scholarly journals Intuitionistic-Fuzzy Goals in Zero-Sum Multi Criteria Matrix Games

Symmetry ◽  
2017 ◽  
Vol 9 (8) ◽  
pp. 158 ◽  
Author(s):  
Zia Bashir ◽  
Jarosław Wątróbski ◽  
Tabasam Rashid ◽  
Wojciech Sałabun ◽  
Jawad Ali
Keyword(s):  
Matrix Games ◽  
Intuitionistic Fuzzy ◽  
Fuzzy Goals ◽  
Zero Sum

Resolving Indeterminacy Approach to Solve Multi-Criteria Zero-Sum Matrix Games with Intuitionistic Fuzzy Goals

Mathematics ◽  
2020 ◽  
Vol 8 (3) ◽  
pp. 305 ◽  
Author(s):  
M. G. Brikaa ◽  
Zhoushun Zheng ◽  
El-Saeed Ammar
Keyword(s):  
Intuitionistic Fuzzy Set ◽  
Implementation Process ◽  
Fuzzy Programming ◽  
Matrix Game ◽  
Great Success ◽  
Matrix Games ◽  
Intuitionistic Fuzzy ◽  
Fuzzy Goals ◽  
Linear Programming Problems ◽  
Zero Sum

The intuitionistic fuzzy set (IFS) is applied in various decision-making problems to express vagueness and showed great success in realizing the day-to-day problems. The principal aim of this article is to develop an approach for solving multi-criteria matrix game with intuitionistic fuzzy (I-fuzzy) goals. The proposed approach introduces the indeterminacy resolving functions of I-fuzzy numbers and discusses the I-fuzzy inequalities concept. Then, an effective algorithm based on the indeterminacy resolving algorithm is developed to obtain Pareto optimal security strategies for both players through solving a pair of multi-objective linear programming problems constructed from two auxiliary I-fuzzy programming problems. It is shown that this multi-criteria matrix game with I-fuzzy goals is an extension of the multi-criteria matrix game with fuzzy goals. Moreover, two numerical simulations are conducted to demonstrate the applicability and implementation process of the proposed algorithm. Finally, the achieved numerical results are compared with the existing algorithms to show the advantages of our algorithm.

Solving bi-matrix games with intuitionistic fuzzy goals and intuitionistic fuzzy payoffs

2017 ◽  
Vol 33 (6) ◽  
pp. 3723-3732 ◽  
Author(s):  
Jiang-Xia Nan ◽  
Deng-Feng Li ◽  
Jing-Jing An
Keyword(s):  
Matrix Games ◽  
Intuitionistic Fuzzy ◽  
Fuzzy Goals

scholarly journals Max-min solution approach for multi-objective matrix game with fuzzy goals

2016 ◽  
Vol 26 (1) ◽  
pp. 51-60 ◽  
Author(s):  
Sandeep Kumar
Keyword(s):  
Linear Programming ◽  
Linear Programming Problem ◽  
Optimization Problem ◽  
Matrix Game ◽  
Game Model ◽  
Solution Approach ◽  
Multi Objective ◽  
Fuzzy Goals ◽  
Fuzzy Goal ◽  
Zero Sum

In this paper, we consider a multi-objective two person zero-sum matrix game with fuzzy goals, assuming that each player has a fuzzy goal for each of the payoffs. The max-min solution is formulated for this multi-objective game model, in which the optimization problem for each player is a linear programming problem. Every developed model for each player is demonstrated through a numerical example.

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