A New Method for Solving Interval Neutrosophic Linear Programming Problems

Year 2020, Volume: 33 Issue: 4, 796 - 808, 01.12.2020

Amirhossein Nafeı , Wenjun Yuan , Hadi Nasserı

https://doi.org/10.35378/gujs.689125

Cited By: 8

Abstract

Neutrosophic set theory is a generalization of the intuitionistic fuzzy set which can be considered as a powerful tool to express the indeterminacy and inconsistent information that exist commonly in engineering applications and real meaningful science activities. In this paper an interval neutrosophic linear programming (INLP) model will be presented, where its parameters are represented by triangular interval neutrosophic numbers (TINNs) and call it INLP problem. Afterward, by using a ranking function we present a technique to convert the INLP problem into a crisp model and then solve it by standard methods.

Keywords

Neutrosophic set, Neutrosophic numbers, Linear programming, Ranking function, Interval values

References

• [1] Akyar,E.,Akyar,H., Düzce, S. A., “A new method for ranking triangular fuzzy numbers”, International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, 20(05):729-740, (2012).
• [2] Allahviranloo, T., Lotfi, F. H., Kiasary, M. K. , Kiani, N. A. & Alizadeh, L., “Solving fully fuzzy linear programming problem by the ranking function”, Applied mathematical sciences, 2(1): 19-32, (2008).
• [3] Atanassov,K., “Intuitionistic fuzzy sets. Fuzzy Sets and Systems”, 20: 87–96, (1986).
• [4] K.Atanassov,K., Gargov,G., “Interval-valued intuitionistic fuzzy sets”, Fuzzy Sets and Systems, 31(3), 343–349, (1989).
• [5] Buckley,J.J., Feuring,T.,“Evolutionary algorithm solution to fuzzy problems: fuzzy linear programming”, Fuzzy sets and systems, 109(1): 35-53, (2000).
• [6] Deli, I., Şubaş, S.,“A ranking method of single valued neutrosophic numbers and its applications to multi-attribute decision making problems”, International Journal of Machine Learning and Cybernetics, 8(4):1309-1322,(2017).
• [7] Dubey,D., Mehra,A., “Linear programming with triangular intuitionistic fuzzy number”, (Published Conference Proceedings style),” 7th Annu. European Society for Fuzzy Logic and Technology, 563-569, Atlantis Press.
• [8] Hashemi,S.M., Modarres,M., Nasrabadi, E., & Nasrabadi, M. M., “Fully fuzzified linear programming, solution and duality”, Journal of Intelligent & Fuzzy Systems, 17(3):253-261, (2006).
• [9] Kivija¨rvi,H., Korhonen,P., Wallenius,J., “Operations research and its practice in Finland”, Interfaces, 16:53–59, (1986).
• [10] Kumar,A., Kaur,J., Singh,P., “A new method for solving fully fuzzy linear programming problems”, Applied mathematical modelling, 35(2):817-823, (2011).
• [11] Lilien,G. L., “MS/OR: a mid-life crisis”, Interfaces, 17:35–38, (1987).
• [12] Mohamed,M., AbdelBasset,M., Zaied,A.N., & Smarandache,F., “Neutrosophic integer programming problem”, Neutrosophic sets and systems,15:3–7, (2017). [13] Nafei,A., Yuan,W., Nasseri, H., “Group multi-attribute decision making based on interval neutrosophic sets”, Studies in Informatics and Control, 28(3):309-316, (2019).
• [14] Selhausen, H. M. Z.,“Repositioning OR’s products in the market”, Interfaces, 19:79–87, (1989).
• [15] Smarandache, F., “ A generalization of the intuitionistic fuzzy set,” International journal of Pure and Applied Mathematics”, 24: 287-297, (2005).
• [16] F. Smarandache, F., “A geometric interpretation of the neutrosophic set-A generalization of the intuitionistic fuzzy set,” arXiv preprint math/0404520.
• [17] S¸ubas¸,Y., “Neutrosophic numbers and their application to Multi-attribute decision making problems,” (In Turkish) (Masters Thesis, Kilis 7 Aralık University, Graduate School of Natural and Applied Science)
• [18] Tingley, G.A.,“ Can MS/OR sell itself well enough?”, Interfaces, 17: 41–52, (1987).
• [19] Wang, H., Smarandache, F., Zhang,Y.Q., & Sunderraman,R., “Interval neutrosophic sets and logic: Theory and applications in computing,” Hexis, Phoenix, AZ, (2005).
• [20] Wang, H., Smarandache, F., Zhang,Y. Q., & Sunderraman, R.,“ Single valued neutrosophic sets”, Multispace and Multistructure, infinite study.
• [21] Wang, Y. M., Elhag, T. M., “A fuzzy group decision making approach for bridge risk assessment”, Computers & Industrial Engineering,53(1): 137-148, (2007).
• [22] Zadeh,L.A., “Fuzzy sets,” Information and control, 8(3):38-353, (1965).
• [23] Zadeh,L.A., “The concept of a linguistic variable and its application to approximate reasoning—I”, Information sciences, 8(3): 199-249, (1975).