Volume 24 , Issue 1 , PP: 74-86, 2024 | Cite this article as | XML | Html | PDF | Full Length Article
Florentin Smarandache 1 , V. Inthumathi 2 , M. Amsaveni 3 *
Doi: https://doi.org/10.54216/IJNS.240107
In this study, we offer a hypersoft set theory-based game model for handling uncertainties. The term ”hypersoft game” refers to this newly suggested game. Four techniques of game solution are identified: hypersoft saddle points, hypersoft upper and lower values, hypersoft dominated strategy and hypersoft nash equilibrium. We build a two-person hypersoft game first. Additionally, we present real-world problems that the hypersoft saddle point approaches and hypersoft dominating strategy are used to tackle. In conclusion, we expand the hypersoft games from two players to n players.
hypersoft set , two person hypersoft games , hypersoft payoff functions , hypersoft dominated strategies , hypersoft lower and hypersoft upper values , hypersoft nash equilibrium.
[1] M.Abbas, G.Murtaza and F.Smarandache, Basic Operations on Hypersoft Sets and Hypersoft Point, Neutrosophic Sets and Systems, 35, 407-421, 2020.
[2] C.D.Aliprantis and S.K.Chakrabarti, Games and Decision Making, Oxford University Press, 2000.
[3] R.J.Aumann, Game Theory-Introduction , The New Palgrave Dictionary of Economics, 2nd Edition 2008.
[4] C.R Bector, S.Chandra and V.Vijay, Duality in Linear Programming with Fuzzy Parameters and Matrix Games with Fuzzy Pay-offs, Fuzzy Sets and Systems, 146, 253-269, 2004.
[5] C.R Bector, Fuzzy Mathematical Programming and Fuzzy Matrix Games, Springer-Verlag Berlin Heidelberg, 2005.
[6] K.Binmore, Fun and Games, A Text on Game Theoy, Chancellor Press London, 1982.
[7] L.Campos, Fuzzy Liner Programming Models to Solve Fuzzy Matrix Games, Fuzzy Sets and Systems, 32, 275-289, 1989.
[8] A.C.Cevikel and M.Ahlatcioglu, A New Solution Concept in Fuzzy Matrix Games, World Applied Sciences Journal, 7(7), 866-871, 2009.
[9] Y.W.Chena and M.Larbanib, Two-person Zero-sum Game Approach for Fuzzy Multiple Attribute Decision Making Problems, Fuzzy Sets and Systems, 157, 34-51,2006.
[10] N.Cagman and S.Enginoglu, Soft Set Theory and Uni-int Decision Making, Eur. J. Oper. Res. 207, 848- 855, 2010.
[11] V.Inthumathi, M.Amsaveni and M.Arun vignesh , Application of Hypersoft Sets in Covid-19 Decision Making Model, International Journal of Research and Analytical Reviews 9(3), 2022.
[12] V.Inthumathi and M.Amsaveni, Hypersoft Matrices, Paper Presented in 87th Annual Conference of the Indian Mathematics Society, an International Meet, 2021.
[13] V.Inthumathi and M.Amsaveni, Product Hypersoft Matrices and its Applications in Multi-attribute Decision Making Problems, (Submitted).
[14] V.Inthumathi, M.Amsaveni and M. Nathibrami, On Hypersoft Semi-open Sets, Neutrosophic Sets and Systems, 57, 294-305, 2023.
[15] Irfan Deli, Naim Cagman, Application of Soft Sets in Decision Making Based on Game Theory, Annals of Fuzzy Mathematics and Informatics 11(3), 425-438, 2016.
[16] T.Maeda, On Characterization of Equilibrium Strategy of Two Person Zero-sum Games with Fuzzy Payoffs, Fuzzy sets and systems 139, 283-296, 2003.
[17] P.K.Maji, A.R.Roy and R.Biswas, An Application of Soft Sets in Decision Making Problem, Computers and Mathematics with Applications 44, 1077-1083, 2002.
[18] D.A.Molodtsov, Soft Set Theory-First Results, Computers and Mathematics with Applications, 37, 19- 31, 2009.
