Analysing interval and multi-choice bi-level programming for Stackelberg game using intuitionistic fuzzy programming

2020 ◽  
Vol 16 (3) ◽  
pp. 354
Author(s):  
Sumit Kumar Maiti ◽  
Sankar Kumar Roy
Keyword(s):  
Stackelberg Game ◽  
Fuzzy Programming ◽  
Intuitionistic Fuzzy ◽  
Intuitionistic Fuzzy Programming

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.

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