Scalarizing fuzzy multi-objective linear fractional programming with application

Multi-objective linear fractional programming (MOLFP) is an important field of research. As in several real-world problems, the decision-makers (DMs) need to find a solution to a MOLFP. In making a decision, the DM needs to deal with several imprecise numerical quantities due to fluctuating environments. This work presents a novel fuzzy multi-objective linear fractional programming (FMOLFP) model in an ambiguous environment. Since fuzzy set theory has been shown to be a useful tool to handle decisive parameters' uncertain nature in several research articles. The proposed model attempts to minimize multiple conflicting objectives, simultaneously having some uncertain/fuzzy parameters. An equivalent crisp MOLFP model has been derived using the arithmetic operations on fuzzy numbers. After that, applying the Charnes-Cooper transformation effectively, the problem reduces to a deterministic multi-objective linear programming (MOLP). The MOLP is scalarized by using Gamma-connective and minimum bounded sum operator techniques to solve to optimality. The proposed algorithm's computation phase's basic idea is to transform the FMOLFP into a deterministic MOLP. Then to scalarize the MOLP into a single objective linear problem (LP) to optimize further. Later, the proposed model is applied to solve an integrated production-transportation problem.