Opacity of Fuzzy Discrete Event Systems

Abstract

Finite automata (FAs) model is a popular tool to characterize discrete event systems (DESs) due to its succinctness. However, for some complex systems, it is difficult to describe the necessary details by means of FAs model. In this paper, we consider a kind of extended finite automata (EFAs) in which each transition carries a predicate over state and event parameters. We also consider a type of simplified EFAs, called Event-Parameters EFAs (EP-EFAs), where the state parameters are removed. Based upon these two parametric models, we investigate the problem of opacity analysis for parametric DESs. First of all, it is shown that EFAs model is more expressive than EP-EFAs model. Secondly, it is proved that the opacity properties for EFAs are undecidable in general. Moreover, the decidable opacity properties for EP-EFAs are investigated. We present the verification algorithms for current-state opacity, initial-state opacity and infinite-step opacity, and then discuss the complexity. This paper establishes a preliminary theory for the opacity of parametric DESs, which lays a foundation for the opacity analysis of complex systems.

Design and Analysis of a Laminar Diffusion-Based Micromixer with Microfluidic Chip

“…Fuzzy logic is not based on Aristotelian (classical) logic but uses functions expressing fuzzy sets. There is a binary value (0-1) logic in classical logic [38]. Fuzzy logic derives results by considering binary values and expresses them with verbal variables such as less, less, more, medium, long, and regular.…”

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