A new method to solve multi-objective linear fractional programming problem in fuzzy stochastic environment

Abstract

Fuzzy stochastic optimization has emerged as an effective approach for dealing with probabilistic and imprecise uncertainties, which makes it useful for problems when data is simultaneously impacted by vagueness and randomness. When these uncertainties involve in decision making problem where, it is required to determine the relative merits between different alternatives, we have often used the fuzzy stochastic fractional programming problem. This paper developed a new approach to derive the acceptable range of objective values for a Multi-objective fuzzy stochastic linear fractional programming problem (MOFSLFPP). In this problem, the fuzzy random variables coefficient is involved as the parameters of the objective function as well as system constraints. The proposed method constructs an expectation model based on the mean of the fuzzy random variable. For the satisfaction level of decision-makers, the level set properties of the fuzzy set are applied in the objective function. The chance-constrained programming method is utilized to transform the MOFSLFPP into its equivalent crisp form. For validation of the proposed methodology, an existing numerical has been solved, and the comparison of the proposed methodology has been discussed with the existing one. Also to demonstrate the practical application of this methodology, an inventory management problem has been discussed.