Study On Single Valued Neutrosophic Graph With Application In Shortest Path Problem

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Study on single-valued neutrosophic graph with application in shortest path problem

Author : Ruxiang Liu
Publisher : Infinite Study
Page : 6 pages
File Size : 41,9 Mb
Release : 2024-06-30
Category : Mathematics
ISBN : 8210379456XXX

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Study on single-valued neutrosophic graph with application in shortest path problem by Ruxiang Liu Pdf

This study introduces some new concepts of single-valued neutrosophic graph (SVNG). The authors have discussed the definition of regular SVNG, complete SVNG and strong SVNG. The shortest path problem is a well-known combinatorial optimisation problem in the field of graph theory due to its various applications. Uncertainty is present in almost every application of shortest path problem which makes it very hard to decide the edge weight properly.

Shortest Path Problem on Single Valued Neutrosophic Graphs

Author : Said Broumi, Mohamed Talea,Assia Bakali,Florentin Smarandache,Kishore Kumar P.K.
Publisher : Infinite Study
Page : 6 pages
File Size : 50,6 Mb
Release : 2024-06-30
Category : Electronic
ISBN : 8210379456XXX

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Shortest Path Problem on Single Valued Neutrosophic Graphs by Said Broumi, Mohamed Talea,Assia Bakali,Florentin Smarandache,Kishore Kumar P.K. Pdf

A single valued neutrosophic graph is a generalized structure of fuzzy graph, intuitionistic fuzzy graph that gives more precision, flexibility and compatibility to a system when compared with systems that are designed using fuzzy graphs and intuitionistic fuzzy graphs.

Shortest Path Problem Under Interval Valued Neutrosophic Setting

Author : Said Broumi,Assia Bakali,Mohamed Talea,Florentin Smarandache,P. Krishnan Kishore,Rıdvan Şahin
Publisher : Infinite Study
Page : 7 pages
File Size : 41,9 Mb
Release : 2024-06-30
Category : Mathematics
ISBN : 8210379456XXX

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Shortest Path Problem Under Interval Valued Neutrosophic Setting by Said Broumi,Assia Bakali,Mohamed Talea,Florentin Smarandache,P. Krishnan Kishore,Rıdvan Şahin Pdf

This paper presents a study of neutrosophic shortest path with interval valued neutrosophic number on a network. A proposed algorithm also gives the shortest path length using ranking function from source node to destination node. Here each arc length is assigned to interval valued neutrosophic number. Finally, a numerical example has been provided for illustrating the proposed approach.

Operations on single valued neutrosophic graphs with application

Author : Sumera Naz ,Hossein Rashmanlou,M. Aslam Malika
Publisher : Infinite Study
Page : 15 pages
File Size : 40,5 Mb
Release : 2024-06-30
Category : Mathematics
ISBN : 8210379456XXX

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Operations on single valued neutrosophic graphs with application by Sumera Naz ,Hossein Rashmanlou,M. Aslam Malika Pdf

The concepts of graph theory are applied in many areas of computer science including image segmentation, data mining, clustering, image capturing and networking. Fuzzy graph theory is successfully used in many problems, to handle the uncertainty that occurs in graph theory. A single valued neutrosophic graph (SVNG) is an instance of a neutrosophic graph and a generalization of the fuzzy graph, intuitionistic fuzzy graph, and interval-valued intuitionistic fuzzy graph. In this paper, the basic operations on SVNGs such as direct product, Cartesian product, semi-strong product, strong product, lexicographic product, union, ring sum and join are defined. Moreover, the degree of a vertex in SVNGs formed by these operations in terms of the degree of vertices in the given SVNGs in some particular cases are determined. Finally, an application of single valued neutrosophic digraph (SVNDG) in traval time is provided.

Interval Valued Neutrosophic Shortest Path Problem by A* Algorithm

Author : S. Krishna Prabha,Said Broumi,Florentin Smarandache
Publisher : Infinite Study
Page : 9 pages
File Size : 46,9 Mb
Release : 2020-10-01
Category : Mathematics
ISBN : 8210379456XXX

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Interval Valued Neutrosophic Shortest Path Problem by A* Algorithm by S. Krishna Prabha,Said Broumi,Florentin Smarandache Pdf

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.

Research on the Shortest Path Solution Method of Interval Valued Neutrosophic Graphs Based on the Ant Colony Algorithm

Author : Lehua Yang,Dongmei Li,Ruipu Tan
Publisher : Infinite Study
Page : 17 pages
File Size : 53,6 Mb
Release : 2024-06-30
Category : Mathematics
ISBN : 8210379456XXX

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Research on the Shortest Path Solution Method of Interval Valued Neutrosophic Graphs Based on the Ant Colony Algorithm by Lehua Yang,Dongmei Li,Ruipu Tan Pdf

The shortest path problem (SPP) is considerably important in several fields. After typhoons, the resulting damage leads to uncertainty regarding the path weight that can be expressed accurately. A neutrosophic set is a collection of the truth membership, indeterminacy membership, and falsity membership degrees of the elements. In an uncertain environment, neutrosophic numbers can express the edge distance more effectively.

Shortest path on interval-valued nether trapezoidal neutrosophic fuzzy graphs

Author : K. Kalaiarasi,R. Divya
Publisher : Infinite Study
Page : 5 pages
File Size : 51,5 Mb
Release : 2024-06-30
Category : Mathematics
ISBN : 8210379456XXX

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Shortest path on interval-valued nether trapezoidal neutrosophic fuzzy graphs by K. Kalaiarasi,R. Divya Pdf

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.

