Dijkstra’s Algorithm for Solving the Shortest Path Problem on Networks Under Intuitionistic Fuzzy Environment

Mukherjee, Sampad

doi:10.1007/s10852-012-9191-7

Cited by 31 publications

(18 citation statements)

References 53 publications

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“…Driving distance refers to the shortest distance between parking lot's entrance and the parking space, and we use the Dijkstra algorithm to determine the driving distance. Edsgar Wybe Dijkstra, a Dutch computer scientist, put forward Dijkstra algorithm in 1959, it computes the shortest path from a vertex to other vertex [3]. The main idea of this algorithm is as follows:…”

Section: Driving Distancementioning

confidence: 99%

Parking Lot Optimal Routing Based on Grey Entropy Relation Grade Multi-Attribute Decision Making

Zhang¹,

Wuchen²,

Li³

et al. 2015

IJSH

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By analyzing the drivers' main consideration about how to choose a parking space, this paper is committed to path optimization of parking lot by grey entropy relation grade multi-attribute decision making. The decision attribute matrix is identified by driving distance which is deduced through Dijkstra algorithm, walking distance deduced through Euclidean distance and parking space environment value deduced through the expectation of triangular fuzzy number. Finally, an example would be analyzed to verify the feasibility of the method.

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Section: Driving Distancementioning

confidence: 99%

Parking Lot Optimal Routing Based on Grey Entropy Relation Grade Multi-Attribute Decision Making

Zhang¹,

Wuchen²,

Li³

et al. 2015

IJSH

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“…So far, we have discussed the concepts of FGs, IVFGs, IFGs, and IVIFGs. These structures have been extensively applied to many problems such as cluster analysis, optimization of networks, decision making (DM), algorithms, and shortest path problem . In DM, using a graphical approach and aggregation techniques, we get an optimal solution, whereas in the shortest path problem, we find a shortest path in a network from the starting node to the final node.…”

Section: Introductionmentioning

confidence: 99%

“…These structures have been extensively applied to many problems such as cluster analysis, 29,30 optimization of networks, 31 decision making (DM), 32,33 algorithms, 34 and shortest path problem. [35][36][37] In DM, using a graphical approach and aggregation techniques, we get an optimal solution, whereas in the shortest path problem, we find a shortest path in a network from the starting node to the final node.Recent developments in FSs have shown some good improvements, among which the concept of Pythagorean fuzzy set (PyFS) 38 is a prominent one. A PyFS improves the concept of IFSs by enlarging its domain.…”

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confidence: 99%

An approach towards decision making and shortest path problems using the concepts of interval‐valued Pythagorean fuzzy information

et al. 2019

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A pythagorean fuzzy set is a generalized fuzzy structure that copes with imprecisions of real life accurately and with a larger domain. The aim of this manuscript is to develop the notion of graph for newly established concept of interval‐valued Pythagorean fuzzy set. We introduced the concept of interval‐valued Pythagorean fuzzy graph (IVPyFG) and discussed its related ideas with the help of examples. The significance of using interval‐valued fuzzy concepts over non‐interval‐valued fuzzy concepts are demonstrated numerically. Further, the advantages of using the new approach over the pre‐existing ideas are demonstrated with the help of numerical examples. The main goal of this article is to study three types of decision‐making problems using the framework of IVPyFGs. These three problems include the problem of selection of the best university in a network of universities, a supply chain management problem and the shortest path problem. The comparison of the new approach toward these problems with existing approaches is also established.

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“…Under IFS environment, some researchers pay more attention to solving SP problem with intuitionistic fuzzy arc costs. Mukherjee [9] considered the SP problem in an intuitionistic fuzzy environment. Geetharamani and Jayagowri [10] proposed a new algorithm to deal with the IFSP problem using intuitionistic fuzzy shortest path length procedure and similarity measure.…”

Section: Introductionmentioning

confidence: 99%

Dijkstra algorithm for shortest path problem under interval-valued Pythagorean fuzzy environment

Enayattabar

Ebrahimnejad

Motameni

2018

Complex Intell. Syst.

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Pythagorean fuzzy set as an extension of fuzzy set has been presented to handle the uncertainty in real-world decision-making problems. In this work, we formulate a shortest path (SP) problem in an interval-valued Pythagorean fuzzy environment. Here, the costs related to arcs are taken in the form of interval-valued Pythagorean fuzzy numbers (IVPFNs). The main contributions of this paper are fourfold: (1) the interval-valued Pythagorean fuzzy optimality conditions in directed networks are described to design of solution algorithm. (2) To do this, an improved score function is used to compare the costs between different paths with their arc costs represented by IVPFNs. (3) Based on these optimality conditions and the improved score function, the traditional Dijkstra algorithm is extended to find the cost of interval-valued Pythagorean fuzzy SP (IVPFSP) and corresponding IVPFSP. (4) Finally, a small sized telecommunication network is provided to illustrate the potential application of the proposed method.

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Dijkstra’s Algorithm for Solving the Shortest Path Problem on Networks Under Intuitionistic Fuzzy Environment

Cited by 31 publications

References 53 publications

Parking Lot Optimal Routing Based on Grey Entropy Relation Grade Multi-Attribute Decision Making

Parking Lot Optimal Routing Based on Grey Entropy Relation Grade Multi-Attribute Decision Making

An approach towards decision making and shortest path problems using the concepts of interval‐valued Pythagorean fuzzy information

Dijkstra algorithm for shortest path problem under interval-valued Pythagorean fuzzy environment

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