Title: Fuzzy programming technique for solving the shortest path problem on networks under triangular and trapezoidal fuzzy environment

Authors: Sathi Mukherjee

Addresses: Bengal College of Engineering and Technology, SS Banerjee Sarani, Bidhannagar, Durgapur-713212, West Bengal, India

Abstract: In this paper, a well-known problem called the shortest path problem (SPP) has been considered in an uncertain environment. The cost parameters for travelling each arc have been considered as triangular or trapezoidal fuzzy numbers (TFNs or TrFNs) which are the more generalised form of fuzzy numbers involving a lower limit and an upper limit. A methodology has been developed for solving the fuzzy shortest path problem (FSPP), which results in lowest cost solution corresponding to the minimum-cost path or the shortest path. In the proposed method, the FSPP has been written in the form of single-objective fuzzy linear programming problem with fuzzy costs, which has been transformed into a crisp multi-objective linear programming problem. This in turn has been solved by the well-known fuzzy programming technique. Comparisons of the proposed methodology with some latest researches in this field have been discussed. Numerical examples illustrate the effectiveness of the proposed method.

Keywords: shortest path problem; SPP; operations research; triangular fuzzy numbers; TFNs; trapezoidal fuzzy numbers; TrFNs; fuzzy programming; decision making; networks; uncertainty; fuzzy costs; multi-objective linear programming.

DOI: 10.1504/IJMOR.2015.071282

International Journal of Mathematics in Operational Research, 2015 Vol.7 No.5, pp.576 - 594

Received: 28 Oct 2013
Accepted: 08 May 2014
Published online: 19 Aug 2015 *

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