Geometrical digraphs as models of heterogeneous computer networks

2020 ◽  
Vol 4 ◽  
pp. 50-59
Author(s):  
Alexander Mikov ◽  
Keyword(s):  
Mathematical Models ◽  
Computer Networks ◽  
Connected Components ◽  
Strongly Connected Components ◽  
Oriented Graphs ◽  
Strong Connectivity ◽  
Network Nodes ◽  
Strongly Connected

New mathematical models of networks are considered — geometrical oriented graphs. Such models adequately reflect the structure of heterogeneous wireless computer, sensor and other networks. The strongly connected components of geometric digraphs, their dependence on the number of network nodes in a given area, on the distributions of the radii of the zones of reception and transmission of signals are investigated. The probabilistic characteristics of random geometric digraphs, the features of the dependences of the probability of strong connectivity on the number of nodes in the digraphs for various combinations of radii are analyzed.

ENHANCING ADEQUACY OF GRADING STUDY PROJECTS ON THE BASE OF PARAMETRIC RELAXATION OF PAIRWISE COMPARISONS

2021 ◽  
Vol 1 ◽  
pp. 122-133
Author(s):  
Alexey V. Oletsky ◽  
◽  
Mikhail F. Makhno ◽  
◽  
Keyword(s):  
Center Of Mass ◽  
Estimation Algorithm ◽  
Relaxation Parameter ◽  
Connected Components ◽  
Pairwise Comparisons ◽  
Strongly Connected Components ◽  
Standard Scale ◽  
Relaxation Parameters ◽  
Strongly Connected ◽  
The One

A problem of automated assessing of students’ study projects is regarded. A heuristic algorithm based on fuzzy estimating of projects and on pairwise comparisons among them is proposed. For improving adequacy and naturalness of grades, an approach based on introducing a parameter named relaxation parameter was suggested in the paper. This enables to reduce the spread between maximum and minimum values of projects in comparison with the one in the standard scale suggested by T. Saati. Reasonable values of this parameter were selected experimentally. For estimating the best alternative, a center of mass of a fuzzy max-min composition should be calculated. An estimation algorithm for a case of non-transitive preferences based on getting strongly connected components and on pairwise comparisons between them is also suggested. In this case, relaxation parameters should be chosen separately for each subtask. So the combined technique of evaluating alternatives proposed in the paper depends of the following parameters: relaxation parameters for pairwise comparisons matrices within each strongly connected components; relaxation parameter for pairwise comparisons matrices among strongly connected components; membership function for describing the best alternative.

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