An approach for solving fuzzy transportation problem using octagonal fuzzy numbers

Abstract

In this paper, a general fuzzy transportation problem model is discussed. There are several approaches by different authors to solve such a problem viz., [1,2,3,6,7,8]. We introduce octagonal fuzzy numbers using which we develop a new model to solve the problem. By defining a ranking to the octagonal fuzzy numbers, it is possible to compare them and using this we convert the fuzzy valued transportation problem (cost, supply and demand appearing as octagonal fuzzy numbers) to a crisp valued transportation problem, which then can be solved using the MODI Method. We have proved that the optimal value for a fuzzy transportation problem, when solved using octagonal fuzzy number gives a much more optimal value than when it is solved using trapezoidal fuzzy number as done by Basirzadeh [3] which is illustrated through a numerical example.

Extension of fuzzy Johnson algorithm to three machines fuzzy flow-shop scheduling problem

“…• Convert the fuzzy execution times into crisp numbers using the ranking method Ranking Method(Malini et al, [6]):…”

“…,25) (0,2,4,6,8,10,12,14) (12,14,16,18,20,22,24,26) 2 (4,6,8,10,14,16,18,20) (6,7,10,11,12,15,16,19) (5,7,9,11,13,15,17 ,19) 3 (22,24,26,28,30,32,34,36) (3,5,7,9,13,15,17,19) (16,18,20,22,24,26,28,30) 4 (29,31,33,35,37,39,41,43) (0,2 12 12 w − Divergence(Ã) = ( f − c) 8 5…”

A New Membership Function on Hexagonal Fuzzy Numbers

“…The three operations that can be performed on hexagonal fuzzy numbers, suppose = ( 1 , 2 , 3 , 4 , 5 , 6 ) and = ( 1 , 2 , 3 , 4 , 5 , 6 ) are two hexagonal fuzzy numbers then (i) Addition : [3,6,9,13,16,19] hence all the points coincide with the sum of the two hexagonal fuzzy number. Therefore addition of two cuts lies within the interval.…”

Performance Measure of Fuzzy Simple Queue with Balking and Feedback Customers using Symmetric Heptagonal Fuzzy Numbers

“…Thus, fuzzy queueing models have been described by a many researchers such as S. U. Malini and Felbin [6], Mueen et al [4], Rajalakshmi and Julia [2], Usha and Chanda [3] and Noor et al [5]. Fuzzy problem has been studied by using heptagonal fuzzy number by Shanmugasundaram and Thamilselvi [8].…”