Volume 10 , Issue 2 , PP: 105-115, 2020 | Cite this article as | XML | Html | PDF | Full Length Article
Bhimraj Basumatary 1 , Said Broumi 2
Doi: https://doi.org/10.54216/IJNS.0100204
In this paper, we have proposed an Interval-valued triangular neutrosophic number (IV-TNN) as a key factor to solve the neutrosophic linear programming problem. In the present neutrosophic linear programming problem IV-TNN is expressed in lower, upper truth membership function, indeterminacy membership function, and falsity membership function. Here, we try the compare our proposed method with existing methods.
  ,
Neutrosophic Set, Interval-valued triangular neutrosophic number, Neutrosophic Linear Programming Problem.
  ,
[1] L.A. Zadeh, Fuzzy Sets, Inform and Control 8, pp.338-353, 1965.
[2] L.A. Zadeh, “The concept of a linguistic variable and its application to approximate reasoning, Information Sciences, 8, pp.199-249, 1975.
[3] K.T. Atanassov, Intutionistic fuzzy sets, Fuzzy Sets Syst. 20, pp.87–96, 1986.
[4] K.T. Atanassov, Interval valued intuitionistic fuzzy sets, Fuzzy Sets Syst. 31, pp.343–349, 1989.
[5] D. Dubey and A. Mehra, Linear Programming with Triangular Intuitionistic Fuzzy Number. European Society for Fuzzy Logic and Technology, pp.563-569, 2011. https://doi.org/10.2991/eusflat.2011.78
[6] F.Smarandache, Neutrosophic set-a generalization of the intuitionistic fuzzy set,Inter- national Journal of Pure and Applied Mathematics, 24(3), 287–297, 2005.
[7] I. M. Hezam, M. Abdel-Baset, F. Smarandache. Taylor Series Approximation to Solve Neutrosophic Multiobjective Programming Problem. In: Neutrosophic Sets and Systems. An International Journal in Information Science and Engineering, Vol. 10,, pp. 39-45, 2015.
[8] N. El-Hefenawy, M. A. Metwally, Z. M. Ahmed, & El-Henawy, I. M. A Review on the Applications of Neutrosophic Sets. Journal of Computational and Theoretical Nanoscience, 13(1), pp. 936-944, 2016.
[9] M. Abdel-Baset, I. M. Hezam & F. Smarandache, Neutrosophic Goal Programming. In: Neutrosophic Sets & Systems, vol. 11, 2016.
[10] H. Wang, F. Smarandache, Y. Zhang, Sunderraman, R. Single valued neutrosophic sets. Multispace Multistruct. Neutrosophic Transdiscipl, 4, pp.410–413, 2010.
[11] J. Ye, ; F. Smarandache, Similarity measure of refined single-valued neutrosophic sets and its multicriteria decision making method. Neutrosophic Sets Syst, 12, pp.41–44, 2016
[12]J. Ye, Vector similarity measures of simplified neutrosophic sets and their application in multicriteria decision making. Int. J. Fuzzy Syst. 16, pp.204–211, 2014,
[13] P. Liu, The aggregation operators based on archimedean t-conorm and t-norm for single-valued neutrosophic numbers and their application to decision making. Int. J. Fuzzy Syst., 18, pp.849–863, 2016.
[14] J.Ye, Multicriteria decision-making method using the correlation coefficient under single-valued neutrosophic environment. Int. J. Gen. Syst, 42, pp.386–394, 2013
[15] Q. Hu, Zhang, X. New similarity measures of single-valued neutrosophic multisets based on the decomposition theorem and its application in medical diagnosis. Symmetry, 10, 466, 2018.
[16] J. Wang, ; Zhang, X. Two types of single-valued neutrosophic covering rough sets and an application to decision making. Symmetry, 10, 710, 2018.
[17 R.E.Bellman, L.A. Zadeh, Decision making in a fuzzy environment, Manag. Sci. 17,pp.141–164,1970.
[18]H.J. Zimmerman, Fuzzy programming and linear programming with several objective Functions, Fuzzy Sets Syst. 1, pp.45–55,1978
[19]H.Tanaka, K. Asai, A formulation of fuzzy linear programming based on coparison of fuzzy number, Control and Cybernet. 13, pp.185–194, 1984.
[20]L.Campos, J.L.Verdegay, Linear programming problems and ranking of fuzzy numbers, Fuzzy Sets Syst. 32,pp.1–11,1989.
