Journal of Mathematical Modelling and Algorithms

, Volume 11, Issue 4, pp 345–359

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

Article

Abstract

In this paper, a well known problem called the Shortest Path Problem (SPP) has been considered in an uncertain environment. The cost parameters for traveling each arc have been considered as Intuitionistic Fuzzy Numbers (IFNs) which are the more generalized form of fuzzy numbers involving a degree of acceptance and a degree of rejection. A heuristic methodology for solving the SPP has been developed, which aim to exploit tolerance for imprecision, uncertainty and partial truth to achieve tractability, robustness and low cost solution corresponding to the minimum-cost path or the shortest path. The Modified Intuitionistic Fuzzy Dijkstra’s Algorithm (MIFDA) has been proposed in this paper for solving Intuitionistic Fuzzy Shortest Path Problem (IFSPP) using the Intuitionistic Fuzzy Hybrid Geometric (IFHG) operator. A numerical example illustrates the effectiveness of the proposed method.

Keywords

Shortest path problem Intuitionistic fuzzy sets (IFSs) Intutionistic fuzzy value (IFV) Intuitionistic fuzzy numbers (IFNs) Intutionistic fuzzy hybrid geometric (IFHG) operator Decision making problem Dijkstra’s algorithm 

Mathematics Subject Classifications (2010)

05C85 05C22 05C30 90B10 68T20 68T30 68T37 03E72 47S40 90B50 

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Copyright information

© Springer Science+Business Media B.V. 2012

Authors and Affiliations

  1. 1.Bengal College of Engineering and TechnologyDurgapurIndia

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