhan, J.; Herrera-Viedma, E.; Herrera, F. Regret theory-based three-way decision method on incomplete multi-scale decision information systems with interval fuzzy numbers. IEEE Transactions on Fuzzy Systems, 2022, doi:
[14] Deng, J.; Zhan, J.; Xu, Z.; Herrera-Viedma, E. Regret-Theoretic Multiattribute Decision-Making Model Using Three-Way Framework in Multiscale Information Systems. IEEE Transactions on Cybernetics, 2022, doi: 10.1109/TCYB.2022.3173374
[15] Fei, Y. Study on neutrosophic graph with application in wireless network. CAAI Trans. Intell. Technol. 2020, 5, 301-307.
[16] Hussain, S.; Satham, R.; Hussain, Florentin Smarandache. Domination number in neutrosophic soft graphs. NSS. 2019, 28, 228-244.
[17] Smarandache, F. Neutrosophic set - A generalization of the intuitionistic fuzzy set. Int J Pure Appl Math. 2005, 24(3), 287-297.
[18] Smarandache, F. Re ned Literal Indeterminacy and the Multiplication Law of Sub-Indeterminacies. NSS. 2015, 9, 58-63.
[19] Smarandache, F. Symbolic Neutrosophic theory. Brussels, Europanova, 2015, 103-120.
[20] Turksen, I. Interval valued fuzzy sets based on normal forms. Fuzzy Sets Syst. 1986, 20, 191-210.
[21] Wang, W.; Zhan, J.; Herrera-Viedma, E. A three-way decision approach with a probability dominance relation based on prospect theory for incomplete information systems. Information Sciences. 2021, 611, 199-224.
[22] Wang, W.; Zhan, J.; Zhang, C.; Herrera-Viedma, E.; Kou, G. A regret-theory-based three-way decision method with a priori probability tolerance dominance relation in fuzzy incomplete information systems. Information Fusion. 2023, 89, 382-396.
[23] Zadeh, L. A. Fuzzy sets. Inf. Control. 1965, 8, 338-353.