Fuzzy rough approximations of process data

This paper concerns the variable precision fuzzy rough set (VPFRS) model with asymmetric bounds. The discussion of the presented approach is preceded by a comparison of the original crisp rough set paradigm to the variable precision crisp rough set model. As a new aspect, a unified form of expressing the lower and upper crisp approximations is considered. It can be applied to defining new fuzzy rough set models. Crucial notions of the VPFRS model are redefined and explained. A new way of determining the upper variable precision fuzzy rough approximation is proposed. The VPFRS model is used for describing and analyzing the control actions which are accomplished by a human operator, who controls a complex dynamic system. The decision model is expressed by means of a decision table with fuzzy attributes. Decision tables are generated by the fuzzification of crisp data based on a set of fuzzy linguistic values of the attributes. A T-similarity relation is chosen for comparing elements of the universe. In an illustrative example, the task of stabilization of the aircraft’s bank angle during a turn maneuver is analyzed.