Shortest path problem using Bellman algorithm under neutrosophic environment

Author : Said Broumi ,Arindam Dey,Mohamed Talea,Assia Bakali,Florentin Smarandache,Deivanayagampillai Nagarajan, Malayalan Lathamaheswari,Ranjan Kumar
Publisher : Infinite Study
Page : 8 pages
File Size : 54,5 Mb
Release : 2024-06-30
Category : Mathematics
ISBN : 8210379456XXX

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Shortest path problem using Bellman algorithm under neutrosophic environment by Said Broumi ,Arindam Dey,Mohamed Talea,Assia Bakali,Florentin Smarandache,Deivanayagampillai Nagarajan, Malayalan Lathamaheswari,Ranjan Kumar Pdf

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.

Certain Single-Valued Neutrosophic Graphs with Application

Author : Muhammad Akram , Saba Siddique
Publisher : Infinite Study
Page : 17 pages
File Size : 43,6 Mb
Release : 2024-06-30
Category : Electronic
ISBN : 8210379456XXX

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Certain Single-Valued Neutrosophic Graphs with Application by Muhammad Akram , Saba Siddique Pdf

In this research paper, we present certain types of single-valued neutrosophic graphs, including edge regular single-valued neutrosophic graphs and totally edge regular single-valued neutrosophic graphs. We investigate some of their related properties. We describe an application of single-valued neutrosophic graph in decision making process and present the procedure of our method that is used in our application in an algorithm.

Constant single valued neutrosophic graphs with applications

Author : Naeem Jan,Lemnaouar Zedam,Tahir Mahmood,Kifayat Ullah,Said Broumi,Florentin Smarandache
Publisher : Infinite Study
Page : 13 pages
File Size : 50,5 Mb
Release : 2024-06-30
Category : Mathematics
ISBN : 8210379456XXX

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Constant single valued neutrosophic graphs with applications by Naeem Jan,Lemnaouar Zedam,Tahir Mahmood,Kifayat Ullah,Said Broumi,Florentin Smarandache Pdf

In this paper, we introduced a new concept of single valued neutrosophic graph (SVNG) known as constant single valued neutrosophic graph (CSVNG). Basically, SVNG is a generalization of intuitionistic fuzzy graph (IFG). More specifically, we described and explored somegraph theoretic ideas related to the introduced concepts of CSVNG. An application of CSVNG in a Wi-Fi network system is discussed and a comparison of CSVNG with constant IFG is established showing the worth of the proposed work. Further, several terms like constant function and totally constant function are investigated in the frame-work of CSVNG and their characteristics are studied.

Shortest Path Problem Under Triangular Fuzzy Neutrosophic Information

Author : Said Broumi ,Assia Bakali,Mohamed Talea ,Florentin Smarandache
Publisher : Infinite Study
Page : 6 pages
File Size : 41,6 Mb
Release : 2024-06-30
Category : Electronic
ISBN : 8210379456XXX

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Shortest Path Problem Under Triangular Fuzzy Neutrosophic Information by Said Broumi ,Assia Bakali,Mohamed Talea ,Florentin Smarandache Pdf

In this paper, we develop a new approach to deal with neutrosphic shortest path problem in a network in which each edge weight (or length) is represented as triangular fuzzy neutrosophic number.

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

Author : Said Broumi, Deivanayagampillai Nagarajan,Assia Bakali, Mohamed Talea,Florentin Smarandache,Malayalan Lathamaheswari
Publisher : Infinite Study
Page : 14 pages
File Size : 50,8 Mb
Release : 2024-06-30
Category : Mathematics
ISBN : 8210379456XXX

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The shortest path problem in interval valued trapezoidal and triangular neutrosophic environment by Said Broumi, Deivanayagampillai Nagarajan,Assia Bakali, Mohamed Talea,Florentin Smarandache,Malayalan Lathamaheswari Pdf

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.

Neutrosophic Shortest Path Problem

Author : Ranjan Kumar,S A Edaltpanah,Sripati Jha,Said Broumi,Arindam Dey
Publisher : Infinite Study
Page : 11 pages
File Size : 41,7 Mb
Release : 2024-06-30
Category : Mathematics
ISBN : 8210379456XXX

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Neutrosophic Shortest Path Problem by Ranjan Kumar,S A Edaltpanah,Sripati Jha,Said Broumi,Arindam Dey Pdf

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.

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

Author : Lehua Yang ,Dongmei Li ,Ruipu Tan
Publisher : Infinite Study
Page : 22 pages
File Size : 55,5 Mb
Release : 2024-06-30
Category : Mathematics
ISBN : 8210379456XXX

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Shortest Path Solution of Trapezoidal Fuzzy Neutrosophic Graph Based on Circle‐Breaking Algorithm by Lehua Yang ,Dongmei Li ,Ruipu Tan Pdf

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.

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

Author : Lehua Yang,Dongmei Li,Ruipu Tan
Publisher : Infinite Study
Page : 22 pages
File Size : 48,5 Mb
Release : 2024-06-30
Category : Mathematics
ISBN : 8210379456XXX

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Shortest Path Solution of Trapezoidal Fuzzy Neutrosophic Graph Based on Circle-Breaking Algorithm by Lehua Yang,Dongmei Li,Ruipu Tan Pdf

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.