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Zero-point maximum allocation method for solving intuitionistic fuzzy transportation problem. (English) Zbl 1456.90029

Summary: Transportation problems (TP) can be solved by various methods when the parameters are in crisp nature. But when the parameters are vague in nature or have imperfect knowledge or have partial information then we have to use the fuzzy optimization. Sujatha et al. [Solving fuzzy transportation problem (FTP) using zero point maximum allocation method] proposed the procedure for fuzzy transportation problem (FTP) with parameters are in the form of trapezoidal fuzzy numbers. But fuzzy logic is not adequate to describe all the characteristics of the system. To describe all the properties of the system, we have to consider the membership as well as the non-membership including the hesitation part. In the present research paper, we have proposed the solution of the transportation problem (TP) in the form of intuitionistic fuzzy logic by using zero point maximum allocation method. By using this technique, we can observe that the method applied to solve the fuzzy transportation problem (FTP) gives the most suitable optimal solution. A numerical example has also been given to elaborate this technique to solve the intuitionistic fuzzy transportation problem (IFTP).

MSC:

90B06 Transportation, logistics and supply chain management
90C70 Fuzzy and other nonstochastic uncertainty mathematical programming
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[1] Hitchcock, FL, The distribution of product from several sources to numerous localities, MIT J. Math. Phys., 20, 224-230 (1941) · JFM 67.0528.04
[2] Zadeh, LA, Fuzzy sets, Inf. Control, 8, 338-353 (1965) · Zbl 0139.24606
[3] Bellman, R.; Zadeh, LA, Decision making in fuzzy environment, Manag. Sci., 17, B, 141-164 (1970) · Zbl 0224.90032
[4] Zadeh, LA, The concept of a linguistic variable and its application to approximate reasoning, Inf. Sci., 8, 3, 199-249 (1975) · Zbl 0397.68071
[5] Zimmermann, HJ, Fuzzy programming and linear programming with several objective functions, Fuzzy Sets Syst., 1, 45-55 (1978) · Zbl 0364.90065
[6] Oheigeartaigh, M., A fuzzy transportation algorithm, Fuzzy Sets Syst., 8, 235-243 (1982) · Zbl 0493.90058
[7] Atanassov, KT, Intuitionistic fuzzy sets, Fuzzy Sets Syst., 20, 1, 87-96 (1986) · Zbl 0631.03040
[8] Chiang, J., The optimal solution of the transportation problem with fuzzy demand and fuzzy product, J. Inf. Sci. Eng., 21, 451-493 (2005)
[9] Pandian, P.; Natarajan, G., A new algorithm for finding a fuzzy optimal solution for fuzzy transportation problems, Appl. Math. Sci., 4, 79-90 (2010) · Zbl 1192.90122
[10] Pandian, P.; Natarajan, G., An appropriate method for real life fuzzy transportation problems, Int. J. Inf. Sci. Appl., 3, 2, 127-134 (2011)
[11] Gani, AN; Abbas, S., Solving intuitionistic fuzzy transportation problem using zero suffix algorithm, Int. J. Math. Sci. Eng. Appl., 6, 3, 73-82 (2012)
[12] Rai, D.; Subramanian, N.; Mishra, VN, The generalised difference of \(\int\chi^{2 I }\) of fuzzy real number over \(p\)-metric spaces defined by Musielak Orlicz function, New Trend Math. Sci., 4, 3, 296-306 (2016)
[13] Gani, AN; Abbas, S., A new method on solving Intuitionistic fuzzy transportation problem, Ann Pure Appl Math, 15, 2, 163-171 (2017)
[14] Sujatha, L.; Vinothini, P.; Jothilakshmi, R., Solving fuzzy transportation problem using zero point maximum allocation method, Int. J. Curr. Adv. Res, 7, 173-178 (2018)
[15] Vandana, D.; Subramanian, M.; Mishra, VN, The intuitionistic triple \(\chi\) of fuzzy real number over \(p\)-metric spaces defined by Musielak Orlicz function, Asia Pac J. Math., 5, 1, 1-13 (2018) · Zbl 1415.40003
[16] Vandana, DR; Deepmala, MLN; Mishra, VN, Duality relations for a class of a Multiobjective fractional programming problem involving support functions, Am. J. Oper. Res., 8, 4, 294-311 (2018)
[17] Dubey, R.; Mishra, VN; Ali, R., Duality for unified higher-order minimax fractional programming with support function under type-I assumptions, Mathematics, 7, 11, 1034-1045 (2019)
[18] Dubey, R.; Deepmala, A.; Mishra, VN, Higher-order symmetric duality in non-differentiable Multiobjective fractional programming problem over cone constraints, Stat. Optim. Inf. Comput., 8, 187-205 (2020)
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