Solution of fuzzy transportation problem based upon pentagonal and hexagonal fuzzy numbers

The given study focuses on a novel approach to handle the pentagonal and hexagonal fuzzy transportation problems. The parameters of a transportation problem have been fuzzified into pentagonal and hexagonal fuzzy numbers. The study's innovation resides in its proposal of two distinct defuzzification methods to transform pentagonal and hexagonal fuzzy numbers into deterministic form, both of which are based on the centroid approach. The classical Vogel's approximation method and Modified distribution methods are used to obtain the initial feasible and optimal solution of the above-stated problems. A numerical illustration is given to prove the efficiency of the proposed algorithm. A comparison of the suggested technique has been made with the existing methods. Also, the results obtained using pentagonal and hexagonal fuzzy numbers are compared.