An Approach to Theory of Fuzzy Signals—Basic Definitions

The paper presents a new approach to the description of Fourier transform and correlation function, taking into consideration the uncertainty of the transformed function. A conventional approach to uncertainty employs probabilistic description. Here, fuzzy logic theory is applied to describe this uncertainty. New definitions, namely, fuzzy Fourier transform, fuzzy correlation, and possibility correlation, are proposed. The definition of correlation function is based on the concept of fuzzy functional spaces. Some examples of applications and a comparison with the conventional approach are shown.