Linguistic coordinate transformations for complex fuzzy sets

Complex fuzzy sets were introduced as a model for the fuzzification of the complex domain. This model projects the two-dimensional features of the complex domain, apparent in mathematical analysis, to the linguistic domain. One important operation that surfaced as a result of using complex fuzzy sets was the linguistic coordinate transformations. In this paper, the linguistic coordinate transformations are investigated through an application to the design of second order adaptive microelectromechanical systems. It is shown that using complex fuzzy sets together with the linguistic coordinate transformations, the adaptive control may be implemented in one linguistic coordinate system and the linguistic outputs may then be transformed to another for further operations. As in the case of the example, it is demonstrated that this transformation could result in a reduction of the complexity of a given problem.