# Evaluation of the Minimum Transportation Cost of Asymmetric/Symmetric Triangular Fuzzy Numbers with -Cut by the Row-Column Minima Method

## Keywords:

Asymmetric/symmetric triangular fuzzy transportation problem, Interval integer transportation problem, Row-column minima method, Transportation problem, α -cut method

## Abstract

In this article, the main idea is to obtain the minimum transportation total fuzzy cost of the triangular transportation problem using the row-column minima (RCM) method. Here, the capacity of supply, the destination of demand, and transportation cost are all fully triangular fuzzy numbers with asymmetric or symmetric but not with the negative triangular fuzzy number (TFN). Vagueness plays an active role in many fields, such as science, engineering, medicine, management, etc. In this idea, the TFN problem is decomposed into two interval integer transportation problems (IITP) using the -cut method, by putting  and  to get the upper bound interval transportation problem and the lower bound interval transportation problem. These two interval problems are decomposed again into two problems: the right-bound transportation problem (RBTP) and the left-bound transportation problem (LBTP). First, compute an initial basic feasible solution for RBTP, then also obtain the optimum solution by the existing method; there is no need to solve LBTP directly because the solution of RBTP is the initial solution of LBTP. Apply the RCM method to LBTP, getting interval solutions for both interval transportation problems. Then the combined and computed the minimum fuzzy triangular transportation cost, in which an asymmetric or symmetric triangular fuzzy transportation problem (TFTP) is not changed into classical TP without using ranking methods, and the same result was obtained using the existing method. Some numerical examples are illustrated, and it is very suitable to clarify the idea of this concept. This idea is an easy way to understand the uncertainty that happens in a real-life situation.

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