Volume 1 , Issue 1 , PP: 40-51, 2020 | Cite this article as | XML | Html | PDF | Full Length Article
Avishek Chakraborty 1 *
Pentagonal neutrosophic number is an extended version of a single typed neutrosophic number. Real-humankind problems have different sorts of ambiguity in nature and among them; one of the important problems is solving the networking problem. In this contribution, the conception of pentagonal neutrosophic number has been focused on a distinct framework of reference. Here, we develop a new score function and its estimation has been formulated from different perspectives. Further, a time computing-based networking problem is considered herein the pentagonal neutrosophic arena and solved it using an influx of dissimilar logical & innovative thinking. Lastly, the computation of the total completion time of the problem reflects the impotency of this noble work.
Pentagonal neutrosophic number , Networking problem , Score function
[1] Zadeh L.A; (1965); Fuzzy sets. Information and Control, 8(5): 338- 353.
[2] Atanassov K.;(1986); Intuitionistic fuzzy sets. Fuzzy Sets and Systems 20: 87-96.
[3] Yen, K. K.; Ghoshray, S.; Roig, G.; (1999); A linear regression model using triangular fuzzy
number coefficients, fuzzy sets and system, doi: 10.1016/S0165-0114(97)00269-8.
[4] Abbasbandy, S. and Hajjari, T.; (2009); A new approach for ranking of trapezoidal fuzzy numbers; Computers and Mathematics with Applications, 57(3), 413-419.
[5] A.Chakraborty, S.P Mondal, A.Ahmadian, N.Senu, D.Dey, S.Alam, S.Salahshour; (2019); “The Pentagonal Fuzzy Number: Its Different Representations, Properties, Ranking, Defuzzification and Application in Game Problem”, Symmetry, Vol-11(2), 248; doi: 10.3390/sym11020248.
[6] A.Chakraborty, S. Maity, S.Jain, S.P Mondal, S.Alam; (2020); “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.
[7] Liu F, Yuan XH; (2007); Fuzzy number intuitionistic fuzzy set. Fuzzy Systems and Mathematics, 21(1): 88-91.
[8] Ye J.; (2014); prioritized aggregation operators of trapezoidal intuitionistic fuzzy sets and their application to multi criteria decision making, Neural Computing and Applications, 25(6): 1447-1454.
[9] Smarandache, F. A unifying field in logics neutrosophy: neutrosophic probability, set and logic.American Research Press, Rehoboth. 1998.
[10] H. Wang, F. Smarandache, Q. Zhang and R. Sunderraman; (2010); Single valued neutrosophic sets, Multispace and Multistructure 4 ;410–413.
[11] A.Chakraborty, S.P Mondal, A.Ahmadian, N.Senu,S.Alam and S.Salahshour; (2018); Different Forms of Triangular Neutrosophic Numbers, De-Neutrosophication Techniques, and their Applications, Symmetry, Vol-10, 327.
[12] A. Chakraborty, S. P Mondal, S.Alam, A. Mahata; (2019); 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.
[13] S. Maity, A.Chakraborty, S.K De, S.P.Mondal, S.Alam; (2019); A comprehensive study of a backlogging EOQ model with nonlinear heptagonal dense fuzzy environment,Rairo Operations Research; DOI: 10.1051/ro/2018114.
[14] P. Bosc and O. Pivert; (2013); On a fuzzy bipolar relational algebra,Information Sciences 219, 1–16.
[15] K.M. Lee;( 2000); Bipolar-valued fuzzy sets and their operations,Proc IntConf on Intelligent Technologies, Bangkok, Thailand , pp. 307–312.
[16] M.K. Kang & J.G. Kang; (2012); Bipolar fuzzy set theory applied to sub-semigroups with operators in semigroups, J KoreanSoc Math EducSer B Pure Appl Math 19(1),23–35.
[17] I. Deli, M. Ali and F. Smarandache;(2015); Bipolar Neutrosophic Sets and Their Application Based on Multi-CriteriaDecision Making Problems, Proceedings of the 2015 InternationalConference on Advanced Mechatronic Systems,Beijing, China.
[18] S. Broumi, A. Bakali, M. Talea, F. Smarandache and M. Ali; (2016); Shortest path problem under bipolar neutrosphic setting, Applied Mechanics and Materials 859, 59–66.
[19] M. Ali & F. Smarandache;(2016); Complex neutrosophic set, Neural Computing and Applications 25,1–18.
[20] A. Chakraborty, S. P Mondal, S. Alam ,A. Ahmadian, N. Senu, D. De and S. Salahshour; (2019); Disjunctive Representation of Triangular Bipolar Neutrosophic Numbers, De-Bipolarization Technique and Application in Multi-Criteria Decision-Making Problems, Symmetry, Vol-11(7), 932.
[21] Le Wang, Hong-yu Zhang, Jian-qiang Wang; (2016) ; Frank Choquet Bonferroni Mean Operators of BipolarNeutrosophic Sets and Their Application to Multi-criteria Decision-Making Problems Harish Garg, A novel accuracy function under interval-valued Pythagorean fuzzy environment for solving multicriteria decision making problem, Journal of Intelligent & Fuzzy Systems 31;529–540, Int. J. Fuzzy Syst.DOI 10.1007/s40815-017-0373-3.
[22] Vakkas Ulucay,Irfan Deli, Mehmet Sahin, Similarity measures of bipolar neutrosophic setsand their application to multiple criteria decision making, Neural Comput&Applic DOI 10.1007/s00521-016-2479-1.
