Title: A new fuzzy transportation algorithm for finding fuzzy optimal solution

Authors: Muhammad Sam'an; Farikhin

Addresses: Department of Mathematics, Jl. Prof Soedarto, SH Tembalang, Semarang, 1269, Indonesia ' Department of Mathematics, Jl. Prof Soedarto, SH Tembalang, Semarang, 1269, Indonesia

Abstract: Based on the literature, many algorithms have been proposed to solve fuzzy transportation problems in real life. Among the existing algorithms, some do not use the ranking method to convert fuzzy numbers into crisp numbers, whereas some use ranking methods that fail to rank non-normal fuzzy numbers correctly and compensate with the use of areas. Therefore, in this paper, a new fuzzy transportation algorithm, i.e., the NNWC, NLC and NVA, is used to solve a fuzzy transportation problem. The ranking methods involving non-normal trapezoidal fuzzy numbers and triangular fuzzy numbers as well as a new ranking method using total integral value are used to solve case studies 1 and 2, and the results are compared with the results from existing methods. Because of the proposed method is a direct extension of a classical method, it is reasonable to apply it to real-life transportation problems.

Keywords: fuzzy transportation problem; new fuzzy transportation algorithm; new total integral value; non-normal trapezoidal fuzzy numbers.

DOI: 10.1504/IJMMNO.2021.111715

International Journal of Mathematical Modelling and Numerical Optimisation, 2021 Vol.11 No.1, pp.1 - 19

Received: 30 Jan 2019
Accepted: 19 Oct 2019
Published online: 11 Dec 2020 *

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