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A new approach for solving fully intuitionistic fuzzy transportation problems

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Abstract

In this paper, a well-known network-structured problem called the transportation problem (TP) is considered in an uncertain environment. The transportation costs, supply and demand are represented by trapezoidal intuitionistic fuzzy numbers (TrIFNs) which are the more generalized form of trapezoidal fuzzy numbers involving a degree of acceptance and a degree of rejection. We formulate the intuitionistic fuzzy TP (IFTP) and propose a solution approach to solve the problem. The IFTP is converted into a deterministic linear programming (LP) problem, which is solved using standard LP algorithms. The main contributions of this paper are fivefold: (1) we convert the formulated IFTP into a deterministic classical LP problem based on ordering of TrIFNs using accuracy function; (2) in contrast to most existing approaches, which provide a crisp solution, we propose a new approach that provides an intuitionistic fuzzy optimal solution; (3) in contrast to existing methods that include negative parts in the obtained intuitionistic fuzzy optimal solution and intuitionistic fuzzy optimal cost, we propose a new method that provides non-negative intuitionistic fuzzy optimal solution and optimal cost; (4) we discuss about the advantages of the proposed method over the existing methods for solving IFTPs; (5) we demonstrate the feasibility and richness of the obtained solutions in the context of two application examples.

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Acknowledgements

Research supported through Projects TIN2014-55024-P and P11-TIC-8001 from the Spanish Ministry of Economy and Competitiveness, and Consejería de Economía, Innovación y Ciencia, Junta de Andalucía (both including FEDER funds) respectively. The first author would also like to thank the office of Vice Chancellor for Research and Technology at Islamic Azad University, Qaemshahr Branch, for their financial support.

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Authors and Affiliations

  1. Department of Mathematics, Qaemshahr Branch, Islamic Azad University, Qaemshahr, Iran

    Ali Ebrahimnejad

  2. Department of Computer Science and A.I., Universidad de Granada, 18014, Granada, Spain

    Jose Luis Verdegay

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  1. Ali Ebrahimnejad
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  2. Jose Luis Verdegay
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Correspondence to Ali Ebrahimnejad.

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Ebrahimnejad, A., Verdegay, J.L. A new approach for solving fully intuitionistic fuzzy transportation problems. Fuzzy Optim Decis Making 17, 447–474 (2018). https://doi.org/10.1007/s10700-017-9280-1

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