An extended Vogel’s approximation algorithm for efficiently solving Fermatean fuzzy solid transportation problems

Abstract

This paper aims to solve a solid transportation problem, wherein the uncertain parameters related to the problem are represented using triangular Fermatean fuzzy numbers. Fermatean fuzzy sets offer a relatively novel and wider alternative by providing the decision-makers with more versatile means of managing the uncertain information throughout the decision-making process. As per our literature survey, no algorithm exists in the literature for fuzzy solid transportation problems with parameters as triangular Fermatean fuzzy numbers. Therefore, in this study, the existing Vogel’s approximation method for the initial basic feasible solution (IBFS) of the traditional transportation problems is extended for the Fermatean fuzzy solid transportation problems. Further, a new method for getting the optimal solution from the obtained IBFS is proposed. The computational complexity and operational efficacy of the proposed algorithm are also discussed. Two application examples have been solved to illustrate the practicality of the proposed algorithm. For the comparative study, the problems are also solved with LINGO 20.0 software. The obtained results of IBFS are found to be significantly lower than those obtained by certain existing methods and the optimal values are comparable with those generated by the LINGO 20.0 optimization solver. Through a comparative analysis, it has been found that the proposed algorithm consistently produces optimal transportation costs for both application examples, adding to the novelty of the proposed work. Finally, the conclusion and future scope of this study are described.

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