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)...

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Main Authors: M. G. Brikaa, Zhoushun Zheng, El-Saeed Ammar
Format: Article
Language:English
Published: MDPI AG 2020-02-01
Series:Mathematics
Subjects:
Online Access:https://www.mdpi.com/2227-7390/8/3/305
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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.
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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