Fuzzy Diagnosis Of Discrete Event Systems

Discrete event system is a natural and man-made dynamic system whose state space is discrete and instantaneous events over time. However, there are always some imprecise, vague and subjective in our real life. Fuzzy discrete event system, which is incorporated fuzzy set theory together with discrete event system, is a good-solution to this problem. Failure diagnosis and detection play a crucial role in the study of complex systems. So far, some work have been done for this issue.In this paper, we model the fuzzy discrete event system with fuzzy max-min au-tomaton, and propose a new notion of diagnosability of fuzzy discrete event system based on the concept of undistinguishable strings. Moreover, a necessary and suf-ficient condition for fuzzy diagnosability is obtained in terms of certain properties of the diagnoser which is constructed to find all of the collections of the undis-tinguishable strings. Some examples serving to illuminate the applications of the diagnosability of fuzzy discrete event systems are described.In the first chapter, some preliminaries about discrete event systems, diagnos-ability of discrete event systems and observability are introduced.In the second chapter, we first recall something about fuzzy max-min discrete event systems, and then a new definition of fuzzy diagnosability is proposed based on the concept of undistinguishable strings (strings with the same observability regardless of how long the strings are in the language generated by fuzzy discrete event system). Finally, the diagnoser is constructed to find all of the collections of the undistinguishable strings. one correspondence between the collections of the undistinguishable strings and the cycles in the diagnoser is established in terms of certain properties of the diagnoser. And a necessary and sufficient condition for fuzzy diagnosability is obtained, which still holds even in crisp discrete event systems.In the third chapter, we obtain that the overall complexity of the comput-ing process to check the diagnosability of fuzzy discrete event systems is at most O(2|Q|×(|∑|+1)×|∑|). And the algorithm we proposed in this paper is successfully used in the treatment of animal.