Shortest path problem on single valued neutrosophic graphs

Real-life decision-making problem has been demonstrated to cover the indeterminacy through single valued neutrosophic set. It is the extension of interval valued neutrosophic set. Most of the problems of real life involve some sort of uncertainty in it among which, one of the famous problem is finding a shortest path of the network. In this paper, a new score function is proposed for interval valued neutrosophic numbers and SPP is solved using interval valued neutrosophic numbers. Additionally, novel algorithms are proposed to find the neutrosophic shortest path by considering interval valued neutrosophic number, trapezoidal and triangular interval valued neutrosophic numbers for the length of the path in a network with illustrative example. Further, comparative analysis has been done for the proposed algorithm with the existing method with the shortcoming and advantage of the proposed method and it shows the effectiveness of the proposed algorithm.Keywords Interval valued triangular neutrosophic number · Interval valued trapezoidal neutrosophic number · Ranking methods · Deneutrosophication · Neutrosophic shortest path problem · Network Introduction and literature of reviewIn this part, introduction to the objective of the paper is given by presenting basic concepts and procedure of the shortest path problem (SPP) and the literature of review have been collected to know the recent work related to the presented concept which shows the novelty of the presented work * Said Broumi Publisher's Note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

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“…Broumi et al [31] solved SPP using SVNG. Broumi et al [32] solved SSP under bipolar neutrosophic environment.…”

Section: Literature Of Reviewmentioning

confidence: 99%

The shortest path problem in interval valued trapezoidal and triangular neutrosophic environment

Nagarajan

Bakali

Talea

et al. 2019

Complex Intell. Syst.

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“…Broumi et al [38][39][40] first introduced a technique of finding SP under SV-trapezoidal and triangular fuzzy neutrosophic environment. In [41], the authors proposed another approach to solve SPP on a network using trapezoidal neutrosophic numbers.…”

Section: Introduction and Review Of The Literaturementioning

confidence: 99%

Shortest path problem using Bellman algorithm under neutrosophic environment

Dey¹,

Talea

Bakali

et al. 2019

Complex Intell. Syst.

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An elongation of the single-valued neutrosophic set is an interval-valued neutrosophic set. It has been demonstrated to deal indeterminacy in a decision-making problem. Real-world problems have some kind of uncertainty in nature and among them; one of the influential problems is solving the shortest path problem (SPP) in interconnections. In this contribution, we consider SPP through Bellman's algorithm for a network using interval-valued neutrosophic numbers (IVNNs). We proposed a novel algorithm to obtain the neutrosophic shortest path between each pair of nodes. Length of all the edges is accredited an IVNN. Moreover, for the validation of the proposed algorithm, a numerical example has been offered. Also, a comparative analysis has been done with the existing methods which exhibit the advantages of the new algorithm.Publisher's Note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

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“…A new theory is developed and called single valued neutrosophic graph theory (SVNGT) by applying the concept of single valued neutrosophic sets on graph theory. The concept of SVNGT and their extensions finds its applications in diverse fields [6][7][8][9][10][11][12][13][14][15][16][17][18][19]. To search the minimum spanning tree in neutrosophic environment recently few researchers have used neutrosophic methods.…”

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 on single valued neutrosophic graphs

Cited by 49 publications

References 31 publications

The shortest path problem in interval valued trapezoidal and triangular neutrosophic environment

The shortest path problem in interval valued trapezoidal and triangular neutrosophic environment

Shortest path problem using Bellman algorithm under neutrosophic environment

Bipolar Neutrosophic Minimum Spanning Tree

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