A Lexicographic Method for Matrix Games with Payoffs of Triangular Intuitionistic Fuzzy Numbers
The intuitionistic fuzzy set (IF-set) has not been applied to matrix game problems yet since it was introduced by K.T.Atanassov. The aim of this paper is to develop a methodology for solving matrix games with payoffs of triangular intuitionistic fuzzy numbers (TIFNs). Firstly the concept of TIFNs an...
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Series: | International Journal of Computational Intelligence Systems |
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doaj-7a2579e1c71d45fc913613afd6892e2f2020-11-25T03:35:55ZengAtlantis PressInternational Journal of Computational Intelligence Systems 1875-68832010-09-013310.2991/ijcis.2010.3.3.4A Lexicographic Method for Matrix Games with Payoffs of Triangular Intuitionistic Fuzzy NumbersJiang-Xia NanDeng-Feng LiMao-Jun ZhangThe intuitionistic fuzzy set (IF-set) has not been applied to matrix game problems yet since it was introduced by K.T.Atanassov. The aim of this paper is to develop a methodology for solving matrix games with payoffs of triangular intuitionistic fuzzy numbers (TIFNs). Firstly the concept of TIFNs and their arithmetic operations and cut sets are introduced as well as the ranking order relations. Secondly the concept of solutions for matrix games with payoffs of TIFNs is defined. A lexicographic methodology is developed to determine the solutions of matrix games with payoffs of TIFNs for both Players through solving a pair of bi-objective linear programming models derived from two new auxiliary intuitionistic fuzzy programming models. The proposed method is illustrated with a numerical example. https://www.atlantis-press.com/article/1979.pdfTriangular intuitionistic fuzzy number; Intuitionistic fuzzy set; Matrix game; Mathematical programming; Lexicographic method. |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Jiang-Xia Nan Deng-Feng Li Mao-Jun Zhang |
spellingShingle |
Jiang-Xia Nan Deng-Feng Li Mao-Jun Zhang A Lexicographic Method for Matrix Games with Payoffs of Triangular Intuitionistic Fuzzy Numbers International Journal of Computational Intelligence Systems Triangular intuitionistic fuzzy number; Intuitionistic fuzzy set; Matrix game; Mathematical programming; Lexicographic method. |
author_facet |
Jiang-Xia Nan Deng-Feng Li Mao-Jun Zhang |
author_sort |
Jiang-Xia Nan |
title |
A Lexicographic Method for Matrix Games with Payoffs of Triangular Intuitionistic Fuzzy Numbers |
title_short |
A Lexicographic Method for Matrix Games with Payoffs of Triangular Intuitionistic Fuzzy Numbers |
title_full |
A Lexicographic Method for Matrix Games with Payoffs of Triangular Intuitionistic Fuzzy Numbers |
title_fullStr |
A Lexicographic Method for Matrix Games with Payoffs of Triangular Intuitionistic Fuzzy Numbers |
title_full_unstemmed |
A Lexicographic Method for Matrix Games with Payoffs of Triangular Intuitionistic Fuzzy Numbers |
title_sort |
lexicographic method for matrix games with payoffs of triangular intuitionistic fuzzy numbers |
publisher |
Atlantis Press |
series |
International Journal of Computational Intelligence Systems |
issn |
1875-6883 |
publishDate |
2010-09-01 |
description |
The intuitionistic fuzzy set (IF-set) has not been applied to matrix game problems yet since it was introduced by K.T.Atanassov. The aim of this paper is to develop a methodology for solving matrix games with payoffs of triangular intuitionistic fuzzy numbers (TIFNs). Firstly the concept of TIFNs and their arithmetic operations and cut sets are introduced as well as the ranking order relations. Secondly the concept of solutions for matrix games with payoffs of TIFNs is defined. A lexicographic methodology is developed to determine the solutions of matrix games with payoffs of TIFNs for both Players through solving a pair of bi-objective linear programming models derived from two new auxiliary intuitionistic fuzzy programming models. The proposed method is illustrated with a numerical example. |
topic |
Triangular intuitionistic fuzzy number; Intuitionistic fuzzy set; Matrix game; Mathematical programming; Lexicographic method. |
url |
https://www.atlantis-press.com/article/1979.pdf |
work_keys_str_mv |
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