Newly Proposed Matrix Reduction technique Under Mean Ranking Method for Solving Trapezoidal Fuzzy Transportation problems Under Fuzzy Environment

In this paper, improved matrix Reduction Method is proposed for the solution of fuzzy transportation problem in which all inputs are taken as fuzzy numbers. Since ranking fuzzy number is important tool in decision making, Fuzzy trapezoidal number is converting in to crisp set by using Mean techniques and solved by proposed method for fuzzy transportation problem. We give suitable numerical example for unbalanced and compare the optimal value with other techniques. The Result shows that the optimum profit of transportation problem using proposed technique under robust ranking method is better than the other method. Novelty: The numerical illustration demonstrates that the new projected method for managing the transportation problems on fuzzy algorithms.

A MODIFICATION OF THE INDEX OF LIOU AND WANG FOR RANKING FUZZY NUMBER

Different methods have been proposed for ranking fuzzy numbers. These include methods based on distances, centroid point, coefficient of variation, and weighted mean value. However, there is still no method that can always give a satisfactory result to every situation; some are counterintuitive and not discriminating. This paper presents an approach for ranking fuzzy numbers with integral value that is an extension of the index of Liou and Wang. This method, that is independent of the type of membership function used, can rank more than two fuzzy numbers simultaneously. This ranking method use an index of optimism to reflect the decision maker's optimistic attitude, but rather it also contains an index of modality that represents the neutrality of the decision maker. The approach is illustrated with numerical examples.

RANKING FUZZY NUMBER BASED ON LEXICOGRAPHIC SCREENING PROCEDURE

Fuzzy numbers are used for representing the numerical quantities in a vague environment. Their ranking order has been an important issue for application purposes. Most of the existing ranking methods transform a fuzzy number into a real number based on certain criteria. There is yet no method that can always give a satisfactory solution. This study pointed out that it cannot be avoided for different fuzzy numbers to be corresponding to the same real number by any type of ranking functions. Therefore, sequential screening approach would be necessary for a complete order of fuzzy numbers. We summarize the properties for a sufficient and necessary set of ranking criteria. Then, based on the ranking order of these criteria, a Lexicographical Screening Procedure is proposed, which has shown to be promising in ranking fuzzy number with efficient computation and ease of understanding. Six counterexamples of the existing methods were used for comparison.