Title: Solution of linear programming problem with trapezoidal fuzzy coefficients using score functions

Authors: K. Suriyapriya; Jagadeeswari Murugan; V. Lakshmana Gomathi Nayagam

Addresses: Department of Mathematics, National Institute of Technology, Tiruchirappalli, India ' Department of Mathematics, National Institute of Technology, Tiruchirappalli, India ' Department of Mathematics, National Institute of Technology, Tiruchirappalli, India

Abstract: Numerous real-life problems depend on incomplete and implausible information. To overcome the enigma and obscurity, Zadeh promoted fuzzy set theory in 1965. After introducing fuzzy set theory, many researchers have made numerous developments in engineering and medicine. Different ranking principles on trapezoidal fuzzy numbers are established and are applied by eminent authors in multi-criteria decision-making problems in the literature. Linear programming models are essential tools to solve optimisation problems in healthcare, production planning, financial sectors, etc. The ranking principle plays a vital role in the constraints. Recently, a complete ranking principle on the class of trapezoidal fuzzy numbers was suggested in 2018. This study proposes a method to solve the fuzzy linear programming problem whose coefficients are trapezoidal fuzzy numbers using the total ordering principle by score functions defined in 2018. Here, we formulate an equivalent multi-objective linear programming problem for the given fuzzy linear programming problem to attain the optimal solution. Furthermore, the proposed method's efficiency is illustrated through numerical examples and comparison with the existing techniques is also discussed.

Keywords: linear programming problem; trapezoidal fuzzy coefficients; total ordering principle.

DOI: 10.1504/IJMOR.2022.123126

International Journal of Mathematics in Operational Research, 2022 Vol.22 No.1, pp.41 - 73

Received: 02 Dec 2020
Accepted: 28 Mar 2021
Published online: 30 May 2022 *

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