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In solving real life transportation problem we often face the state of uncertainty as well as hesitation due to various uncontrollable factors. To deal with uncertainty and hesitation many authors have suggested the intuitionistic fuzzy representation for the data. So, in this paper, we consider a transportation problem having uncertainty and hesitation in supply, demand and costs. We formulate the problem and utilize triangular intuitionistic fuzzy numbers (TrIFNs) to deal with uncertainty and hesitation. We propose a new method called PSK method for finding the intuitionistic fuzzy optimal solution for fully intuitionistic fuzzy transportation problem in single stage. Also the new multiplication operation on TrIFN is proposed to find the optimal object value in terms of TrIFN. The main advantage of this method is computationally very simple, easy to understand and also the optimum objective value obtained by our method is physically meaningful. Finally the effectiveness of the proposed method is illustrated by means of a numerical example which is followed by graphical representation of the finding.