## Fuzzy Hungarian MODI Algorithm to Solve Fully Fuzzy Transportation Problems

Publisher : International Journal of Fuzzy Systems

Source : International Journal of Fuzzy Systems, Springer Berlin Heidelberg, Volume 19, Number 5, p.1479-1491 (2017)

Keywords : Fuzzy arithmetic operations, Fuzzy numbers, Fuzzy optimal solutions, Fuzzy rules, Fuzzy sets, Fuzzy systems, Fuzzy transportation problem, Optimal systems, Transportation, Transportation routes, Trapezoidal fuzzy numbers, Triangular fuzzy numbers

Campus : Coimbatore

School : School of Engineering

Department : Mathematics

Year : 2017

Abstract : In this paper, a new method is proposed to solve fully fuzzy transportation problems using the approach of the Hungarian and MODI algorithm. The objective of the proposed algorithm, namely, fuzzy Hungarian MODI algorithm, is to obtain the solution of fully fuzzy transportation problems involving triangular and trapezoidal fuzzy numbers. The introduced method together with Yager’s ranking technique gives the optimal solution of the problem. It also satisfies the conditions of optimality, feasibility, and positive allocation of cells using the elementwise subtraction of fuzzy numbers. A comparative study of the proposed method with existing procedure reveals that the solution of the proposed method satisfies the necessary conditions of a Transportation Problem (TP) to be an optimal solution in which the other methods do not guarantee. The proposed method is the extension of the Hungarian MODI method with fuzzy values. It is easy to understand and implement, as it follows the standard steps of the regular transportation problems. The method can be extended to other kinds of fuzzy transportation problems, such as unbalanced fuzzy TP, fuzzy degeneracy problem, fuzzy TP with prohibited routes, and many more. © 2016, Taiwan Fuzzy Systems Association and Springer-Verlag Berlin Heidelberg.

Cite this Research Publication : S. Dhanasekar, Hariharan, S., and Sekar, P., “Fuzzy Hungarian MODI Algorithm to Solve Fully Fuzzy Transportation Problems”, International Journal of Fuzzy Systems, vol. 19, pp. 1479-1491, 2017.