Resolving Indeterminacy Approach to Solve Multi-criteria Zero-sum Matrix Games with Intuitionistic Fuzzy Goals
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)...
Main Authors: | , , |
---|---|
Format: | Article |
Language: | English |
Published: |
MDPI AG
2020-02-01
|
Series: | Mathematics |
Subjects: | |
Online Access: | https://www.mdpi.com/2227-7390/8/3/305 |
_version_ | 1819047603166248960 |
---|---|
author | M. G. Brikaa Zhoushun Zheng El-Saeed Ammar |
author_facet | M. G. Brikaa Zhoushun Zheng El-Saeed Ammar |
author_sort | M. G. Brikaa |
collection | DOAJ |
description | 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. |
first_indexed | 2024-12-21T11:02:59Z |
format | Article |
id | doaj.art-14e222662fab4e749894542706a24e1b |
institution | Directory Open Access Journal |
issn | 2227-7390 |
language | English |
last_indexed | 2024-12-21T11:02:59Z |
publishDate | 2020-02-01 |
publisher | MDPI AG |
record_format | Article |
series | Mathematics |
spelling | doaj.art-14e222662fab4e749894542706a24e1b2022-12-21T19:06:17ZengMDPI AGMathematics2227-73902020-02-018330510.3390/math8030305math8030305Resolving Indeterminacy Approach to Solve Multi-criteria Zero-sum Matrix Games with Intuitionistic Fuzzy GoalsM. G. Brikaa0Zhoushun Zheng1El-Saeed Ammar2School of Mathematics and Statistics, Central South University, Changsha 410083, Hunan, ChinaSchool of Mathematics and Statistics, Central South University, Changsha 410083, Hunan, ChinaDepartment of Mathematics Faculty of Science, Tanta University, Tanta 31527, EgyptThe 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.https://www.mdpi.com/2227-7390/8/3/305intuitionistic fuzzy setmulti-criteria matrix gamesintuitionistic fuzzy goalsgame theorymulti-objective programmingindeterminacy resolving approach |
spellingShingle | M. G. Brikaa Zhoushun Zheng El-Saeed Ammar Resolving Indeterminacy Approach to Solve Multi-criteria Zero-sum Matrix Games with Intuitionistic Fuzzy Goals Mathematics intuitionistic fuzzy set multi-criteria matrix games intuitionistic fuzzy goals game theory multi-objective programming indeterminacy resolving approach |
title | Resolving Indeterminacy Approach to Solve Multi-criteria Zero-sum Matrix Games with Intuitionistic Fuzzy Goals |
title_full | Resolving Indeterminacy Approach to Solve Multi-criteria Zero-sum Matrix Games with Intuitionistic Fuzzy Goals |
title_fullStr | Resolving Indeterminacy Approach to Solve Multi-criteria Zero-sum Matrix Games with Intuitionistic Fuzzy Goals |
title_full_unstemmed | Resolving Indeterminacy Approach to Solve Multi-criteria Zero-sum Matrix Games with Intuitionistic Fuzzy Goals |
title_short | Resolving Indeterminacy Approach to Solve Multi-criteria Zero-sum Matrix Games with Intuitionistic Fuzzy Goals |
title_sort | resolving indeterminacy approach to solve multi criteria zero sum matrix games with intuitionistic fuzzy goals |
topic | intuitionistic fuzzy set multi-criteria matrix games intuitionistic fuzzy goals game theory multi-objective programming indeterminacy resolving approach |
url | https://www.mdpi.com/2227-7390/8/3/305 |
work_keys_str_mv | AT mgbrikaa resolvingindeterminacyapproachtosolvemulticriteriazerosummatrixgameswithintuitionisticfuzzygoals AT zhoushunzheng resolvingindeterminacyapproachtosolvemulticriteriazerosummatrixgameswithintuitionisticfuzzygoals AT elsaeedammar resolvingindeterminacyapproachtosolvemulticriteriazerosummatrixgameswithintuitionisticfuzzygoals |