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The ultimate goal of the decision maker (DM) is to take right decisions to optimize the profit or loss of the organization when the parameters of the transportation problem are ambiguous because of some uncontrollable effects. In this paper, mathematical models are proposed using fuzzy non-linear membership functions and the inverse uncertain normal distribution has been used to eliminate the uncertainty in the parameters which will help the DM to find a compromise solution of the uncertain multi-objective transportation problem (UMOTP) and to achieve the desired goals for a chosen level of confidence for the uncertain parameters. The compromise solutions of the uncertain multi-objective transportation problem are presented to obtain the DM satisfaction if the problem becomes achievable for this preferred confidence level of the parameters. Numerical illustration is given where Linear Programming Problems (LPPs) are resolved with LINGO and the graphs are designed with the help of MATLAB 18.00. J. Bangladesh Acad. Sci. 46(1); 101-115: June 2022

The goal of this research is to focuses on multi-objective transportation problems, to reduce the cost of transporting a good from a variety of sources or origins to a range of destinations while adhering to a predetermined mathematical framework. By using interval values, the policy maker indicated the parameters of source and destination. In this work, a novel approach for finding initial basic feasible solutions (IBFS) that are extremely near to the best ones for a variety of transportation problems is presented. The proposed method can become a milestone in resolving the constraints to achieve the goal in solving transport problem. For the decision maker, regarding logistics and supply chains, it may be quite profitable. The prediction model is supported by an illustration drawn from mathematical view. All the LPPs are evaluated with the help of LINGO. Bangladesh Acad. Sci. 46(2); 155-164: December 2022

<abstract> <p>Considering the uncertainty of transporting goods from numerous origins to diverse destinations is a critical task for the decision-maker (DM). The ultimate goal of the DM is to make the right decisions that optimize the profit or loss of the organization under the vagueness of the uncontrollable effects. In this paper, mathematical models are proposed using fuzzy non-linear membership functions for the transportation problem considering the parameters' uncertainty that can help the DM to optimize the multi-objective transportation problems (MOTP) and to achieve the desired goals by choosing a confidence level of the uncertain parameters. Based on DM's selection of the confidence level, a compromise solution of the uncertain multi-objective transportation (UMOTP) is obtained along with the satisfaction level in percent for the DM. Two non-linear fuzzy membership functions are considered: the exponential and the hyperbolic functions. Using both membership functions, the sensitivity analysis was implemented by considering different confidence levels. According to the experimental results, the hyperbolic membership function gives 100% DM's satisfaction in many instances. Moreover, it shows stability against the exponential and linear functions.</p> </abstract>