A solid transportation problem with type-2 fuzzy variables

We give this figure to show the searching process in the tabu search algorithm. Clearly, for the initial several iterations, the best objective encountered decreases drastically. After iteration 6, the best objective changes with a fairly slow ratio, and at iteration 27, the optimal objective is found. This result shows the effectiveness of the proposed algorithm. Three new defuzzification methods are proposed for type-2 fuzzy variables.The solid transportation problem is formulated as a chance-constrained expected value model.Fuzzy simulation based on tabu search algorithm is designed to solve the proposed model.The effectiveness of the model and algorithm is verified by the numerical experiments. This paper focuses on generating the optimal solutions of the solid transportation problem under fuzzy environment, in which the supply capacities, demands and transportation capacities are supposed to be type-2 fuzzy variables due to the instinctive imprecision. In order to model the problem within the framework of the credibility optimization, three types of new defuzzification criteria, i.e., optimistic value criterion, pessimistic value criterion and expected value criterion, are proposed for type-2 fuzzy variables. Then, the multi-fold fuzzy solid transportation problem is reformulated as the chance-constrained programming model with the least expected transportation cost. To solve the model, fuzzy simulation based tabu search algorithm is designed to seek approximate optimal solutions. Numerical experiments are implemented to illustrate the application and effectiveness of the proposed approaches.

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