Identification of Single-Event Stochastic Fuzzy Discrete Event Systems: An Equation-Systems-Based Approach

We recently proposed a new class of fuzzy discrete event systems called the stochastic fuzzy discrete event systems (SFDES), which has the potential to be useful in a variety of applications, including those in healthcare. An SFDES is comprised of multiple fuzzy automata with different occurrence probabilities. Assuming the number of states is known, goals of SFDES identification are: 1) determining number of fuzzy automata and their event transition matrices, and 2) estimating the occurrence probabilities of the fuzzy automata. In this article, we develop an innovative technique, named the equation-systems-based technique, which uses whatever pre- and post-event state vector pairs available to establish and solve equation systems to achieve the identification goals. The ability of using arbitrary state vector pairs is a crucial and practical advantage over another SFDES identification technique that we previously published. That technique, called the prerequired-pre-event-state-based technique, requires the system of interest to be subject to some special pre-event states during the identification process, which may not be feasible for many real-world systems. The new equation-systems-based technique has no adjustable parameter to set or hyperparameter to experiment with. Theoretical analysis is conducted on the Technique, resulting in necessary or sufficient conditions as well as formulas for computing the minimal (or near minimal) number of state vector pairs needed for various SFDES settings. Computer simulation results are provided to demonstrate the effectiveness of the Technique.