A Comparative Study of Fuzzy Techniques to Handle Uncertainty: An Industrial Grinding Process

Abstract

AbstractThe deterministic optimization models for chemical processes assume perfect information, i.e., the system parameters involved in the models should have fixed values. However, the knowledge about these parameters is often either not easy to obtain or, if available, subjected to uncertainty involved in determining them (e.g. experiments, regression etc.). The optimization results obtained using these deterministic models are, therefore, not robust to uncertainties in the parameters of the system. In this work, fuzzy based approaches, e.g. fuzzy chance constrained programming (FCCP) and fuzzy expected value model (FEVM), have been applied to a multi‐objective optimization problem of the industrial grinding process to carry out the uncertainty analysis and the results are compared with respect to the power of risk averseness adopted in the approaches used. These methods assume the uncertain parameters as fuzzy numbers and membership function is used to represent the degree of uncertainty in them. The extent of constraint satisfaction due to the presence of uncertain parameters can be accommodated assuming credibility of constraint satisfaction under FCCP framework whereas the robust set of parameters in the FEVM approach is determined by considering the expectation terms for objectives and constraints. Moreover, the issue of nonlinear relation of uncertain parameters has been handled by adopting simulation based approaches while computing the credibility. The results obtained by FCCP technique show how the presence of uncertainty leads to an operating zone of varied risk appetite of a decision maker by using different uncertain measures such as credibility, possibility and necessity. These approaches are very generic and can be adopted for the study of parametric sensitivity for any process model in a novel manner.