Volume 4 , Issue 2, PP: 82-92 , 2020 | Cite this article as | XML | Html |PDF

1 **Affiliation :
**Department of Mathematics, National Institute of Technology, Jamshedpur, India

** Email : **cool.sapankumar@gmail.com

2 **Affiliation :
**Department of Applied Mathematics, Ayandegan Institute of Higher Education, Tonekabon, Iran

** Email : **saedalatpanah@gmail.com

**Abstract : **

Real humankind problems have different sorts of ambiguity in the creation, and amidst them, one of the significant issues in solving the integer linear programming issues. In this commitment, the conception of aggregation of ranking function has been focused on a distinct framework of reference. Here, we build up another framework for neutrosophic integer programming issues having triangular neutrosophic numbers by using the aggregate ranking function. To legitimize the proposed technique, scarcely numerical analyses are given to show the viability of the new model. At long last, conclusions are talked about.

**Keywords : **

Neutrosophic triangular numbers , integer programming , aggregate ranking function

**References : **

[1] L. A. Zadeh, Fuzzy Sets, Inf.and Cont.8, pp.338-353, 1965.

[2] N. Mahdavi-Amiri, S.H. Nasseri, Duality in fuzzy number linear programming by use of a certain linear ranking function, Appl.Math.Comp.180, pp.206-216, 2006.

[3] T. Allahviranloo, KH. Shamsolkotabi, N. A. Kiani and L. Alizadeh, Fuzzy integer linear programming problems, Int. J. Contemp. Math. Sciences, 2, pp.167 -181, 2007.

[4] Y. R. Fan,G. H. Huang, K. Huang, L. Jin, and M. Q. Suo, A generalized fuzzy integer programming approach for environment management under uncertainty, Mathematical Problems in engineering, pp.1-17, 2014.

[5] S. Das, T. Mandal, S. A. Edalatpanah, A mathematical model for solving fully fuzzy linear programming problem with trapezoidal fuzzy numbers, Applied Intelligence, 46, pp.509-519, 2016.

[6] S. Das, T. Mandal, S.A. Edalatpanah, A new method for solving linear fractional programming problem with absolute functions, International Journal of Operation Research, 36, pp.455-466, 2019.

[7] A. H. Nafei, S.H. Nasseri, A new approach for solving neutrosophic integer programming problems, International Journal of Applied Operational Research, 9, pp.1-9, 2019.

[8] S. Das, T. Mandal, Diptiranjan Behera, A new approach for solving fully fuzzy linear programming problem, International Journal of Mathematics in Operational Research, 15(3), pp.296-309, 2019.

[9] S. K. Das, T. Mandal, & S. A. Edalatpanah, Erratum to: A mathematical model for solving fully fuzzy linear programming problem with trapezoidal fuzzy numbers. Applied Intelligence, 46(3), pp.520-520, 2017.

[10] S. K. Das, T. Mandal, A new model for solving fuzzy linear fractional programming problem with ranking function. Journal of applied research on industrial engineering, 4(2), pp.89-96, 2017.

[11] S. K. Das, T. Mandal, A MOLFP Method for Solving Linear Fractional Programming under Fuzzy Environment. International Journal of Research in Industrial Engineering, 6(3), pp.202-213, 2017.

[12]S. K. Das, Modified method for solving fully fuzzy linear programming problem with triangular fuzzy numbers. International Journal of Research in Industrial Engineering, 6(4), pp.293-311, 2017.

[13] S. A. Edalatpanah, A nonlinear approach for neutrosophic linear programming. Journal of Applied Research on Industrial Engineering, 6(4), pp.367-373,2019.

[14] S. H. Najafi, S. A. Edalatpanah ,A note on “A new method for solving fully fuzzy linear programming problems”. Applied mathematical modelling, 37(14-15), pp.7865-7867, 2013.

[15] S. H. Najafi, S. A. Edalatpanah, & H. Dutta, A nonlinear model for fully fuzzy linear programming with fully unrestricted variables and parameters. Alexandria engineering journal, 55(3), pp.2589-2595, 2016.

[16] F. Smarandache, A unifying field in logics: Neutrosophic logic. neutrosophy, neutrosophic set, neutrosophic probability: Neutrosophic logic: neutrosophy, neutrosophic set, neutrosophic probability. Infinite Study, 2003.

[17] S .A. Edalatpanah, Neutrosophic perspective on DEA. Journal of Applied Research on Industrial Engineering, 5(4), pp.339-345, 2018.

[18] S. A. Edalatpanah & F. Smarandache, Data envelopment analysis for simplified neutrosophic sets. Neutrosophic Sets and Systems, 29, pp.215-226, 2019.

[19] S. A. Edalatpanah, Data envelopment analysis based on triangular neutrosophic numbers. CAAI Transactions on Intelligence Technology, 2020, Article DOI: 10.1049/trit.2020.0016.

[20] S. A. Edalatpanah, Neutrosophic structured element, Experty System, 2020, Article DOI: 10.1111/exsy.12542 .

[21] S. A. Edalatpanah, A Direct Model for Triangular Neutrosophic Linear Programming, International Journal of Neutrosophic Science, 1(1), pp.15-24, 2020.

[22] W. Yang, L. Cai, S, A. Edalatpanah, F. Smarandache, Triangular single valued neutrosophic data envelopment analysis: application to hospital performance measurement. Symmetry 2020, 12, 588.

