440 215
Full Length Article
Volume 3 , Issue 1, PP: 21-28 , 2020

Title

Application of Pentagonal Neutrosophic Number in Shortest Path Problem

Authors Names :   Avishek Chakraborty   1 *  

1  Affiliation :  Department of Basic Science, Narula Institute of Technology, Agarpara, Kolkata-700109, India. Department of Mathematics, Indian Institute of Engineering Science and Technology, Shibpur, Howrah-711103, India.

    Email :  tirtha.avishek93@gmail.com



Doi   :  10.5281/zenodo.3732659


Abstract :

Real-human kind issues have distinct sort of ambiguity and among them; one of the critical troubles is solving the shortest path problem. In this contribution, we applied the developed score function and accuracy function of pentagonal neutrosophic number (PNN) into a shortage path selection problem. Further, a time dependent and heuristic cost function related shortest path algorithm is considered here in PNN area and solved it utilizing an influx of dissimilar rational & pioneer thinking. Lastly, estimation of total ideal time of the graph reflects the importance of this noble work.

 

Keywords :

PNN , Score and accuracy function , shortest path algorithm

References :

[1] L.A Zadeh “Fuzzy sets,” Information and Control”, 8(5): 338- 353; 1965. 

 

 [2] A.Chakraborty, S.P Mondal, A.Ahmadian, N.Senu, D.Dey, S.Alam, S.Salahshour; “The Pentagonal Fuzzy Number: Its Different Representations, Properties, Ranking, Defuzzification and Application in Game Problem,” Symmetry, Vol-11(2), 248; doi: 10.3390/sym11020248, 2019.

 

[3] A.Chakraborty, S. Maity, S.Jain, S.P Mondal, S.Alam “Hexagonal Fuzzy Number and its Distinctive Representation, Ranking, Defuzzification Technique and Application in Production Inventory Management Problem,” Granular Computing, Springer, DOI: 10.1007/s41066-020-00212-8, 2020.

 

[4] S. Maity, A.Chakraborty, S.K De, S.P.Mondal, S.Alam “A comprehensive study of a backlogging EOQ model with nonlinear heptagonal dense fuzzy environment”,Rairo Operations Research,” Vol-54 (1); pp-267-286  DOI: 10.1051/ro/2018114,201, 2020.

 

[5] K .Atanassov “Intuitionistic fuzzy sets,” Fuzzy Sets and Systems 20: 87-96, 1986.

 

[6] F. Smarandache, “A unifying field in logics neutrosophy: neutrosophic probability, set and logic,” American Research Press, Rehoboth. 1998.

 

[7] A.Chakraborty, S.P Mondal, A.Ahmadian, N.Senu, S.Alam and S.Salahshour “Different Forms of Triangular Neutrosophic Numbers, De-Neutrosophication Techniques, and their Applications,” Symmetry, Vol-10, 327, 2018.

 

[8] A. Chakraborty, S. P Mondal, S.Alam, A. Mahata “Different Linear and Non-linear Form of Trapezoidal Neutrosophic Numbers, De-Neutrosophication Techniques and its Application in Time-Cost Optimization Technique, Sequencing Problem,” Rairo Operations Research, doi: 10.1051/ro/2019090, 2019.

 

[9] A. Chakraborty, S. Broumi and P.K Singh “Some properties of Pentagonal Neutrosophic Numbers and its Applications  in  Transportation  Problem  Environment”,  Neutrosophic  Sets  and  Systems, vol.28, pp.200-215, 2019.

 

[10] A. Chakraborty, S. Mondal and S. Broumi “De-neutrosophication technique of pentagonal neutrosophic number and application in minimal spanning tree,” Neutrosophic Sets and Systems; vol. 29, pp. 1-18, doi: 10.5281/zenodo.3514383, 2019.

 

[11] A. Chakraborty, “A New Score Function of Pentagonal Neutrosophic Number and its Application in Networking Problem,” International Journal of Neutrosophic Science; Vol-1(1), p.p-35-46, 2020.

 

[12] A Chakraborty, B.Banik, S. P.Mondal, and S. Alam, “Arithmetic and Geometric Operators of Pentagonal Neutrosophic Number and its Application in Mobile Communication Based MCGDM Problem,” Neutrosophic Sets and System, Vol-32, P.p-61-79, 2020.

 

[13] A.Chakraborty “Minimal Spanning Tree in Cylindrical Single-Valued Neutrosophic Arena,” Neutrosophic Graph theory and algorithm,” DOI-10.4018/978-1-7998-1313-2.ch009, 2019.

