An efficient fuzzy mathematical approach to solve multi-objective fractional programming problem under fuzzy environment

To tackle the uncertainty in some decision making problems, suitable fuzzy optimization models can be formulated which need simultaneous optimization of fuzzy fractional functions. In this paper, a multi-objective linear fractional programming problem is studied in an environment of fuzzy numbers and a solution methodology is proposed to generate an efficient solution. This solution approach first transforms the objective functions in fuzzy valued forms. Subsequently, the deterministic values of the fuzzy constraints are obtained using the centroids of fuzzy numbers. A new technique is proposed to linearize the fuzzy valued fractional functions. Fuzzy aspiration levels of the objective functions are ascertained using variable transformation method. Finally, fuzzy goal programming is used to derive the efficient solution where ranking function is implemented to defuzzify the linear fuzzy valued objective function of the final model. To demonstrate the proposed method, existing two numerical examples and one practical problem are solved and the results obtained are comparatively analysed with the existing methods which justifies its feasibility and effectiveness.