modeling uncertainty in logistics: application of interval-valued trapezoidal fuzzy numbers in transportation optimization

This research models the transportation problem in an imprecise environment using intervalvalued trapezoidal fuzzy numbers (ivtrfns). the primary innovation lies in optimization based on a weighted linear ranking function and the development of some of its theoretical concepts. this function converts ivtrfns parameters into crisp values by incorporating the decision-maker s risk preference through the parameter z, thereby reducing the need for complex computations. the efficacy of the proposed method is validated through a numerical example involving two sources and three destinations. the results indicate that a shift in the decision-maker s attitude from conservative (z=1) to risk-seeking (z=0) can lead to an over threefold increase in the total cost. this finding underscores the importance of balancing risk and cost in imprecise environments and provides a practical framework for managers to design optimal transportation strategies.