Intuitionistic Fuzzy Approach Toward Evolutionary Robust Optimization of an Industrial Grinding Operation Under Uncertainty

Abstract

The existence of uncertainty is inherent and unavoidable in process systems. The sources of it might be linked, though not limited, to the estimation of model parameters through experimental/regression exercises and their related errors apart from the regular variations in the process operations. Thus, the outcomes of an optimization study by assuming uncertain parameters as non-varying one, as opposite to the actual scenario, would prompt to incorrect results and sometimes even infeasible solutions. One of the ways to handle such situations is by using intuitionistic fuzzy numbers (IFNs) to represent the uncertainty which considers both the membership and the nonmembership degree and carry out the uncertainty analysis based on the intuitionistic fuzzy logic. In this study, the above approach has been adopted to a real-life case study which contains highly nonlinear parameters named industrial grinding process considering different moods of a decision-maker under uncertain situations, i.e., optimistic, pessimistic, and mixed. Various sources of uncertainties are categorized as uncertainties related to model parameters (e.g., tuning parameters inside the model) and operational parameters (e.g., feed stream uncertainties), and their individual and amalgamated effects on the grinding process which is a multi-objective optimization problem have been analyzed. A novel way of determining the parametric sensitivity in presence of number of uncertain parameters has also been proposed. Based on the extent of non-determinacy to be resolved, the newly defined membership degree enables conducting comparative study of fuzzy and intuitionistic fuzzy robust optimization under different scenarios. Additionally, comparative analysis has been carried out for the proposed IFRO algorithm with the benchmark robust worst-case formulation (Ben-Tal and Nemirovskii 2001) and it has been observed that IFRO gives better results when compared with the worst-case formulation.