Modified Ranking Function to Compute Fuzzy Matrix Games

Rasha Jalal Mitlif

doi:10.30526/35.2.2765

Authors

Rasha Jalal Mitlif Department of Applied Sciences, Branch of Mathematics and Computer Applications, University of Technology, Baghdad, Iraq.

DOI:

https://doi.org/10.30526/35.2.2765

Abstract

Game theory problems (GTP) frequently occur in Economy, Business Studies, Sociology, Political Science, Military Activities, and so on are some of the subjects covered. To tackle the uncertainty in Games, the analysis of games in which the payoffs are represented by fuzzy numbers (FN) will benefit from fuzzy set theory (FST).

The purpose of this paper is to develop an efficient technique for solving constraint matrix games (MG) with payoff trapezoidal fuzzy numbers (TFN). The description of the new ranking method is introduced for a constrained matrix with TFN and values. Stock market forecasting has been one of the most important research areas for decades. Stock market values are volatile, non-linear, complicated and chaotic. Based on a ranking function (RF), we used a new algorithm to solve the fuzzy game problem (FGP) employing TFN and also to try to get a desirable gain. Centered on the latest proposed ranking algorithm, the Fuzzy decision method is designed to analyze possible stock opportunists.

The paper considers a zero-sum game for two persons in which TFN are fuzzy payoffs. A ranking method (RM) is proposed to convert TFN into crisp numbers (CN) and it is used to solve FGP. The fuzzy game (FG) issue with concept strategies pure minimax maximin is presented. This problem is converted into the crisp problem by a new RF and then solved using the arithmetic (oddment) method. With the help of numerical examples, the suggested technique is explained. This paper finalizes the conclusion and includes an outlook for future study in this direction

References

Newmann , J.; Morgenstern, O. Theory of Games and Economic Behaviour,

Princeton University Press, Princeton, New Jersey (1947) .

Raju , V.; vathana, M. P. Discourse on Fuzzy Game Problem in Icosagonal Fuzzy Number, International Journal of Scientific Research and Review. 2019,8, 1384 – 1390.

Selvakumari, K.; Lavanya, S. On Solving Fuzzy Game Problem using Octagonal Fuzzy

Numbers, Annals of Pure and Applied Mathematics. 2014, 8(2), 211-217.

Hussein, I H. ; Mitlif, R J. Ranking Function to Solve a Fuzzy Multiple Objective Function, Baghdad Science Journal, 2021,18, 1, 144-148.

Namarta, U.; Gupta, Ch.; Thakur, N.I. Solving Game Problems involving Heptagonal and Hendecagonal Fuzzy Payoffs, International Journal of Innovative Technology and Exploring Engineering (IJITEE). 2019, 8, 2114-2120.

Namarta, U.; Gupta, Ch.; Thakur, N. Applications of Game Problems in Fuzzy Enviornment, International Journal for Research in Engineering Application & Management (IJREAM), 2019, 4, 228-232.

Mitlif ,R J., Computation the Optimal Solution of Octagonal Fuzzy Numbers, Journal of Al-Qadisiyah for Computer Science and Mathematics, 2020, 12, 4, 71–78.

Krishnaveni, G.; Ganesan, K. A new approach for the solution of fuzzy games, National Conference on Mathematical Techniques and its Applications , 2018,1-6.

Monisha, P.; Sangeetha, K. To Solve Fuzzy Game Problem Using Pentagonal Fuzzy Numbers, International Journal for Modern Trends in Science and Technology, 2017, 03( 09), , 152-154.

Mitlif, R J.; Fatema Ahmad Sadiq, Finding the Critical Path Method for Fuzzy Network with Development Ranking Function, Journal of Al-Qadisiyah for Computer Science and Mathematics. 2021 ,13, 3 , 98–106.

Raju, V.; Vathana, M. P. Discourse on Fuzzy Game Problem in Icosagonal Fuzzy Number, International Journal of Scientific Research and Review, 2019, 8, 1384-1390.

