Zero-Point Maximum Allocation Method for Solving Intuitionistic Fuzzy Transportation problem
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Zero-Point Maximum Allocation Method for Solving Intuitionistic Fuzzy Transportation problem Kamini1 · M. K. Sharma1 © Springer Nature India Private Limited 2020
Abstract 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). Keywords Fuzzy transportation problem (FTP) · Intuitionistic fuzzy transportation problem (IFTP) · Triangular intuitionistic fuzzy number (TIFN) · Zero-point allocation method Mathematics Subject Classification 90C70
Introduction Fuzzy transportation problem (FTP) received most concentration in research from a long time. This is most important optimization and decision-making problem in fuzzy environment. The basic TP was developed by “Hitchcock” [1] in 1941. It is a special type linear programming problem in which single commodity is transported from many sources to many destinations at the minimum transportation cost to satisfy total demand and supply restrictions. In real life situations; the given information is not precise. There is uncertainty in given problem. So, to
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M. K. Sharma [email protected]
Department of Mathematics, Ch. Charan Singh University, Meerut, U.P. 250004, India 0123456789().: V,-vol
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Int. J. Appl. Comput. Math
(2020) 6:115
deal these situations, fuzzy theory is applied in decision making. Thus, fuzzy set theory is an important tool to deal these imprecise situations. In 1965, Zadeh [2] gave the concept of fuzzy logic and in 1970 Bellman and Zadeh [3] used fuzzy set theory in decision making. Zadeh [4] in 1975 gave an approximate reasoning using the fuzzy logic. A FTP is the problem in which supply, demand and cost are in the form of fuzzy parameters. In 1982, Oheigeartaigh [6] gave an algorithm to solve the FTP. Zimmerman [5] gave the optimal solution of FTP by fuzzy linear programming approach. In 1986, Atanassov [8] introduced the concept of intuitionistic fuzzy sets (IFSs) which is most useful to deal with vagueness. IFSs are dif
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