A multi-item transportation problem with mode of transportation preference by MCDM method in interval type-2 fuzzy environment

In this paper, we employ all the parameters as trapezoidal interval type-2 fuzzy numbers to cope with ambiguity and vagueness problem. There are two issues being addressed in this paper. The first is the selection of the most convenient transportation mode. We present a method for solving multi-criteria decision-making problem to deal with evaluating and ranking alternatives from the best to the worst with respect to decision maker(s) preferences. This is applied to find the most preferred transportation mode among available modes concerning some evaluation criteria for a transportation problem. A possibility degree is used for comparisons between the overall values of alternatives to raise a possibility degree matrix. Based on that matrix, the alternatives are ranked according to the ranking vector derived from the matrix, and the best one is selected. The second is to construct a multi-item transportation problem using that preferred mode of transportation. To get the crisp model, a defuzzification approach is adopted. To convert multi-objective transportation problem into a single-objective problem, two different techniques (i) fuzzy goal programming method and (ii) convex combination method are used. Then the reduced single-objective problem is solved by generalized reduced gradient method (LINGO-14.0) and a set of optimal solutions are obtained and presented graphically.