Namarta, U. Ch. Gupta, N. I. Thakur, A New -Cut Approach to Solve Fuzzy Game Problem, International Journal of Management, Technology And Engineering.2018,8,2761-2766.

J.C. Liu, Y.F. Zhu, W. J.Zhao, Quadratic Programming Method for Cooperative Games with Coalition Values Expressed by Triangular Fuzzy Numbers and Its Application in the Profit Distribution of Logistics Coalition, Hindawi Mathematical Problems in Engineering, 2019, 1-10.

Mitlif, R J, An Efficient Algorithm for Fuzzy Linear Fractional Programming Problems via Ranking Function, Baghdad Science Journal, 2022, 19, 1, 71-76.

Ch. Cui; Feng, Z.; Ch Tan, Credibilistic Loss Aversion Nash Equilibrium for Bimatrix Games with Triangular Fuzzy Payoffs, Hindawi Complexity, 2018,1-16.

Mitlif R J, Ranking Function Application for Optimal Solution of Fractional Programming Problem, Al-Qadisiyah Journal Of Pure Science, 2020, 25 , 1,27-35.

Narmatha, S.; Glory Bebina, E. ; Vishnu Priyaa, R. SOLVING GAME PROBLEM USING ICOSIKAITETRAGONAL FUZZY NUMBERS, The International journal of analytical and experimental modal analysis2020, 12, 55-60.

Jahir Hussain, R.; Priya, A. SOLVING FUZZY GAME PROBLEM USING HEXAGONAL FUZZY NUMBER, Journal of Computer . 2016, JoC, l, 53-59.

Hamiden Abdelwahed Khalifa , An approach for solving two- person zero- sum matrix games in neutrosophic environment, Journal of Industrial and Systems Engineering, 2019,12(2),186-198.

Salman, Israa M., and Eman A. Abdul-Razzaq. "Solving Nonlinear Second Order Delay Eigenvalue Problems by Least Square Method." Ibn AL-Haitham Journal For Pure and Applied Sciences, 2020, 33(4)59-64.

Kalaf, Bayda Atiya Bakar RA, Soon LL, Monsi MB, Bakheet AJ, Abbas IT. A modified fuzzy multi-objective linear programming to solve aggregate production planning. International Journal of Pure and Applied Mathematics, 2015,104(3) .339-352

Thirucheran, M. ; Meena kumari, E.R. ; Lavanya, S. A NEW APPROACH FORSOLVING FUZZY GAME PROBLEM, International Journal of Pure and Applied Mathematics, 2017,114(6), 67 – 75.

Krishnaveni, G. ; Ganesan, K. New approach for the solution of two person zero sum fuzzy games, International Journal of Pure and Applied Mathematics, 2018, 119 ( 9 ), 405-414.

Hamiden bdelwahed Khalifa , An approach for solving two- person zero- sum matrix games in neutrosophic environment , Journal of Industrial and Systems Engineering , 2017,12(2),186-198.

Tharani R., S. Rekha , A New Approach of Solving Fuzzy Game Problem of Order 3 X 3 Using Dodecagonal Fuzzy Numbers , International Journal of Scientific Research in Science, Engineering and Technology , 2017, 3 ( 6 ) , 131- 134.

Selvakumari, K. ; Lavanya, S. On Solving Fuzzy Game Problem using Octagonal Fuzzy Numbers , Annals of Pure and Applied Mathematics . 2014, 8 (2) , 211-217.

Savitha, M T.; Mary, G. New Methods for Ranking of Trapezoidal Fuzzy Numbers, Advances in Fuzzy Mathematics, 2017, 12(5), 1159-1170.

Zhong, Y.; Jia, Y.;Chen, D.; Yang, Y. Interior Point Method for Solving Fuzzy Number Linear Programming Problems Using Linear Ranking Function, Journal of Applied Mathematics, 2013, 1-9.