Design and Implementation of Embedded Fuzzy Controllers Based on Fourier computation of Membership Functions

In an earlier paper, we derived explicit Fourier series expressions for systematic computation of grade of membership in the overlap and non-overlap regions of triangular fuzzy sets; and by implication, computation of union and intersection of the fuzzy sets. In this paper, we hereby extend the methodology to cover cases of the cosine, exponential and Gaussian fuzzy sets by presenting explicit Fourier series representation for encoding fuzziness in the overlap and non-overlap domains of membership functions of cosine and Gaussian fuzzy sets. The paper further present the development of a corresponding embedded "Fuzzy controller", which incorporates the formal mathematical representation, to measure temperature and pressure and produce output that can serve as input to other sub-systems or systems. In particular, it is established that the technique can indeed be incorporated in engineering systems for dynamic determination of grade of membership of adjoining Fuzzy sets and thus provides a basis for the design and implementation of embedded Fuzzy controller for mission-critical applications.