Solving intuitionistic fuzzy transportation problem using linear programming

Abstract

The real life transportation problems (TP) face a lot of problems due to uncertainties and lack of precise data. The present paper focuses on the two methods for solving intuitionistic fuzzy TP. One of the methods uses intuitionistic fuzzy programming technique together with the three different membership functions—linear, exponential and hyperbolic and the other method uses crisp linear programming taking intuitionistic fuzzy data in both the methods for the cost objective functions in the TP. The first method uses the membership and non-membership degrees separately to find the crisp solution using the fuzzy programming technique and then the optimal solution is calculated in terms of intuitionistic fuzzy data with the help of defined cost membership functions using the different membership functions. The satisfaction degree is then calculated to check the better solution. The second method directly solves the TP to find crisp solution considering a single objective function. The cost objective function is taken as intuitionistic fuzzy data and the methods have been used as such for the first time. A large scale real life intuitionistic TP has been solved using the two methods. The results obtained for different membership functions have been compared.