[21]H.Rommelfanger, R. Hanuscheck, J. Wolf, Linear programming with fuzzy objective, Fuzzy Sets Syst. 29, pp.31-48, 1998.
[22]J. L. Verdegay, Using FuzzyNumbers in Linear Programming, System.Man.Cybernetics.PartB: Cybernetics.IEE E Transactions on . 27,pp. 1016-1022,1997.
[23] R. Parvati, C. Malathi, Intuitionistic fuzzy linear optimization, Notes on Intuitionistic Fuzzy Sets, 18, pp.48-56, 2012.
[24]S.K.Das, T. Mandal, &S.A. Edalatpanah,A mathematical model for solving fully fuzzy linear programming problem with trapezoidal fuzzy numbers. Applied intelligence, 46(3), pp.509-519, 2017.
[25]Abdel-Baset M, Hezam IM, Smarandache F., Neutrosophic goal programming, Neutrosophic Sets Syst 11, pp.112–118, 2016.
[26] Pramanik, S., Neutrosophic multi-objective linear programming.Global Journal of Engineering Science and Research Management, 3(8), pp.36-46,2016.
[27] A. Nafei, M. Arif, W. Yuan and H. Nasseri, A new method for solving interval neutrosophic linear programming problems, Easy Chair preprints(Acta Polytechnica Hungarica), No.- 2346, January 9, 2020
[28] Abdel-Baset M, Gunasekaran M, Mai M, Smarandache F , A novel method for solving the fully neutrosophic linear programming problems, Neural Computing and Application, 2018, doi.org/10.1007/s00521-018-3404-6
[29]Ye, J. (2014). Similarity measures between interval neutrosophic sets and their applications in multicriteria decision-making. Journal of Intelligent & Fuzzy Systems, 26(1), pp.165-172.
[30]Ji, P.,Wang, J. Q., & Zhang, H. Y., Frank prioritized Bonferroni mean operator with single-valued neutronsophic sets and its application in selecting third party logistics providers. Neural Computing and Applications, 30(3), pp799-823, 2018.
[31]S. Broumi, Assia Bakali, Mohamed Talea, Florentin Smarandache,K. P. Krishnan Kishore, Rıdvan Şahin, Shortest Path Problem under Interval Valued Neutrosophic Setting, International Journal of Advanced Trends in Computer Science and Engineering, Volume 8, No.1.1,pp.216-222, 2019.
[32]S. Broumi, A. Dey, M. Talea, A. Bakali, F. Smarandache, D. Nagarajan, M. Lathamaheswari and Ranjan Kumar, “Shortest Path Problem using Bellman Algorithm under Neutrosophic Environment,” Complex & Intelligent Systems ,pp-1-8, 2019. https://doi.org/10.1007/s40747-019-0101-8,
[33]H.Tanaka, K. Asai, A formulation of fuzzy linear programming based on comparison of fuzzy number, Control and Cybernet. 13, pp.185–194,1984.
[34]L.Campos ,J.L.Verdegay, Linear programming problems and ranking of fuzzy numbers, Fuzzy Sets Syst. 32,pp.1–11,1989.
[35] Abdel-Basset M, Mohamed M, Zhou Y, Hezam I.,Multi- criteria group decision making based on neutrosophic analytic hierarchy process. J Intell Fuzzy Syst 33(6),pp.4055–4066, 2017.
[36] M. Mohamed,M. Abdel-Basset, A. N. Zaied, F. Smarandache, Neutrosophic integer programming problem, Neutrosophic Sets Syst 15,pp.3–7, 2017. https://doi.org/10.5281/zenodo.570944.
[37]G. Nordo, A. Mehmood , Said Broumi; Single valued neutrosophic filter, International Journal of Neutrosophic Science, Vol.6, Issue-1, pp.8-21, 2020.
[38] S. K. Das , S.A. Edalatpanah, A new ranking function of triangular neutrosophic number and its application in integer programming, International Journal of Neutrosophic Science, Vol.6, Issue-2, pp.82-92, 2020.
[39] Khatter, K. Neutrosophic linear programming using possibilistic mean. Soft Comput, 2020. https://doi.org/10.1007/s00500-020-04980-y
[40] Bera, T., Mahapatra, N.K. Neutrosophic linear programming problem and its application to real life. Afr. Mat. 31, pp.709–726, 2020. https://doi.org/10.1007/s13370-019-00754-4
[41] Ye J., Neutrosophic number linear programming method and its application under neutrosophic number environments. Soft Comput 22(14), pp.4639–4646,2018.