Fuzzy Rough Programming Models: An Expected Value Perspective

Usually, the quasi-normal fluctuations in practical applications are described via symmetric uncertainty variables, which is a common phenomenon in the manufacturing industry. However, it is relatively scarce in the literature to discuss two-fold uncertainty due to the its complexity. To deal with roughness and ambiguity to accommodate inherent uncertainties, fuzzy rough programming approaches are put forward. In this paper, we pay attention to exploring two kinds of programming problems, namely fuzzy rough single-objective programming and fuzzy rough multi-objective programming, in which objective functions and/or constraints involve fuzzy rough variables (FRV). In accordance with the related existing research of FRVs, such as the chance measure and the expected value (EV) operator, this paper further discusses the EV model, convexity theory, and the crisp equivalent model of fuzzy rough programming. After that, combined with the latest published NIA-S fuzzy simulation technique, a new fuzzy rough simulation algorithm is developed to calculate the EVs of complicated functions for handling the presented fuzzy rough programming problems. In the end, the two types of numerical examples are provided for demonstration.