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An Intuitionistic Fuzzy Zero Suffix Method for Solving the Transportation Problem

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Advances in High Performance Computing (HPC 2019)

Part of the book series: Studies in Computational Intelligence ((SCI,volume 902))

Abstract

The transportation problem (TP) is a special class of linear programming problem. Its main objective is to determine the amount of a shipment from source to destination to maintain the supply and demand requirements at the lowest total transportation cost. The TP was originally developed by Hitchcock in 1941. There are different approaches for solving the TP with crisp data, but in many situations the cost coefficients, the supply and demand quantities of the TP may be uncertain. To overcome this Zadeh introduce fuzzy set concepts to deal with an imprecision and a vagueness. The values of membership and non-membership cannot handle such uncertainty involved in real-life problems. Thus Atanassov in 1983 first proposed the concept of intuitionistic fuzzy sets (IFSs).

In this paper, a new type of the TP is formulated, in which the transportation costs, supply and demand quantities are intuitionistic fuzzy pairs (IFPs), depending on the diesel prices, road condition and other market factors. Additional constraints are formulated to the problem: upper limits to the transportation costs for delivery. The main contribution of the paper is that it proposes for the first time the Zero suffix method for finding an optimal solution of the intuitionistic fuzzy TP (IFTP), interpreted by the IFSs and index matrix (IM) concepts, proposed by Atanassov. The example in the paper illustrates the efficiency of the algorithm. An advantage of the proposed algorithm is that it can be applied to problems with imprecise parameters and can be extended in order to obtain the optimal solution for other types of multidimensional transportation problems in fuzzy environment.

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Acknowledgements

The work is supported by the “Asen Zlatarov” University project under Ref. No. NIX-423/2019 “Innovative methods for extracting knowledge management”.

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Authors and Affiliations

  1. “Prof. Asen Zlatarov” University, “Prof. Yakimov” Blvd, 8000, Burgas, Bulgaria

    Velichka Traneva & Stoyan Tranev

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  1. Velichka Traneva
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  2. Stoyan Tranev
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Correspondence to Velichka Traneva .

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Editors and Affiliations

  1. Institute of Information and Communication Technology, Bulgarian Academy of Sciences, Sofia, Bulgaria

    Ivan Dimov

  2. Institute of Information and Communication Technology, Bulgarian Academy of Sciences, Sofia, Bulgaria

    Stefka Fidanova

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Traneva, V., Tranev, S. (2021). An Intuitionistic Fuzzy Zero Suffix Method for Solving the Transportation Problem. In: Dimov, I., Fidanova, S. (eds) Advances in High Performance Computing. HPC 2019. Studies in Computational Intelligence, vol 902. Springer, Cham. https://doi.org/10.1007/978-3-030-55347-0_7

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