Title: Three-phase algorithms in solving full fuzzy transportation problem by using fuzzy analytical hierarchy process

Authors: Muhammad Sam'an; Farikhin; Bayu Surarso

Addresses: Department of Informatics, Universitas Muhammadiyah Semarang, Kedungmundu, Semarang City, Central Java, 50273, Indonesia ' Department of Mathematics, Universitas Diponegoro, Jl. Prof Soedarto, SH Tembalang, Semarang, 1269, Indonesia ' Department of Mathematics, Universitas Diponegoro, Jl. Prof Soedarto, SH Tembalang, Semarang, 1269, Indonesia

Abstract: In the fuzzy transportation problem, the ranking function is widely used to order fuzzy number or convert fuzzy number to crisp number. Its process is easy to understand and implement. However, the ranking fuzzy number still has significant weakness in which there is still subjectivity or do not pay attention to real life such that sometimes the input and output disconnected the fully fuzzy transportation problem (FFTP) such as there is negative fuzzy optimal solution. In some cases, it was found that FFTP had equal values of the fuzzy distribution least costs such that the existing methods will be generated two or more fuzzy initial basic feasible values. The proposed algorithm, i.e., three-phase algorithm-based fuzzy AHP, is capable of obtaining the fuzzy optimal solution of FFTP Based on the numerical example used to evaluate the performance of the three phases algorithm. The computational performances have been compared to the existing methods in the literature and the results shown this algorithm can solve the FFTP with similar values fuzzy optimal solution even better minimal solutions than existing methods.

Keywords: fuzzy number; fully fuzzy transportation problem; FFTP; ranking function; fuzzy AHP; fuzzy optimal solution.

DOI: 10.1504/IJOR.2023.135505

International Journal of Operational Research, 2023 Vol.48 No.4, pp.445 - 466

Received: 04 Nov 2020
Accepted: 15 Jan 2021
Published online: 15 Dec 2023 *

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