# Fuzzy Transportation Problem By Using TriangularFuzzy Numbers With Ranking Using Area Of Trapezium, Rectangle And Centroid At Different Level Of α-Cut

## Abstract

The objective of this article is to introduce a new ranking method to order any two fuzzy triangular numbers. This new ranking method is used to find the best approximate solution to the fuzzy transportation problem.  The uncertainty plays a vital role in any branch of science and technology, engineering, medical and management. In Artificial Intelligence Fuzzy Mathematics and fuzzy logic is used to process Natural language and widely used in decision making. The objective of the transportation problem is to control the amount to be transported from several origins to several destinations such that the total transportation cost is minimized. But in real-life situations, the available supply and forecast demand are often fuzzy because some information is incomplete orunavailable.

In this article, the crisp transportation problem is transformed into a fuzzy transportation problem by using triangular fuzzy numbers. To order any two triangular fuzzy numbers the new and simple method is invented which are based on the area of a trapezium, rectangle, and centroid at prominent places using α-cut method at α=0.2,       α= 0.5 and α=0.8 respectively. A computer program was written in MATLAB which is given in this article to make calculation easier and simple. This article is organized as follows. In section first we introduced new ranking method to compare any two triangular fuzzy numbers. I third section we extend this method to solve fuzzy transportation problem using numerical example, while paper is concluded in the last section.