500 396
Full Length Article
International Journal of Neutrosophic Science
Volume 11 , Issue 1, PP: 53-61 , 2020 | Cite this article as | XML | Html |PDF

Title

Interval Valued Neutrosophic Shortest Path Problem by A* Algorithm

Authors Names :   S.Krishna Prabha   1     Said Broumi   2     Florentin Smarandache   3  

1  Affiliation :  Department of Mathematics, PSNA College of Engineering and Technology, Dindigul-624622, Tamilnadu, India

    Email :  jvprbh1@gmail.com


2  Affiliation :  Laboratory of Information Processing, Faculty of Science Ben M’Sik, University Hassan II, Casablanca, Morocco

    Email :  broumisaid78@gmail.com


3  Affiliation :  Dept. Math and Sciences, University of New Mexico, Gallup, NM, USA

    Email :  smarand@unm.edu



Doi   :   https://doi.org/10.54216/IJNS.0110104

Received: Jun 09, 2020 Accepted: September 03, 2020

Abstract :

 

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.

 

Keywords :

Heuristic function , Interval Valued Neutrosophic Graph , Score Function , Shortest Path Problem. Destination node , Source node.

References :

[1]   L.Zadeh, “Fuzzy sets”, Inform and Control, 8, 338-353, 1965.

[2]   H. J. Zimmermann, “Fuzzy set Theory - and Its Applications”, Kluwer-Nijhoff Publishing, Boston-Dordrecht-Lancaster, 1985.

[3]   Florentin Smarandache, “Neutrosophic Overset, Neutrosophic Underset, and Neutrosophic Offset”. Similarly for Neutrosophic Over-/Under-/Off- Logic, Probability, and Statistics, 168 p., Pons Editions, Bruxelles, Belgique.2016.

[4]   S.Broumi, A.Bakali, M.Talea, F.Smarandache, “On Bipolar Single Valued Neutrosophic Graphs”, Journal of New Theory, N11, pp.84-102,2016.

[5]   S.Broumi, A,Bakali,  M.Talea,  F.Smarandache , “ Single Valued Neutrosophic Graphs”, Journal of New Theory, N 10, pp. 86-101,2016.

[6]   S.Broumi, A. Bakali, M.Talea, F.Smarandache, “Single Valued Neutrosophic Graphs: Degree, Order and Size”, IEEE International Conference on Fuzzy Systems (FUZZ), pp.2444-2451,2016. 

[7]   S.Broumi, A,Bakali,  M.Talea,  F.Smarandache , L.Vladareanu, “Computation of Shortest Path Problem in a Network with SV-Trapezoidal Neutrosophic Numbers”, Proceedings of the 2016 International Conference on Advanced Mechatronic Systems, Melbourne, Australia, pp.417-422,2016.

[8]   A.Ngoor and M.Jabarulla , “Multiple labeling Approach For Finding shortest Path with Intuitionstic Fuzzy Arc Length”, InternationalJournal of  Scientific and Engineering Research,V3,Issue  11,pp.102- 106,2012.

[9]   A.Kumar and M.Kaur, “Solution of fuzzy maximal flow problems using fuzzy linear programming”,World Academy of Science and Technology.87,28-31,2011.

[10] Gaurav, & Kumar, Megha & Bhutani, Kanika & Aggarwal, Swati, “Hybrid model for medical diagnosis using Neutrosophic Cognitive Maps with Genetic Algorithms”. 1-7. 10.1109/FUZZ-IEEE.2015.7338015,2015.

[11] G.Kumar, R.K.Bajaj and N.Gandotra, “Algoritm for shortest path problem in a network with interval valued intuitionstic trapezoidal fuzzy number”, Procedia Computer Science, 70, pp.123-129, 2015.

[12] P.Jayagowri and G.Geetha Ramani, “Using Trapezoidal Intuitionistic Fuzzy Number to Find Optimized Path in a Network”, Advances in Fuzzy Systems., Article ID 183607, 6 pages http://dx.doi.org/10.1155/2014/183607,2014.

[13] S.Broumi, A,Bakali,  M.Talea,  F.Smarandache and L.Vladareanu, “Applying Dijkstra  for Solving Neutrosophic Shortest Path Problem”, Proceedings of the 2016 International Conference on Advanced Mechatronic Systems, Melbourne, Australia, pp.412-416,2016.

[14] S.Broumi, F.Smarandache, “New distance and similarity measures of interval neutrosophic sets, Information Fusion (FUSION)”, IEEE 17th International Conference, pp 1 – 7,2014.

[15] S.Broumi, M.Talea, A.Bakali, F.Smarandache, “An Introduction to Bipolar Single Valued Neutrosophic Graph Theory”. Applied Mechanics and Materials, vol.841, 184-191.2016. 

[16] S.Broumi, M.Talea, A.Bakali, F.Smarandache , K. P.Kishore,Şahin, “ Shortest Path Problem under Interval Valued Neutrosophic Setting”, International Journal of Advanced Trends in Computer Science and Engineering, volume 8,pg216-222,2019.

[17] S.Broumi, A.Bakali, M.Talea, F.Smarandache, “Isolated Single Valued Neutrosophic Graphs”. Neutrosophic Sets and Systems, Vol. 11, pp.74-78, 2016.

[18] S.Broumi, A.Bakali, M.Talea, F.Smarandache, “Interval Valued Neutrosophic Graphs”, Critical Review, XII,  pp.5-33, 2016.

[19] F.Smarandache,“Types of Neutrosophic Graphs and neutrosophic AlgebraicStructures together with their Applications in Technology”, seminar, Universitatea Transilvania din Brasov, Facultatea de Design de Produs si Mediu, Brasov, Romania .2015.

[20] Avishek Chakraborty, “A New Score Function of Pentagonal Neutrosophic Number and its Application in Networking Problem”,International Journal of Neutrosophic Science, Volume 1, Issue 1, PP: 40-51, 2020.

[21] R.Thamaraiselvi and R. Santhi, “A New Approach for Optimization of Real Life Transportation Problems in Neutrosophic Environment”, Mathematical Problems in Enginering.Article ID 5950747,9http://dx.doi.org/10.1155/2016/5950747,2016.

[22] Tuhin Bera, Nirmal Kumar Mahapatra, “An Approach to Solve the Linear Programming Problem Using Single Valued Trapezoidal Neutrosophic Number”, International Journal of Neutrosophic Science ,Vol. 3, No. 2, PP. 54-66, 2020.

[23] Sapan Kumar Das, S.A. Edalatpanah, “ A new ranking function of triangular neutrosophic number and its application in integer programming”, International Journal of Neutrosophic Science,Volume 4 , Issue 2, PP: 82-92 , 2020.

[24]                  S.A.Edalatpanah, “A Direct Model for Triangular Neutrosophic Linear Programming”, International Journal of Neutrosophic ScienceVolume 1 , Issue 1, PP: 19-28 , 2020.

[25] S.Majumdar and A.Pal, “Shortest Path Problem on Intuitionistic Fuzzy Network”, Annals of Pure and Applied Mathematics, Vol. 5, 1, 26-36, 2013.

Bhimraj Basumatary, Said Broumi, “Interval-Valued Triangular Neutrosophic Linear Programming Problem”, International Journal of Neutrosophic Science, Volume 10, Issue 2, PP: 105-115, 2020


Cite this Article as :
S.Krishna Prabha , Said Broumi , Florentin Smarandache, Interval Valued Neutrosophic Shortest Path Problem by A* Algorithm, International Journal of Neutrosophic Science, Vol. 11 , No. 1 , (2020) : 53-61 (Doi   :  https://doi.org/10.54216/IJNS.0110104)