Mathematics and Computational Sciences

Two-person games induced by pentapartitioned Neutrosophic Payoffs

Document Type : Original Article

Authors

Simson Jackson
Janakiraman Sivasankar

Department of Mathematics, V. O. Chidambaram College, Thoothukudi.

https://doi.org/10.30511/mcs.2025.2075226.1518
Abstract
Two-person games have been extensively studied in classical game theory, but uncertainty and imprecision in real-world scenarios necessitate more advanced mathematical frameworks. Pentapartitioned Neutrosophic sets, provide a powerful tool for handling contradiction, ignorance, unknown, and inconsistent information. This paper explores two-person games in a Pentapartitioned Neutrosophic environment, where players’ strategies, payoffs, and outcomes are expressed using Pentapartitioned Neutrosophic numbers. We present fundamental definitions, solution concepts, and equilibrium conditions tailored for such games. The findings demonstrate that Pentapartitioned Neutrosophic game theory provides a more flexible and realistic approach to strategic interactions involving indeterminacy.

Keywords

Pentapartitioned Neutrosophic set
Pentapartitioned Neutrosophic Game theory
Two person Games
Pentapartitioned Neutrosophic two person games

Subjects

[1] Aliprantis, C. D., Chakrabarti, S. K. (2000). Games and decision making (Vol. 2). New York: Oxford university press. 
[2] Atanassov K, (1986), Intuitionistic fuzzy set, VII ITKRs Session, Sofia. 
[3] Bandyopadhyay, S., Nayak, P. K., Pal, M. (2013). Solution of matrix game in intuitionistic fuzzy environment. JCER, 3, 84-89.
[4] Binmore K, (1982), Fun and games. A Text on Game Theory. Chancellor Press, London. 
[5] Cevikel, A. C., Ahlatçolu, M. (2010). Solutions for fuzzy matrix games. Computers and Mathematics with Appli- cations, 60(3), 399-410. 
[6] Deli, I. (2018). Matrix games with simplified neutrosophic payoffs. In Fuzzy Multi-criteria Decision-Making Using Neutrosophic Sets (pp. 233-246). Cham: Springer International Publishing.
[7] Ferguson T S, (2008), Game Theory, UCLA. 
[8] Mallick, R., Pramanik, S. (2020). Pentapartitioned neutrosophic set and its properties (Vol. 36). Infinite Study. 
[9] Nash J F, (1951), Non cooperative games, Annals of Mathematics, 54, 286295.
[10] Neumann J V, Morgenstern O, (1944), The Theory of Games and Economic Behavior, Princeton University Press.
[11] Pramanik, S., Roy, T. K. (2014). Neutrosophic game theoretic approach to Indo-Pak conflict over Jammu-Kashmir. Neutrosophic Sets and Systems, 2(1), 11.
[12] Smarandache, F. (2005). Neutrosophic set-a generalization of the intuitionistic fuzzy set. International journal of pure and applied mathematics, 24(3), 287.
[13] Abbasi Shureshjani, R. (2021). A developed Best-Worst method to solve multi-criteria decision-making problems under intuitionistic fuzzy environments. Mathematics And Computational Sciences, 2(3), 43-55.
[14] Abbasi Shureshjani, R., Shirdel, G. H., Farnam, M., Darehmiraki, M. (2024). Parametric distance measure for trapezoidal intuitionistic fuzzy numbers and application in Multi-criteria group decision-making. Mathematics and Computational Sciences, 5(4), 61-84.
[15] Taati, M. (2025). Introduction of some one-searchable graphs. Mathematics and Computational Sciences, 6(2), 72-76. 
[16] Zadeh A L, (1965), Fuzzy sets, Information Control 8:338353.
Mathematics and Computational Sciences
Volume 7, Issue 1
Winter 2026
Pages 9-20

  • Receive Date 20 October 2025
  • Revise Date 24 November 2025
  • Accept Date 24 November 2025

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