Handling Uncertainty and Finding Robust Pareto Frontier in Multiobjective Optimization Using Fuzzy Set Theory

Multiobjective optimization problem with uncertainties in the input data is considered. Due to the uncertainty, the use of deterministic approaches for finding the solution to the problem is problematic. Statistical techniques based on probability distributions are not efficient if the input data are not sufficient to estimate the par ameters of the model accurately enough. An additional problem arises if the probability distribution for the available data is unknown. Meanwhile, the partial information available to the decision maker can be useful if fuzzy information is exploited. In this paper, we introduce the definition of optimality using fuzzy variables to handle the uncertainty in the model. Thereafter, we extend the concept of robust frontier to the model based on fuzzy information. We make it possible to find a less sensitive frontier in multiobjective optimization with partial information. The approach is illustrated by solving a test case, well-known in the literature.