The extreme doubly stochastic quadratic operators on two dimensional simplex

Abdulghafor, Rawad Abdulkhaleq Abdulmolla and Turaev, Sherzod and Abubakar, Adamu and Zeki, Akram M. (2016) The extreme doubly stochastic quadratic operators on two dimensional simplex. In: 2015 4th International Conference on Advanced Computer Science Applications and Technologies (ACSAT 2015), 8th-10th Dec. 2015, Kuala Lumpur.

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Abstract

Multi agent systems and consensus problems are theoretical aspect of Quadratic Stochastic Operators (QSO). The extreme doubly stochastic quadratic operators (EDSQOs) on two-dimensional simplex (2DS) exposes a complex problem within QSO and majorization theories in non-linear model. Previous research studies on EDSQOs fails to present full transition matrices and operators of EDSQOs on 2DS. Crucial to that is the classification of those operators within each permutation. In order to address these gaps, this research designed all the transition matrices for each EDSQO on 2DS under the sufficient conditions of majorization concept. Hence, the study defines all the EDSQOs on 2DS and investigate the sufficient conditions of Majorization concept for EDSQOs on 2DS. Matlab is utilize for analysis of evaluating the number of EDSQOs on 2DS. The result of the analysis of the transition matrices and operators indicates 222 EDSQOs on 2DS. Further analysis enables this research to classify the 222 EDSQOs into 37 groups of EDSQOs based on a permutation of each EDSQOs. This study has impact on a model for consensus problems and multi agent systems.

Item Type:	Conference or Workshop Item (Invited Papers)
Additional Information:	6846/51283 (ISBN: 978-1-5090-0423-2)
Uncontrolled Keywords:	transition matrices; extreme doubly stochastic quadratic operators; two-dimensional simplex; majorization concept.
Subjects:	T Technology > T Technology (General) > T55.4 Industrial engineering.Management engineering. > T58.5 Information technology
Kulliyyahs/Centres/Divisions/Institutes (Can select more than one option. Press CONTROL button):	Kulliyyah of Information and Communication Technology > Department of Computer Science Kulliyyah of Information and Communication Technology > Department of Computer Science
Depositing User:	Dr. Sherzod Turaev
Date Deposited:	13 Jul 2016 15:57
Last Modified:	03 Oct 2019 09:28
URI:	http://irep.iium.edu.my/id/eprint/51283

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