Roman domination problem with uncertain positioning and deployment costs

In a connected simple graph, the weighted Roman domination problem is considered at which the cost of positioning at each vertex is imposed in addition to the costs of potential deployments from a vertex to some of its neighboring vertices. Proper decision in practice is prone to a high degree of in...

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Bibliographic Details
Published in:Soft computing (Berlin, Germany) Vol. 24; no. 4; pp. 2637 - 2645
Main Author: Ghaffari-Hadigheh, Alireza
Format: Journal Article
Language:English
Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.02.2020
Springer Nature B.V
Subjects:
Apexes
Artificial Intelligence
Computational Intelligence
Construction costs
Control
Disaster recovery
Engineering
Fire stations
Focus
Linear programming
Mathematical Logic and Foundations
Mechatronics
Optimization
Optimization models
Probability theory
Provinces
Robotics
Soft computing
Uncertainty
Wireless networks
Integer linear programming
Positioning and deployment costs
Uncertain variable
Roman-dominating set problem
Uncertainty theory
ISSN:1432-7643, 1433-7479
Online Access:Get full text
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Summary:In a connected simple graph, the weighted Roman domination problem is considered at which the cost of positioning at each vertex is imposed in addition to the costs of potential deployments from a vertex to some of its neighboring vertices. Proper decision in practice is prone to a high degree of indeterminacy, mostly raised by unpredictable events that do not obey the rules and prerequisites of the probability theory. In this study, we model this problem with such assumptions in the context of the uncertainty theory initiated by Liu (Uncertainty theory. Studies in fuzziness and soft computing, Springer, Berlin, 2007 ). Two different optimization models are presented, and a concrete example is provided for illustrative purposes. Weaknesses of the probability theory and fuzzy theory in dealing with this problem are also mentioned in detail.
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ISSN:1432-7643
1433-7479
DOI:10.1007/s00500-019-03811-z