 

[14] A. Chakraborty, S. P Mondal, S.Alam, A. Mahata “Cylindrical Neutrosophic Single-Valued Numberand its Application in Networking problem, Multi Criterion Decision Making Problem and Graph Theory,” CAAI Transactions on Intelligence Technology; DOI:  10.1049/trit.2019.0083, 2020.

 

[15] P. K. Singh, “Plithogenic set for multi-variable data analysis,” International Journal of Neutrosophic Science,Volume 1 , Issue 2, pp. 81-89 , 2020.

 

[16] E.O. Adeleke , A.A.A. Agboola , F. Smarandache, “Refined Neutrosophic Rings I,” International Journal of Neutrosophic Science, Volume 2 , Issue 2, pp. 77-81 , 2020.

 

[17] Madeleine Al- Tahan, “Some Results on Single Valued Neutrosophic (Weak) Polygroups,” International Journal of Neutrosophic Science,Volume 2 , Issue 1, pp. 38-46 , 2020.

 

[18] Philippe Schweizer, “Uncertainty: two probabilities for the three states of neutrosophy,” International Journal of Neutrosophic Science, Volume 2 , Issue 1, pp. 18-26 , 2020

 

[19] A. Chakraborty, S. P Mondal, S. Alam ,A. Ahmadian, N. Senu, D. De and S. Salahshour; “Disjunctive Representation of Triangular Bipolar Neutrosophic Numbers, De-Bipolarization Technique and Application in Multi-Criteria Decision-Making Problems,” Symmetry, Vol-11(7), 932, 2019. 

 

[20] S. Pal, A. Chakraborty “Triangular Neutrosophic-based EOQ model for non Instantaneous Deteriorating Item under Shortages,” American Journal of Business and Operations research; Vol-1(1), p.p-28-35, 2020.

 

[21] F. Smarandache “NeutroAlgebra is a Generalization of Partial Algebra”, International Journal of Neutrosophic Science,  Volume 2 , Issue 1, pp. 08-17 , 2020.

 

[22] K. K. Mandal, S. Chatterjee, A. Chakraborty, S. Mondal and S. Samanta “Applying Encryption Algorithm on Text Steganography Based on Number System”; Computational Advancement in Communication Circuits and Systems; pp-255-266, 2020.

 

[23] S. A. Edalatpanah, “A Direct Model for Triangular Neutrosophic Linear Programming”, International Journal of Neutrosophic Science, Volume 1, Issue 1, pp.19-28, 2020.

 

[24] P. Schweizer, “Neutrosophy for physiological data compression: in particular by neural nets usingdeeplearning”, International Journal of Neutrosophic Science, Volume 1, Issue 2, pp. 74-80, 2020.

 

[25] M. Parimala , M. Karthika , F. Smarandache , S. Broumi, “On αω-closed sets and its connectedness in terms of neutrosophic topological spaces”, International Journal of Neutrosophic Science,  Volume 2 , Issue 2, pp. 82-88 , 2020.

 

[26] R. Kumar, S. A. Edalatpanah, S. Jha, S. Broumi and A. Dey “Neutrosophic shortest path problems,” Neutrosophic Sets and Systems, vol. 23, pp. 5-15, 2018.

 

[27] R. Kumar, S A Edalatpanah, S. Jha, S. Broumi, R. Singh, and A. Dey “A multi objective programming approaches to solve integer valued neutrosophic shortest path problems,” Neutrosophic Sets and Systems, vol. 24, pp 134-149, 2019.

 

[28] R. Kumar, S. A. Edalatpanah, S. Jha and R Singh ,“A novel approach to solve Gaussian Valued Neutrosophic  Shortest Path Problems,” International Journal of Engineering and Advanced Technology,  Vol. 8 Issue 3, pp.347-353, 2019.

 

[29] R. Kumar, S. A. Edalatpanah, S. Jha, R Singh, Sripati and Gayen, Sudipta and Singh, Ramayan “Shortest Path Problems Using Fuzzy Weighted Arc Length,” International Journal of Innovative Technology and Exploring Engineering, Vol. 8 Issue 6, pp.724-731, 2019 .

 

[30] S.Broumi, A.Dey, M.Talea, A.Bakali, F.Smarandache, D.Nagarajan, M.Lathamaheswari and R. Kumar “Shortest Path Problem using Bellman Algorithm under Neutrosophic Environment,” Complex & Intelligent Systems ,pp-1-8, 2019.