TY - GEN
T1 - The Extreme Doubly Stochastic Quadratic Operators on Two Dimensional Simplex
AU - Abdulghafor, Rawad
AU - Turaev, Sherzod
AU - Abubakar, Adamu
AU - Zeki, Akram
N1 - Publisher Copyright:
© 2015 IEEE.
PY - 2016/5/25
Y1 - 2016/5/25
N2 - 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.
AB - 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.
KW - extreme doubly stochastic quadratic operators
KW - majorization concept
KW - transition matrices
KW - two-dimensional simplex
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U2 - 10.1109/ACSAT.2015.36
DO - 10.1109/ACSAT.2015.36
M3 - Conference contribution
AN - SCOPUS:84978969993
T3 - Proceedings - 2015 4th International Conference on Advanced Computer Science Applications and Technologies, ACSAT 2015
SP - 192
EP - 197
BT - Proceedings - 2015 4th International Conference on Advanced Computer Science Applications and Technologies, ACSAT 2015
PB - Institute of Electrical and Electronics Engineers Inc.
T2 - 4th International Conference on Advanced Computer Science Applications and Technologies, ACSAT 2015
Y2 - 8 December 2015 through 10 December 2015
ER -