Handling Optimization Under Uncertainty Using Intuitionistic Fuzzy-Logic-Based Expected Value Model

Abstract

Uncertainty in parameters during deterministic optimization studies can have large impact on the outcome of the optimization result. It is pragmatic that these parameters are uncertain as they have direct link with real life scenarios, e.g. fuel price appearing as a parameter in objective function or constraints. However, their variability is ignored while solving the problem in a deterministic optimization framework. While mitigating the above mentioned scenario, it is, therefore, necessary to investigate the development of uncertainty handling techniques for a realistic optimization problem. In this work, we propose intuitionistic fuzzy expected value model (IFEVM), which assumes uncertain parameters as intuitionistic fuzzy variables and derives the solution out of an equivalent transformed deterministic formulation while defining the expected values of the objective functions and constraints. Intuitionistic fuzzy parameters can be regarded as a superset of the conventional fuzzy set where the aspect of non-determinacy of a fuzzy member to a set is additionally taken into account. The proposed IFEVM technique has been applied on two examples: first, with the Binh-korn's multi-objective test function where uncertain parameters are linearly related and next with a real life case study of industrial grinding operation having multiple numbers of non-linearly related uncertain parameters. The technique has been further applied to these case studies considering three different levels of risk scenarios e.g. optimistic, pessimistic and intermediate approaches. The IFEVM technique is fairly generic and advantageous, can be applied to any kind of system for handling uncertainty in parameters.