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Author: Said Broumi
Publisher: Infinite Study
Published:
Total Pages: 5
ISBN-13:
DOWNLOAD EBOOK →The selection of shortest path problem is one the classic problems in graph theory. In literature, many algorithms have been developed to provide a solution for shortest path problem in a network.
Author: Said Broumi
Publisher: Infinite Study
Published:
Total Pages: 8
ISBN-13:
DOWNLOAD EBOOK →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.
Author: Ranjan Kumar
Publisher: Infinite Study
Published:
Total Pages: 11
ISBN-13:
DOWNLOAD EBOOK →Neutrosophic set theory provides a new tool to handle the uncertainties in shortest path problem (SPP). This paper introduces the SPP from a source node to a destination node on a neutrosophic graph in which a positive neutrosophic number is assigned to each edge as its edge cost. We define this problem as neutrosophic shortest path problem (NSSPP). A simple algorithm is also introduced to solve the NSSPP. The proposed algorithm finds the neutrosophic shortest path (NSSP) and its corresponding neutrosophic shortest path length (NSSPL) between source node and destination node.
Author: S. Krishna Prabha
Publisher: Infinite Study
Published: 2020-10-01
Total Pages: 9
ISBN-13:
DOWNLOAD EBOOK →Many researchers have been proposing various algorithms to unravel different types of fuzzy shortest path problems. There are many algorithms like Dijkstra’s, Bellman-Ford,Floyd-Warshall and kruskal’s etc. are existing for solving the shortest path problems. In this work a shortest path problem with interval valued neutrosophic numbers is investigated using the proposed algorithm. A* algorithm is extensively applied in pathfinding and graph traversal.Unlike the other algorithms mentioned above, A* algorithm entails heuristic function to uncover the cost of path that traverses through the particular state. In the structured work A* algorithm is applied to unravel the length of the shortest path by utilizing ranking function from the source node to the destination node. A* algorithm is executed by applying best first search with the help of this search, it greedily decides which vertex to investigate subsequently. A* is equally complete and optimal if an acceptable heuristic is concerned. The arc lengths in interval valued neutrosophic numbers are defuzzified using the score function. A numerical example is used to illustrate the proposed approach.
Author: Lehua Yang
Publisher: Infinite Study
Published:
Total Pages: 22
ISBN-13:
DOWNLOAD EBOOK →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.
Author: Lehua Yang
Publisher: Infinite Study
Published:
Total Pages: 22
ISBN-13:
DOWNLOAD EBOOK →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.
Author: Said Broumi
Publisher: Infinite Study
Published:
Total Pages: 14
ISBN-13:
DOWNLOAD EBOOK →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.
Author: Siddhartha Sankar Biswas
Publisher: Infinite Study
Published:
Total Pages: 12
ISBN-13:
DOWNLOAD EBOOK →One of the important non-linear data structures in Computer Science is graph. Most of the real life network, be it a road transportation network, or airlines network or a communication network etc., cannot be exactly transformed into a graph model, but into a Multigraphs model. The Multigraph is a topological generalization of the graph where multiple links (or edges/arcs) mayexist between two nodes unlike in graph.
Author: K. Kalaiarasi
Publisher: Infinite Study
Published:
Total Pages: 5
ISBN-13:
DOWNLOAD EBOOK →The concept of this research is introduced to interval-valued trapezoidal neutrosophic fuzzy graph which is combined to trapezoidal fuzzy numbers and interval-valued neutrosophic fuzzy graph. In this analysis, proposed algorithm finds source node and destination node because of the shortest path problem. In this research, we apply trapezoidal number with interval-valued neutrosophic fuzzy graph and finding their score function. Eventually an illustrative example to explain, to easy way of shortest path fuzzy graph.
Author: K. Kalaiarasi
Publisher: Infinite Study
Published:
Total Pages: 14
ISBN-13:
DOWNLOAD EBOOK →In this article, inaugurate interval-valued triangular neutrosophic fuzzy graph (IVTNFG) of SPP, which is drew on three-sided numbers and IVTNFG. Hear a genuine application is given an illustrative model for IVTNFG. Additionally Shortest way is determined for this model. This present Dijkstra's Algorithm briefest way was checked through Python Jupiter Notebook (adaptation) programming.
