Properties of Interval-Valued Neutrosophic Graphs

et al. 2019

Complex Intell. Syst.

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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.

Section: Literature Of Reviewmentioning

confidence: 99%

“…This section is based on a numerical problem adapted from Broumi et al [40] to show the potential application of the proposed algorithm and score function.…”

Section: Illustrative Examplementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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

Nagarajan

et al. 2019

Complex Intell. Syst.

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“…Mehmet [18] put forward for analyzing the concept of the interval cut set (ICS) and strong ICS (α, β, γ) of IVNSs with proof and examples. Also, there are other several extensions of NSs described in the literature including intervalvalued bipolar neutrosophic sets [19], hesitant interval neutrosophic linguistic set [20], and interval neutrosophic hesitant fuzzy sets [21]; for more details of neutrosophic set and their extensions, we refer the reader to [22][23][24][25][26][27][28].…”

Section: Introduction and Review Of The Literaturementioning

confidence: 99%

Shortest path problem using Bellman algorithm under neutrosophic environment

Dey¹,

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.

“…Recently, Broumi et al [17][18][19][20][21][22] presented the concept of neutrosophic graphs, interval valued neutrosophic graphs and bipolar single valued neutrosophic graphs. To this day, only a few papers dealing with shortest path problem in neutrosophic environment.…”

Section: Introductionmentioning

confidence: 99%

Computation of shortest path problem in a network with SV-trapezoidal neutrosophic numbers

Smarandache

2016 International Conference on Advanced Mechatronic Systems (ICAMechS)

et al. 2016

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In this work, a neutrosophic network method is proposed for finding the shortest path length with single valued trapezoidal neutrosophic number. The proposed algorithm gives the shortest path length using score function from source node to destination node. Here the weights of the edges are considered to be single valued trapezoidal neutrosophic number. Finally, a numerical example is used to illustrate the efficiency of the proposed approach