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**Contents:**

Despite this, we need to deal inexplicit parameters such as scope, costs, time and requirements in real-world problems. For example, a substantial length of any road is permanent; still, traveling time along the road varies according to weather and traffic conditions. An uncertain fact of those cases directs us to adopt fuzzy logic, fuzzy numbers, intuitionistic fuzzy and so on.

Das and De [ 29 ] employed Bellman dynamic programming problem for solving FSP based on value and ambiguity of trapezoidal intuitionistic fuzzy numbers. De and Bhincher [ 30 ] have studied the FSP in a network under triangular fuzzy number TFN and trapezoidal fuzzy number TpFN using two approaches such as influential programming of Bellman and linear programming with multi-objective. Kumar et al. Based on traditional Dijkstra algorithm, Enayattabar et al. Dey et al.

But, if the indeterminate information has appeared, all these kinds of shortest path problems failed. For this reason, some new approaches have been developed using neutrosophic numbers. Then neutrosophic shortest path was first developed by Broumi et al. The authors in [ 36 ] constructed an extension of Dijkstra algorithm to solve neutrosophic SPP.

Proposed maximizing deviation method with partial weight in a decision-making problem under the neutrosophic environment. IVN interval-valued neutrosophic, PA proposed algorithm. Based on the idea discussed in [ 15 ], we use an addition operation for adding the IVNNs corresponding to the edge weights present in the path.

It is used to find the path length between source and destination nodes. We also use a ranking method to choose the shortest path associated with the lowest value of rank. The remaining part of the paper is presented as follows. The next section contains a few of the ideas and theories as overview of interval neutrosophic set followed by which the Bellman algorithm is discussed.

In the subsequent section, an analytical illustration is presented, where our algorithm is applied. Then contingent study has been done with existing methods. Before the concluding section, advantages of the proposed algorithm are presented. Finally, conclusive observations are given. As we have difficulty of applying NSs to real-time issues, Wang et al. Now we consider a few mathematical operations on interval-valued neutrosophic numbers IVNNs s. In the posterior section, we present a simple illustration to show the brevity of our method.

PDF | This book is organized into seven chapters. Chapter one is introductory in content. The notion of neutrosophic set linear algebras and neutrosophic. The notion of neutrosophic set linear algebras and neutrosophic neutrosophic set linear algebras are introduced and their properties analysed.

This part is based on a numerical problem adapted from [ 43 ] to show the potential application of the proposed algorithm. The details of edge information in terms of interval-valued neutrosophic numbers. The details of deneutrosophication value of edge i, j. Comparison of the sequence of nodes using neutrosophic shortest path and our proposed algorithm. Neutrosophic shortest path with interval-valued neutrosophic numbers [ 43 ]. From the result, it is shown that the introduced algorithm contributes sequence of visited nodes which shown to be similar to neutrosophic shortest path presented in [ 43 ].

From here we come to the conclusion that there exists no unique method for comparing neutrosophic numbers and different methods may satisfy different desirable criteria.

Slow response will be observed when there is a change in the network as this change will spread node-by-node. We use a numerical example to illustrate the efficiency of our proposed algorithm.

The proposed algorithm is very effective for real-life problem. In this paper, we have used a simple numerical example to illustrate our proposed algorithm. Therefore, as future work, we need to consider a large-scale practical shortest path problem using our proposed algorithm and to compare our proposed algorithm with the existing algorithm in terms of strictness of optimality, efficiency, computational time, and other aspects.

Skip to main content Skip to sections. Advertisement Hide. Download PDF. Shortest path problem using Bellman algorithm under neutrosophic environment. Open Access.

Lec 10 - MIT 18.06 Linear Algebra, Spring 2005

First Online: 05 April Introduction and review of the literature A tool which represents the partnership or relationship function is called a Fuzzy Set FS and handles the real-world problems in which generally some type of uncertainty exists [ 1 ]. Broumi et al. In [ 41 ], the authors proposed another approach to solve SPP on a network using trapezoidal neutrosophic numbers.

In another paper, Broumi et al. Liu and You proposed interval neutrosophic Muirhead mean operators and their applications in multiple-attribute group decision-making [ 45 ]. Thus, several papers are published in the field of neutrosophic sets [ 46 , 47 , 48 , 49 , 50 , 51 , 52 , 53 , 54 , 55 ]. This algorithm is not applied yet on neutrosophic network. Author and references Year Contribution Broumi et al.

The main motivation of this study is to introduce an algorithmic approach for SPP in an uncertain environment which will be simple enough and effective in real-life problem.

The main contributions of this paper are as follows. Using the Bellman powerful programming system, the shortest path can be determined by forward pass computation method. Neutrosophic Bellmanâ€”Ford algorithm: Open image in new window. Open image in new window. In this section, the analysis of contingency for the proposed algorithm with existing approaches has been analyzed. Advantages By correlating our PA with Broumi et al.

This approach can be easily extended and applied to other neutrosophic networks with the edge weight as 1. Single-value neutrosophic numbers. If node failure occurs then routing loops may exist.

Zadeh LA Fuzzy sets. Atanassov KT Intuitionistic fuzzy sets. Yager RR Generalized orthopair fuzzy sets. Collectanea Mathematica. Commentarii Mathematici Helvetici. Communications in Advanced Mathematical Sciences.

Communications in Combinatorics and Optimization. Communications in Contemporary Mathematics. Compositio Mathematica.

Vasantha Kandasamy, K. And numerous neutrosophic applications in various fields, such as: multi-criteria decision making, image segmentation, medical diagnosis, fault diagnosis, clustering data, neutrosophic probability, human resource management, strategic planning, forecasting model, multi-granulation, supplier selection problems, typhoon disaster evaluation, skin lesson detection, mining algorithm for big data analysis, etc. November Kavitha; P. Feldman 1 , C. This chapter gives over examples and thirty theorems. To be in the right place at the left time!

Comptes Rendus Mathematique. Computational Methods and Function Theory. Confluentes Mathematici. Contributions to Game Theory and Management. A Mathematical Journal. Demonstratio Mathematica. Dependence Modeling. Dhaka University Journal of Science. Differentsial'nye Uravneniya.

Discussiones Mathematicae - General Algebra and Applications. Diskretnaya Matematika. Dnipropetrovsk University Mathematics Bulletin. Doklady Akademii Nauk.

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