Allocation of Service Centers in the GIS with the Largest Vitality Degree

Bozhenyuk, Alexander; Rozenberg, Igor N.

doi:10.1007/978-3-642-31715-6_12

Cited by 11 publications

(7 citation statements)

References 4 publications

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“…In works [9][10][11], this problem has been considered as a problem of allocation centers on fuzzy graphs of the first kind [12,13], i.e. graphs whose set of vertices is nonfuzzy set, and set of edges is fuzzy set.…”

Section: Hementioning

confidence: 99%

The Method of Allocation Centers in Second Kind Fuzzy Graphs With the Largest Vitality Degree

Bozhenyuk¹,

Belyakov²,

Knyazeva

2021

ITII

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The problem of optimal allocation of service centers is considered in this paper. It is supposed that the information received from GIS is presented like second kind fuzzy graphs. Method of optimal location as method of finding vitality fuzzy set of second kind fuzzy graph is suggested. Basis of this method is building procedure of reachability matrix of second kind fuzzy graph in terms of reachability matrix of first kind fuzzy graph. This method allows solving not only problem of finding of optimal service centers location but also finding of optimal location k-centers with the greatest degree and selecting of service center numbers. The algorithm of the definition of vitality fuzzy set for second kind fuzzy graphs is considered. The example of finding optimum allocation centers in second kind fuzzy graph is considered too.

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Section: Hementioning

confidence: 99%

The Method of Allocation Centers in Second Kind Fuzzy Graphs With the Largest Vitality Degree

Bozhenyuk¹,

Belyakov²,

Knyazeva

2021

ITII

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“…H. Frank and I. Frisch were the first authors, who examined vitality in terms of the networks. In [10,11] searching and increasing of the network's vitality and finding the centers with the largest vitality degree are considered. However, vitality finding wasn't considered in the conventional literature in terms of flows in networks.…”

Section: Literature Reviewmentioning

confidence: 99%

“…We consider the degree of fuzzy graph vitality as a degree of strong connection [10,11], so it will be defined by the following expression:…”

Section: Definitionmentioning

confidence: 99%

Maximum Flow Finding in Fuzzy Dynamic Graph with the Given Vitality Degree

Bozhenyuk¹,

Gerasimenko²

2016

Proceedings of the 2016 Conference on Information Technologies in Science, Management, Social Sphere and Medicine

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The following paper describes the method of the maximum flow finding in fuzzy dynamic graph with the given vitality degree. The peculiarity of the problem is in fuzzy nature of the considered network and given vitality parameters assigned to arcs of the graph. Network's parameters, such as arc capacities and vitality degrees can vary over time, because they have transit character. Such methods can be applied in the real networks solving the task of the optimal cargo transportation.

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“…In the crisp graphs vitality is understood as its sensitivity to damages from the point of view of removal of some edges or vertices [12]. In case of fuzzy graphs, depending on tasks in view, under vitality different concepts, including degree of strong connectivity of the fuzzy graph [13,14] can be understood.…”

Section: Theoretical Analysesmentioning

confidence: 99%

Analysis of Problem Oriented Systems Structure with Uncertainty Based on Fuzzy Graphs

Bozhenyuk¹,

Ginis²

2016

Proceedings of the 2016 Conference on Information Technologies in Science, Management, Social Sphere and Medicine

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It is offered to use the office of fuzzy graphs for modeling of problem oriented systems. The concepts of fuzzy transitive closure, fuzzy reciprocal transitive closure, and vitality degree of fuzzy graph are considered here. The algorithm for finding the vitality degree of fuzzy graph is described. Presented apparatus allows to analyze and to make decisions about the structure of the model of problem-oriented systems.

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Allocation of Service Centers in the GIS with the Largest Vitality Degree

Cited by 11 publications

References 4 publications

The Method of Allocation Centers in Second Kind Fuzzy Graphs With the Largest Vitality Degree

The Method of Allocation Centers in Second Kind Fuzzy Graphs With the Largest Vitality Degree

Maximum Flow Finding in Fuzzy Dynamic Graph with the Given Vitality Degree

Analysis of Problem Oriented Systems Structure with Uncertainty Based on Fuzzy Graphs

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