Abstract
In real path selection decisions, besides the cost of the path which is the major decision factor, the chance of the path connection is also significant. A path which has low weight but low chance of existence is not a good choice for decision-making. In order to make network optimization more in line with the actual situation, this paper studies one model of it on a network whose existence and weight of edges are both indeterminate. The aim of this paper is to obtain a spanning tree which satisfies the connectivity constraint and minimizes the total weight as well. The study uses conditional uncertain variable to describe the relationship between these two aspects of uncertain variables. On this basis, three different models of the UMST problem are suggested, and the equivalence relation between the MST model of uncertain networks with uncertain edge existence and weight and the MST of related deterministic networks is found. Examples of experiments with specific numerical values are provided to verify the variation in the network when two variables are considered simultaneously.
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This work was supported by The Natural Science Foundation of Xinjiang (Grants No. 2020D01C017) and National Natural Science Foundation of China (Grants No. 12061072).
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All authors contributed to the study conception and design. The first draft of the paper was written by Jiaojin Wang, who completed the theoretical analysis and demonstration, model construction and implementation. All the authors commented on previous versions of the manuscript. All authors read and approved the final manuscript.
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Wang, J., Sheng, Y. The MST problem in network with uncertain edge weights and uncertain topology. Soft Comput 27, 13825–13834 (2023). https://doi.org/10.1007/s00500-023-08880-9
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DOI: https://doi.org/10.1007/s00500-023-08880-9