The shortest path problem in the Knödel graph

Grigoryan, Hayk; Harutyunyan, Hovhannes A.

doi:10.1016/j.jda.2014.11.008

Cited by 7 publications

(7 citation statements)

References 23 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Gabrel and Murat [17] presented different models, methods and principle for the stability of the SPP. Grigoryan and Harutyunyan [18] proposed SPP in the Knodel graph. Rostami et al [19] proposed quadratic SPP.…”

Section: Literature Of Reviewmentioning

confidence: 99%

“…Find the score function of every arc length for the given network using Eqs. (18), (19) and (24), (25).…”

Section: Algorithm: a New Approach To Find Spp Using Tpivnn And Tivnnmentioning

confidence: 99%

“…Dubois and Prade solved fuzzy shortest path problem for the first time. The most crucial combinatorial optimization problem is to find the SP to the directed graph and its primary format unable to represent the situations where the value of the detached function should be found not only by the preference of each single arc [15][16][17][18][19].…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

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

Nagarajan

Bakali

Talea

et al. 2019

Complex Intell. Syst.

View full text Add to dashboard Cite

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.

show abstract

Section: Literature Of Reviewmentioning

confidence: 99%

“…Find the score function of every arc length for the given network using Eqs. (18), (19) and (24), (25).…”

Section: Algorithm: a New Approach To Find Spp Using Tpivnn And Tivnnmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

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

Nagarajan

Bakali

Talea

et al. 2019

Complex Intell. Syst.

View full text Add to dashboard Cite

show abstract

“…Step 4: Because S( n p3 ) > S( n p4 ), n p3 > n p4 can be obtained according to Definition 7. Thus, by deleting the last edge, (3,5), in p 3 , the neutrosophic graph depicted in Figure 6 can (3,5), in p3, the neutrosophic graph depicted in Figure 6 can be obtained. Step 5: Another closed circle ②④⑥⑤② in Figure 6 is identified, such that paths Step 5: Another closed circle 2 4 6 5 2 in Figure 6 is identified, such that paths p 5 = (2, 4), (4,6) and p 6 = (2, 5), (5, 6) make up a closed circle, as indicated by the thick lines in Figure 7.…”

Section: S( N P1mentioning

confidence: 99%

“…The key problem of combinatorial optimization is to determine the shortest path of the digraph. Its main format cannot express the situation when the value of the separation function is found based on the preference of each individual arc [3][4][5]. Samarandache first described the theory of Chinese Intelligence in 1995 and proposed an important mathematical mechanism referred to as the theory of the neutrosophic set (NS) to deal with various inaccuracy, uncertainty, and inconsistency problems.…”

Section: Introductionmentioning

confidence: 99%

Shortest Path Solution of Trapezoidal Fuzzy Neutrosophic Graph Based on Circle-Breaking Algorithm

Yang

Tan

2020

Symmetry

View full text Add to dashboard Cite

The shortest path problem is a topic of increasing interest in various scientific fields. The damage to roads and bridges caused by disasters makes traffic routes that can be accurately expressed become indeterminate. A neutrosophic set is a collection of the truth membership, indeterminacy membership, and falsity membership of the constituent elements. It has a symmetric form and indeterminacy membership is their axis of symmetry. In uncertain environments, the neutrosophic number can more effectively express the edge distance. The objectives in this study are to solve the shortest path problem of the neutrosophic graph with an edge distance expressed using trapezoidal fuzzy neutrosophic numbers (TrFNN) and resolve the edge distance according to the score and exact functions based on the TrFNN. Accordingly, the use of a circle-breaking algorithm is proposed to solve the shortest path problem and estimate the shortest distance. The feasibility of this method is verified based on two examples, and the rationality and effectiveness of the approach are evaluated by comparing it with the Dijkstra and Bellman algorithms.

show abstract

A new construction of broadcast graphs

Harutyunyan

2020

Discrete Applied Mathematics

View full text Add to dashboard Cite

The shortest path problem in the Knödel graph

Cited by 7 publications

References 23 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 Solution of Trapezoidal Fuzzy Neutrosophic Graph Based on Circle-Breaking Algorithm

A new construction of broadcast graphs

Contact Info

Product

Resources

About