Fuzzy detectabilities for fuzzy discrete event systems

Fuzzy discrete event systems are useful models for solving complex practical problems in biomedical and other fields. The theory of detectabilities in conventional crisp discrete event systems investigates state determination or estimation based on event observation. The theory is also important to fuzzy discrete event systems (e.g., disease diagnosis and treatment effectiveness evaluation). In this paper, we investigate fuzzy detectabilities for fuzzy discrete event systems. We first introduce fuzzy discrete event systems with constraints, which provide a new and more realistic model for complex systems. We also extend detectabilities of crisp discrete event systems to N-detectabilities and prove the relation between detectabilities and N-detectabilities. We then define fuzzy N-detectabilities and develop an algorithm to check fuzzy N-detectabilities of a fuzzy discrete event system. The computational complexity of the algorithm is analyzed.