Shortest Path Problem by Minimal Spanning Tree Algorithm using Bipolar Neutrosophic Numbers

Mullai, M.; Broumi, S.; Stephen, Andrew

doi:10.14445/22315373/ijmtt-v46p514

Cited by 18 publications

(18 citation statements)

References 5 publications

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“…In order to illustrate the rationality and effectiveness of the proposed method, we apply the algorithm proposed by Mullai et al [18] on our IVBN-graph presented in Section 4. Following the setps of Mullai's algorithm we obtained the results…”

Section: Comparative Studymentioning

confidence: 99%

“…The authors consider a network problem with multiple criteria which are represented by weight of each edge in neutrosophic setsThe approach proposed by the authors is based on similarity measure. Recently Mullai [18] solved the minimum spanning tree problem on a graph in which a bipolar neutrosophic number is associated to each edge as its edge length, and illustrated it by a numerical example.…”

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confidence: 99%

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Computing Minimum Spanning Tree in Interval Valued Bipolar Neutrosophic Environment

Bakali¹,

Talea²,

Smarandache³

et al. 2017

IJMO

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Abstract-Interval valued bipolar neutrosophic sets is a new generalization of fuzzy set, bipolar fuzzy set, neutrosophic set and bipolar neutrosophic set so that it can handle uncertain information more flexibly in the process of decision making. In this paper, an algorithm for finding minimum spanning tree (MST) of an undirected neutrosophic weighted connected graph (UNWCG) in which the edge weights is represented by a an interval valued bipolar neutrosophic number is presented. The proposed algorithm is based on matrix approach to design the MST of UNWCG. A numerical example is provided to show the effectiveness of the proposed algorithm. Lastly, a comparative study with other existing methods is proposed.Index Terms-Score function, interval valued bipolar neutrosophic sets, Neutrosophic sets, Spanning tree problem.

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Section: Comparative Studymentioning

confidence: 99%

mentioning

confidence: 99%

Computing Minimum Spanning Tree in Interval Valued Bipolar Neutrosophic Environment

Bakali¹,

Talea²,

Smarandache³

et al. 2017

IJMO

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show abstract

“…There are many other works studying the problem of getting the shortest path. Readers may refer to, for example, Deng et al (2012), Lozano et al (2013), Zhang et al (2013), Mullai et al (2017), Marinakis et al (2017), Broumi et al (2018), and Kumar et al (2018) for more information.…”

Section: Introductionmentioning

confidence: 99%

Graph Theory and Environmental Algorithmic Solutions to Assign Vehicles: Application to Garbage Collection in Vietnam

et al. 2019

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The authors wish to thank a reviewer for very helpful comments and suggestions. The fifth author would like to thank Robert B. Miller and Howard E. Thompson for their continuous encouragement. Grants from Ton AbstractThe problem of finding the shortest path including garbage collection is one of the most important problems in environmental research and public health. Usually, the road map has been modeled by a connected undirected graph with the edge representing the path, the weight being the length of the road, and the vertex being the intersection of edges. Hence, the initial problem becomes a problem finding the shortest path on the simulated graph.Although the shortest path problem has been extensively researched and widely applied in miscellaneous disciplines all over the world and for many years, as far as we know, there is no study to apply graph theory to solve the shortest path problem and provide solution to the problem of "assigning vehicles to collect garbage" in Vietnam. Thus, to bridge the gap in the literature of environmental research and public health. We utilize three algorithms including Fleury, Floyd, and Greedy algorithms to analyze to the problem of "assigning vehicles to collect garbage" in District 5, Ho Chi Minh City, Vietnam. We then apply the approach to draw the road guide for the vehicle to run in District 5 of Ho Chi Minh city. To do so, we first draw a small part of the map and then draw the entire road map of District 5 in Ho Chi Minh city. The approach recommended in our paper is reliable and useful for managers in environmental research and public health to use our approach to get the optimal cost and travelling time.

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“…One may refer to regarding the basic theory of NS, SVNS and their extensions with applications in several fields. Many researches making particularizations on the T, I, F components which leads to define particular case of neutrosophic sets such as simplified neutrosophic sets [20], interval valued neutrosophic sets [22], bipolar neutrosophic sets [23], trapezoidal neutrosophic set [24], rough neutrosophic set [25] and so on. As a special case of NSs, Ye [24] introduced the concept of single-valued trapezoidal neutrosophic set.…”

Section: Introductionmentioning

confidence: 99%

“…The approach proposed by the authors is based on similarity measure. In another paper, Mullai [20] discussed the MST problem on a graph in which a bipolar neutrosophic number is associated to each edge as its edge length, and illustrated it by a numerical example.…”

Section: Introductionmentioning

confidence: 99%

Bipolar Neutrosophic Minimum Spanning Tree

et al. 2018

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Abstract-The aim of this article is to introduce a matrix algorithm for finding minimum spanning tree (MST) in the environment of undirected bipolar neutrosophic connected graphs (UBNCG). Some weights are assigned to each edge in the form of bipolar neutrosophic number (BNN). The new algorithm is described by a flow chart and a numerical example by considering some hypothetical graph. By a comparison, the advantage of proposed matrix algorithm over some existing algorithms are also discussed.

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Shortest Path Problem by Minimal Spanning Tree Algorithm using Bipolar Neutrosophic Numbers

Cited by 18 publications

References 5 publications

Computing Minimum Spanning Tree in Interval Valued Bipolar Neutrosophic Environment

Computing Minimum Spanning Tree in Interval Valued Bipolar Neutrosophic Environment

Graph Theory and Environmental Algorithmic Solutions to Assign Vehicles: Application to Garbage Collection in Vietnam

Bipolar Neutrosophic Minimum Spanning Tree

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