Intuitionistic-Fuzzy Goals in Zero-Sum Multi Criteria Matrix Games
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Department of Mathematics, Quaid-i-Azam University, Islamabad-45320, Pakistan
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Department of Web Systems Analysis and Data Processing in the Faculty of Computer Science and Information Technology, West Pomeranian University of Technology, Szczecin 71-210, Poland
3
Department of Mathematics, University of Management and Technology, Lahore-54770, Pakistan
4
Department of Artificial Intelligence method and Applied Mathematics in the Faculty of Computer Science and Information Technology, West Pomeranian University of Technology, Szczecin 71-210, Poland
*
Author to whom correspondence should be addressed.
Symmetry 2017, 9(8), 158; https://doi.org/10.3390/sym9080158
Received: 19 July 2017
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Revised: 8 August 2017
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Accepted: 10 August 2017
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Published: 15 August 2017
(This article belongs to the Special Issue Fuzzy Sets Theory and Its Applications)
The classical matrix theory is deficient to express the vagueness of the real life. The fuzzy set theory has been successfully applied to bridge this gap. Much work has already been done on a two-person zero sum matrix game with fuzzy goals. In continuation, this paper is dedicated to define and study a multi-criteria two-person zero sum game with intuitionistic fuzzy goals. It is shown that solving such games is equivalent to solving two crisp multi object linear programming problems. Our work generalizes the previous study on a multi-criteria game with fuzzy goals by adopting the approach of linear programming with intuitionistic fuzzy sets. Finally, an illustrative numerical example is provided to elaborate the proposed approach.
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Keywords:
intuitionistic fuzzy sets; I-fuzzy goals; zero-sum matrix game; Pareto optimal security strategies; multi-criteria linear programming
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MDPI and ACS Style
Bashir, Z.; Wątróbski, J.; Rashid, T.; Sałabun, W.; Ali, J. Intuitionistic-Fuzzy Goals in Zero-Sum Multi Criteria Matrix Games. Symmetry 2017, 9, 158. https://doi.org/10.3390/sym9080158
AMA Style
Bashir Z, Wątróbski J, Rashid T, Sałabun W, Ali J. Intuitionistic-Fuzzy Goals in Zero-Sum Multi Criteria Matrix Games. Symmetry. 2017; 9(8):158. https://doi.org/10.3390/sym9080158
Chicago/Turabian StyleBashir, Zia, Jarosław Wątróbski, Tabasam Rashid, Wojciech Sałabun, and Jawad Ali. 2017. "Intuitionistic-Fuzzy Goals in Zero-Sum Multi Criteria Matrix Games" Symmetry 9, no. 8: 158. https://doi.org/10.3390/sym9080158
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