Close Interval Approximation of Pentagonal Fuzzy Numbers for Interval Data-Based Transportation Problems

Due to globalization in this modern age of technology and other uncontrollable influences, transportation parameters can differ within a certain range of a given period. In this situation, a managerial position’s objective is to make appropriate decisions for the decision-makers. However, in general...

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Veröffentlicht in:Sustainability 2022-06, Vol.14 (12), p.7423
Hauptverfasser: Juman, Z. A. M. S., Mostafa, Salama A., Batuwita, A. P., AlArjani, Ali, Sharif Uddin, Md, Jaber, Mustafa Musa, Alam, Teg, Attia, El-Awady
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container_end_page
container_issue 12
container_start_page 7423
container_title Sustainability
container_volume 14
creator Juman, Z. A. M. S.
Mostafa, Salama A.
Batuwita, A. P.
AlArjani, Ali
Sharif Uddin, Md
Jaber, Mustafa Musa
Alam, Teg
Attia, El-Awady
description Due to globalization in this modern age of technology and other uncontrollable influences, transportation parameters can differ within a certain range of a given period. In this situation, a managerial position’s objective is to make appropriate decisions for the decision-makers. However, in general, the determination of an exact solution to the interval data-based transportation problem (IDTP) becomes an NP-hard problem as the number of choices within their respective ranges increases enormously when the number of suppliers and buyers increases. So, in practice, it is difficult for an exact method to find the exact solution to the IDTP in a reasonable time, specifically the large-sized problems with large interval sizes. This paper introduces solutions to the IDTP where supply, demand, and cost are all in interval numbers. One of the best interval approximations, namely the closed interval approximation of pentagonal fuzzy number, is proposed for solving the IDTP. First, in the proposed closed interval approximation method (Method-1), the pentagonal fuzzification method converts the IDTP to a fuzzy transportation problem (FTP). Subsequently, two new ranking methods based on centroid and in-center triangle concepts are presented to transfer the pentagonal fuzzy number into the corresponding crisp (non-fuzzy) value. Thereafter, the optimal solution was obtained using Vogel’s approximation method coupled with the modified distribution method. The proposed Method-1 is reported against a recent method and shows superior performance over the aforementioned and a proposed Method-2 via benchmark instances and new instances.
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subjects Algorithms
Approximation method
Centroids
Decision making
Exact solutions
Fuzzy sets
Fuzzy systems
Globalization
Linear programming
Mathematical programming
Methods
Set theory
Sustainability
Transportation problem
Traveling salesman problem
title Close Interval Approximation of Pentagonal Fuzzy Numbers for Interval Data-Based Transportation Problems
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