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A transportation problem (TP) is built on the framework of supply-demand and cost parameters which are uncertain in nature. Neutrosophic numbers are capable of handling incomplete information. This paper introduces a new solution approach to optimize TPs with neutrosophic parameters based on a new ranking function. This function utilizes the attitudinal character of a basic unit-interval monotonic function inspired from the domain of continuous ordered weighted average operators. Ranking rules are established followed by defining a neutrosophic transportation problem. A solution methodology followed by solved numerical illustrates the efficiency of the proposed method. Conclusion and future directions summarize the work.