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.

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

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.

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

Zero-Sum Matrix Games

2017 ◽  
Author(s):  
João P. Hespanha
Keyword(s):  
Computational Complexity ◽  
Security Policy ◽  
Matrix Game ◽  
Matrix Games ◽  
Key Concepts ◽  
Finite Set ◽  
Security Levels ◽  
Zero Sum ◽  
Saddle Point Equilibrium ◽  
Rational Players

This chapter discusses a number of key concepts for zero-sum matrix games. A zero-sum matrix game is played by two players, each with a finite set of actions. Player 1 wants to minimize the outcome and Player 2 wants to maximize it. After providing an overview of how zero-sum matrix games are played, the chapter considers the security levels and policies involved and how they can be computed using MATLAB. It then examines the case of a matrix game with alternate play and one with simultaneous play to determine whether rational players will regret their decision to play a security policy. It also describes the saddle-point equilibrium and its relation to the security levels for the two players, as well as the order interchangeability property and computational complexity of a matrix game before concluding with a practice exercise with the corresponding solution and an additional exercise.

The Intuitionistic Fuzzy FlowSort Method for Multicriteria Group Decision Making

2022 ◽  
Vol 11 (1) ◽  
pp. 1-21
Author(s):  
Remadi Daami Fedia ◽  
Frikha Moalla Hela
Keyword(s):  
Decision Making ◽  
Group Decision Making ◽  
Group Decision ◽  
Intuitionistic Fuzzy Set ◽  
Real Life ◽  
Multicriteria Analysis ◽  
Great Success ◽  
Intuitionistic Fuzzy Numbers ◽  
Intuitionistic Fuzzy ◽  
Multicriteria Group Decision Making

The real life problems are multidimensional in nature and may involve some ambiguity when it comes to decision making. It is, therefore, difficult to design the evaluation criteria precisely and determine the exact value of the attributes in the multicriteria analysis. The intuitionistic fuzzy set (IFS) achieved great success in treating this kind of ambiguity in a great deal of research. The study of sorting problems is an active research issue in the multiple criteria decision aid (MCDA) area. This paper investigated one of the sorting methods, FLOWSORT, and extended it to the multicriteria group decision making based on the output aggregation of the individual sorting results. The rating of each alternative was described through linguistic terms that can be expressed in triangular intuitionistic fuzzy numbers. An illustrative example as well as an empirical comparison with other multi-criteria decision making methods were carried out to validate our extension.

Sign in / Sign up

Export Citation Format

Share Document