Iranian Journal of Fuzzy Systems

Current Issue

By Issue

By Author

By Subject

Author Index

Keyword Index

About Journal

Aims and Scope

Editorial Board

Publication Ethics

Indexing and Abstracting

Related Links

FAQ

Peer Review Process

Journal Metrics

News

A note on “A novel defuzzification approach of type-2 fuzzy variable to solving matrix games: An application to plastic ban problem”

Document Type : Research Paper

Authors

1 Department of Mathematics, Thapar Institute of Engineering and Technology, Patiala, Punjab, India

2 Department of Mathematics, Thapar Institute of Engineering and Technology Patiala

3 Department of Mathematics, Thapar Institute of Engineering and Technology, Patiala, Punjab

Abstract

Seikh et al. (Iranian Journal of Fuzzy Systems, 18(5) (2021), 155-172) pointed out that there does not exist any approach to solve type-2 fuzzy variable matrix games (matrix games in which each element of the payoff matrix is represented by a type-2 fuzzy variable). To fill this gap, Seikh et al. proposed an approach to solve triangular type-2 fuzzy variable (TT2FV) matrix games (matrix games in which each element of the payoff matrix is represented by a TT2FV). Seikh et al. also solved a real-life TT2FV matrix game (plastic ban problem) to show the applicability of their proposed approach. In future, other researchers may use Seikh et al.’s approach to solve other real-life TT2FV matrix games. However, it is inappropriate to use Seikh et al.’s approach as it may fail to find a correct optimal solution of TT2FV matrix games. To validate this claim, a TT2FV matrix game is solved by Seikh et al.’s approach and it is shown that the obtained optimal solution is not correct. Also, it is pointed out that this inappropriateness occurs as a mathematically incorrect result is considered in Seikh et al.’s approach. Furthermore, Seikh et al.’s approach is modified to resolve its inappropriateness.