[23] M. Aslam, S. Abdullah and K. Ullah; (2013); Bipolar Fuzzy Soft Sets And Its Applications in Decision Making Problem,arXiv:1303.6932v1 [cs. AI] 23.
[24] Le Wang,Hong-yu Zhang,Jian-qiang Wang, Frank Choquet Bonferroni Mean Operators of BipolarNeutrosophic Sets and Their Application to Multi-criteria Decision-Making Problems, Int. J. Fuzzy Syst. DOI 10.1007/s40815-017-0373-
[25] M. Ali, L. Hoang Son, I. Deli & N. Dang Tien; (2017); Bipolar neutrosophic soft sets and applications in decision making, Journal of Intelligent & Fuzzy Systems 33;4077–4087.
[26] S. Broumi, A. Bakali, M. Talea, Prem Kumar Singh, F. Smarandache;( 2019); Energy and Spectrum Analysis of Interval-valued Neutrosophic graph Using MATLAB, Neutrosophic Set and Systems, vol. 24, pp. 46-60.
[27] P. K. Singh, Interval-valued neutrosophic graph representation of concept lattice and its (α, β, γ)-decomposition, Arabian Journal for Science and Engineering, Year 2018, Vol. 43, Issue 2, pp. 723-74
[28] S. Broumi, F. Smarandache, M. Talea and A. Bakali. An Introduction to Bipolar Single Valued Neutrosophic Graph Theory. Applied Mechanics and Materials, vol.841,2016, 184 -191.
[29] S. Broumi, M. Talea, A. Bakali, F. Smarandache. Single Valued Neutrosophic, Journal of New Theory. N 10. 2016, pp. 86-101.
[30] S. Broumi, M.Talea A.Bakali, F.Smarandache. On Bipolar Single Valued Neutrosophic Graphs. Journal of Net Theory. N11, 2016, pp. 84-102.
[31] A.Kaur and A.Kumar, “A new approach for solving fuzzy transportation problems using generalized trapezoidal fuzzy numbers,” Applied soft computing, vol.12, no.3, pp.1201-1213, 2012.
[32] M. Mullai & S. Broumi;(2018); Neutrosophic Inventory Model without Shortages, Asian Journal of Mathematics and Computer Research, 23(4): 214-219.
[33] Yang, P., & Wee, H.,Economic ordering policy of deteriorated item for vendor and buyer: an integrated approach. Production Planning and Control, 11, 2000,474 -480.
[34] Abdel-Basset, M., Mohamed, R., Zaied, A. E. N. H., &Smarandache, F. (2019). A Hybrid Plithogenic DecisionMaking Approach with Quality Function Deployment for Selecting Supply Chain Sustainability Metrics. Symmetry, 11(7), 903.
[35] A.Chakraborty; (2019); Minimal Spanning Tree in Cylindrical Single-Valued Neutrosophic Arena; Neutrosophic Graph theory and algorithm; DOI-10.4018/978-1-7998-1313-2.ch009.
[36] A. Chakraborty, S. P Mondal, S.Alam, A. Mahata; (2020); “Cylindrical Neutrosophic Single-Valued Numberand its Application in Networking problem, Multi Criterion Decision Making Problem and Graph Theory”; CAAI Transactions on Intelligence Technology; Accepted in 2020.
[37] R.Helen and G.Uma;(2015); A new operation and ranking on pentagon fuzzy numbers, Int Jr.of Mathematical Sciences & Applications, Vol. 5, No. 2, pp 341-346.
[38] M.S. Annie Christi, B. Kasthuri; (2016); Transportation Problem with Pentagonal Intuitionistic Fuzzy Numbers Solved Using Ranking Technique and Russell’s Method; Int. Journal of Engineering Research and Applications; ISSN: 2248-9622, Vol. 6, Issue 2, pp.82-86.
[39] A. Chakraborty, S. Broumi, P.K Singh;(2019); Some properties of Pentagonal Neutrosophic Numbers and its Applications in Transportation Problem Environment, Neutrosophic Sets and Systems, vol.28, pp.200-215.
[40] A. Chakraborty, S. Mondal, S. Broumi; (2019); 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.
[41] Ye, J. (2014). Single valued neutrosophic minimum spanning tree and its clustering method. . J. Intell.Syst. , 311–324 .
[42] Mandal, K., & Basu, K. (2016). Improved similarity measure in neutrosophic environment and its application in finding minimum spanning tree. . J. Intell. Fuzzy Syst. , 1721-1730.
[43] Mullai, M., Broumi, S., & Stephen, A. (2017). Shortest path problem by minimal spanning tree algorithm using bipolar neutrosophic numbers. . Int. J. Math. Trends Technol. , 80-87.
[44] Broumi, S., Talea, M., Smarandache, F., & Bakali, A. (2016). Single valued neutrosophic graphs:degree, order and size. . IEEE International Conference on Fuzzy Systems, (pp. 2444-2451).
[45] Broumi, S., Bakali, A., Talea, M., Smarandache, F., & Vladareanu, L. (2016). Applying Dijkstra algorithm for solving neutrosophic shortest path problem. Proceedings on the International Conference onAdvanced Mechatronic Systems. Melbourne, Australia.
[46] Mahata A., Mondal S.P, Alam S, Chakraborty A., Goswami A., Dey S., Mathematical model for diabetes in fuzzy environment and stability analysis- Journal of of intelligent and Fuzzy System, doi: https://doi.org/10.3233/JIFS-171571.
[47] Abdel-Basset, M., Nabeeh, N. A., El-Ghareeb, H. A., &Aboelfetouh, A. (2019). Utilizing neutrosophic theory to solve transition difficulties of IoT-based enterprises. Enterprise Information Systems, 1-21.
