Applying Dijkstra algorithm for solving neutrosophic shortest path problem

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. One of common algorithms in solving shortest path problem is Dijkstra's algorithm. In this paper, Dijkstra's algorithm has been redesigned to handle the case in which most of parameters of a network are uncertain and given in terms of neutrosophic numbers. Finally, a numerical example is given to explain the proposed algorithm.

[1]  A. Thamaraiselvi,et al.  A New Approach for Optimization of Real Life Transportation Problem in Neutrosophic Environment , 2016 .

[2]  Amit Kumar,et al.  Algorithms for some Fuzzy Network Problems using Ranking Function , 2009 .

[3]  Florentin Smarandache,et al.  On Bipolar Single Valued Neutrosophic Graphs , 2016 .

[4]  Amit Kumar,et al.  Solution of Fuzzy Maximal Flow Problems Using Fuzzy Linear Programming , 2011 .

[5]  Krassimir T. Atanassov,et al.  Intuitionistic fuzzy sets , 1986 .

[6]  Anita Pal,et al.  Shortest Path Problem on Intuitionistic Fuzzy Network , 2013 .

[7]  F. Smarandache,et al.  Shortest Path Problem Under Interval Valued Neutrosophic Setting , 2018 .

[8]  F. Smarandache,et al.  SINGLE VALUED NEUTROSOPHIC GRAPHS , 2016 .

[9]  Paramasivam Jayagowri,et al.  Using Trapezoidal Intuitionistic Fuzzy Number to Find Optimized Path in a Network , 2014, Adv. Fuzzy Syst..

[10]  Manjot Kaur,et al.  A New Algorithm for Solving Shortest Path Problem on a Network with Imprecise Edge Weight , 2011 .

[11]  Florentin Smarandache,et al.  Symbolic Neutrosophic Theory , 2015, ArXiv.

[12]  Florentin Smarandache,et al.  Single valued neutrosophic graphs: Degree, order and size , 2016, 2016 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE).

[13]  F. Smarandache,et al.  Isolated Single Valued Neutrosophic Graphs , 2016 .

[14]  I. Turksen.  Interval valued fuzzy sets based on normal forms , 1986 .

[15]  F. Smarandache,et al.  An Introduction to Bipolar Single Valued Neutrosophic Graph Theory , 2016 .

[16]  Peide Liu,et al.  An Extended TOPSIS Method for the Multiple Attribute Decision Making Problems Based on Interval Neutrosophic Set , 2014 .

[17]  F. Smarandache,et al.  Interval Valued Neutrosophic Graphs , 2016 .

[18]  Rajshekhar Sunderraman,et al.  Single Valued Neutrosophic Sets , 2010 .

[19]  Robert LIN,et al.  NOTE ON FUZZY SETS , 2014 .

[20]  Edsger W. Dijkstra,et al.  A note on two problems in connexion with graphs , 1959, Numerische Mathematik.

[21]  Mitsuo Gen,et al.  Fuzzy shortest path problem , 1994 .