Keywords

Main Subjects

References
[1] C. R. Bector, S. Chandra, Fuzzy mathematical programming and fuzzy matrix games, Springer Verlag, Berlin,
Germany, 2005. https://doi.org/10.1007/3-540-32371-6
[2] A. Bhaumik, S. K. Roy, D. F. Li, Analysis of triangular intuitionistic fuzzy matrix games using robust ranking,
Journal of Intelligent and Fuzzy Systems, 33 (2017), 327-336. https://doi.org/10.3233/JIFS-161631
[3] A. Bhaumik, S. K. Roy, G. W. Weber, Hesitant interval-valued intuitionistic fuzzy-linguistic term set approach in
Prisoners’ dilemma game theory using TOPSIS: A case study on human-trafficking, Central European Journal of
Operations Research, 28 (2020), 797-816. https://doi.org/10.1007/s10100-019-00638-9
[4] L. Campos, A. Gonzalez, M. A. Vila, On the use of ranking function approach to solve fuzzy matrix games in a
direct way, Fuzzy Sets and Systems, 49 (1992), 193-202. https://doi.org/10.1016/0165-0114(92)90324-W
[5] A. Das, U. K. Bera, M. Maity, A solid transportation problem in uncertain environment involving type-
2 fuzzy variable, Neural Computing and Applications, 31 (2019), 4903-4927. https://doi.org/10.1007/
s00521-018-03988-8
[6] B. K. Debnath, P. Majumder, U. K. Bera, Multi-objective sustainable fuzzy economic production quantity (SFEPQ)
model with demand as type-2 fuzzy number: A fuzzy differential equation approach, Hacettepe Journal of Mathematics
and Statistics, 48(1) (2019), 112-139. https://doi.org/10.15672/HJMS.20164512494
[7] J. Jana, S. K. Roy, Dual hesitant fuzzy matrix games: Based on new similarity measure, Soft Computing, 23
(2019), 8873-8886. https://doi.org/10.1007/s00500-018-3486-1
[8] S. Karmakar, M. R. Seikh, O. Castillo, Type-2 intuitionistic fuzzy matrix games based on a new distance measure:
Application to biogas-plant implementation problem, Applied Soft Computing, 106 (2021). https://doi.org/10.
1016/j.asoc.2021.107357
[9] P. Kundu, S. Kar, M. Maity, Fixed charge transportation problem with type-2 fuzzy variables, Information Sciences,
255 (2014), 170-186. https://doi.org/10.1016/j.ins.2013.08.005
[10] P. Kundu, S. Kar, M. Maity, A fuzzy multi-criteria group decision making based on ranking interval type-2 fuzzy
variables and an application to transportation mode selection problem, Soft Computing, 21(11) (2017), 3051-3062.
https://doi.org/10.1007/s00500-015-1990-0
[11] D. F. Li, A fast approach to compute fuzzy values of matrix games with payoffs of triangular fuzzy numbers,
European Journal of Operational Research, 223 (2012), 421-429. https://doi.org/10.1016/j.ejor.2012.06.
020
[12] D. F. Li, An effective methodology for solving matrix games with fuzzy pay-offs, IEEE Transactions on Cybernetics,
43(2) (2013), 610-621. https://doi.org/10.1109/TSMCB.2012.2212885
[13] D. F. Li, Decision and game theory in management with intuitionistic fuzzy sets, Berlin, Germany: Springer Verlag,
2014. https://doi.org/10.1007/978-3-642-40712-3
[14] Z. Q. Liu, Y. K. Liu, Type-2 fuzzy variable and their arithmetic, Soft Computing, 14 (2010), 729-747. https:
//doi.org/10.1007/s00500-009-0461-x
[15] R. Qin, Y. K. Liu, Z. Q. Liu, Methods of critical value reduction for type-2 fuzzy variables and their applications,
Journal of Computational and Applied Mathematics, 235 (2011), 1454-1481. https://doi.org/10.1016/j.cam.
2010.08.031
[16] S. K. Roy, A. Bhaumik, Intelligent water management: A triangular type-2 intuitionistic fuzzy matrix games
approach, Water Resource Management, 32 (2018), 949-968. https://doi.org/10.1007/s11269-017-1848-6
[17] S. K. Roy, S. K. Mondal, An approach to solve fuzzy interval valued matrix game, International Journal of Operational
Research, 26(3) (2016). https://doi.org/10.1504/IJOR2016.076880
[18] M. R. Seikh, S. Dutta, A nonlinear programming model to solve matrix games with pay-offs of single-valued neutrosophic numbers, Neutrosophic Sets and Systems, 47 (2021), 366-383. https://digitalrepository.unm.edu/
nss-journal/vol47/iss1/24
[19] M. R. Seikh, S. Dutta, Solution of matrix games with payoffs of single-valued trapezoidal neutrosophic numbers,
Soft Computing, 26(3) (2022), 921-936. https://doi.org/10.1007/s00500-021-06559-7
[20] M. R. Seikh, S. Dutta, Interval neutrosophic matrix game-based approach to counter cybersecurity issue, Granular
Computing, 8(2) (2023), 271-292. https://doi.org/10.1007/s41066-022-00327-0
[21] M. R. Seikh, S. Karmakar, O. Castillo, A novel defuzzification approach of type-2 fuzzy variable to solving matrix
games: An application to plastic ban problem, Iranian Journal of Fuzzy Systems, 18(5) (2021), 155-172. https:
//doi.org/10.22111/IJFS.2021.6262
[22] M. R. Seikh, S. Karmakar, P. K. Nayak, Matrix games with dense fuzzy payoffs, International Journal of Intelligent
Systems, 36(4) (2021), 1770-1799. https://doi.org/10.1002/int.22360
[23] M. R. Seikh, S. Karmakar, M. Xia, Solving matrix games with hesitant fuzzy pay-offs, Iranian Journal of Fuzzy
Systems, 17(4) (2020), 25-40. https://doi.org/10.22111/IJFS.2020.5404
[24] M. R. Seikh, P. K. Nayak, M. Pal, Matrix games in intuitionistic fuzzy environment, International Journal of
Mathematics in Operational Research, 5(6) (2013), 693-708. https://doi.org/10.1504/IJMOR.2013.057491
[25] M. R. Seikh, P. K. Nayak, M. Pal, Matrix game with intuitionistic fuzzy payoffs, Journal of Information and
Optimization Sciences, 36(1-2) (2015), 159-181. https://doi.org/10.1080/02522667.2014.961785
[26] T. Verma, A. Kumar, Ambika methods for solving matrix games with Atanassov’s intuitinistic fuzzy pay-offs, IEEE
Transactions on Fuzzy Systems, 26(1) (2018), 270-283. https://doi.org/10.1109/TFUZZ.2017.2651103
[27] T. Verma, A. Kumar, Fuzzy solution concepts for non-cooperative games, Springer International Publishing, 2020.
https://doi.org/10.1007/978-3-030-16162-0
Iranian Journal of Fuzzy Systems
Volume 21, Issue 4
July and August 2024
Pages 35-47
Files
Share
How to cite
Statistics