[23] M. Abdel-Basset, M. Gunasekaran, M. Mohamed, F. Smarandache, A novel method for solving the fully neutrosophic linear programming problems. Neural Computi and Applications, 31(5), pp.1595-1605, 2019.

[24]S. Pramanik, S., & P.P., Dey, Bi-level linear programming problem with neutrosophic numbers. Neutrosophic Sets and Systems, 12, pp.110-121, 2018

[25] D. Banerjee, & S. Pramanik, Single-objective linear goal programming problem with neutrosophic numbers. Infinite Study,2018.

[26] I. Maiti, T. Mandal , S. Pramanik, Neutrosophic goal programming strategy for multi-level multi-objective linear programming problem. J Ambient Intell Humaniz Comput. 2019, Article DOI: 10.1007/s12652-019-01482-0

[27] S. Pramanik, & P.P., Dey, Multi-level linear programming problem with neutrosophic numbers: A goal programming strategy. Neutrosophic Sets & Systems, 29, pp.242-254, 2019.

[28] J.Ye, Neutrosophic number linear programming method and its application under neutrosophic number environments, Soft Computing, 22, pp.4639-4646, 2018.

[29] A. H. Hussian, M. Mohamed, M. Abdel-Baset and F. Smarandache, Neutrosophic Linear programming Problem, Mathematical Sciences Letters, 6, pp.1-5, 2017.

[30] H.J. Zimmerman, Fuzzy programming and linear programming with several objective Functions, Fuzzy Sets Syst. 1, pp.45–55, 1978.

[31] L.Campos, J.L.Verdegay, Linear programming problems and ranking of fuzzy numbers, Fuzzy Sets Syst. 32, pp.1–11, 1989.

[32] H. Rommelfanger, R. Hanuscheck, J. Wolf , Linear programming with fuzzy objective, Fuzzy Sets Syst. 29,pp.31-48, 1989.

[33] J. M. Cadenas, J. L. Verdegay, Using fuzzy numbers in linear programming, system.Man.Cybernetics.PartB: Cybernetics.IEEE Transactions on . 27,pp.1016-1022, 1997.

[34] J.J. Buckley, T. Feuring, Evolutionary algorithm solution to fuzzy problems: Fuzzy linear programming, Fuzzy Sets Syst. 109,pp.35-53, 2000.

[35] I.Ramik, M. Vlach, Fuzzy mathematical programming: a unified approach based on fuzzy relation.Fuzzy Optim. Decis. Mak. 1,pp.335–346, 2002.

[36] A.Kumar, J. Kaur , P. Singh, A new method for solving fully fuzzy linear programming problems, Appl. Math. Modell. 35, pp.817-823, 2011.

[37] S. A. Edalatpanah, & S. Shahabi. A new two-phase method for the fuzzy primal simplex algorithm. International Review of Pure and Applied Mathematics 8, pp.157-164, 2012.

[38] M. Dehghan, B. Hashemi, M. Ghatee, Computational methods for solving fully fuzzy linear systems, Appl. Math. Comput. 179, pp.328–343, 2006.

[39] F.H. Lotfi, T. Allahviranloo, M.A. Jondabeha, L. Alizadeh, Solving a fully fuzzy linear programming using lexicography method and fuzzy approximate solution, Appl. Math. Modell. 33, pp.3151–3156, 2009.

[40] K. T. Atanassov, Intuitionistic fuzzy sets, Fuzzy sets, 20,87-96, 1986.

[41] S. Broumi, A. Dey, M. Talea, A. Bakali, F. Smarandache, D. Nagarajan, R. Kumar, Shortest path problem using Bellman algorithm under neutrosophic environment. Complex & Intelligent Systems, 5(4), 409-416, 2019.

[42] SP.Wan, JY. Dong, Possibility linear programming with trapezoidal fuzzy numbers. Appl Math Model, 38, pp.1660-1672, 2014.

[43] S. Das, J. K. Dash , Modified solution for Neutrosophic Linear Programming Problems with mixed constraints. International Journal of Research in Industrial Engineering, 2020, Article DOI: 10.22105/riej.2020.224198.1127

[44] H. Wang, F. Smarandache, YQ Zhang, R. Sunderraman, Single valued neutrosophic sets, Multispace and Multistruct,4, pp.410-413, 2010.

[45] M. Abdel-Basset, I. M. Hezam, F. Smarandache, Neutrosophic goal programming, Neutrosophic Sets and Systems, 11, pp.25-34.

[46] J.J. Buckley, T. Feuring, Evolutionary algorithm solution to fuzzy problems: fuzzy linear programming, Fuzzy Sets and Systems, 109, pp.35-53, 2000.

[47] M. Mohamed, M. Abdel-Baset, A.N.H. Zaied and F. Smarandache, Neutrosophic Integer programming Problem, Neutrosophic Sets and Systems 15, pp. 3-7, 2017.

[48] A. Chakraborty, A new score function of pentagonal neutrosophic number and its application in networking problem, International Journal of Neutrosophic Sciences, 1, pp.40-51, 2020.

[49] S. Broumi, M.Talea, A. Bakali, F. Smarandache, D.Nagarajan, M. Lathamaheswari and M.Parimala, Shortest path problem in fuzzy, intuitionistic fuzzy and neutrosophic environment: an overview, Complex & Intelligent Systems, 5, pp.371–378, 2019, https://doi.org/10.1007/s40747-019-0098-z.

Sapan Kumar Das , S.A. Edalatpanah,