Detectability of Fuzzy Discrete Event Systems

We propose a detectability method based on the concept of undistinguishable strings for the detection issue of fuzzy discrete event systems (FDES). First, the undistinguishable strings are introduced to characterize the same observable behavior for any minimal observable events. Then, an observer based on minimal observable events is constructed, and the one-to-one correspondence between the undistinguishable strings and the nonunit cycle of the observer is established, thus obtaining a necessary and sufficient condition for fuzzy detectability. An algorithm for verifying the detectability of FDES is also presented. The detectability applications of FDES are illustrated by an example analysis.