Decision Making in Fuzzy Discrete Event Systems1

Supervised Learning of Multievent Transition Matrices in Fuzzy Discrete-Event Systems

In this article, supervised learning of fuzzy discrete-event systems (FDES) is investigated. A learning algorithm that performs supervised learning for multievent transition matrices of a sequence of fuzzy discrete events is derived. FDES can be used to describe a large class of practical systems that consist of fuzzy discrete states, fuzzy discrete events, and transitions among fuzzy discrete states via fuzzy discrete events. Because fuzzy discrete states, fuzzy discrete events, and fuzzy transitions are well defined in FDES, the FDES model is highly explainable, which is important in many applications, especially in biomedical applications. Based on this explainable model, the proposed learning algorithm can be used to learn events and event sequences in the model. Hence, it allows system developers to build an explainable model for a complex system based on the data available. Simulations using MATLAB are conducted to verify the effectiveness of the proposed algorithm.

Learning Fuzzy Automaton's Event Transition Matrix When Post-Event State Is Unknown

Compared to other system modeling techniques, the fuzzy discrete event systems (FDESs) methodology has the unique capability of modeling a class of event-driven systems as fuzzy automata with ambiguous state and event-invoked state transition. In two recent papers, we developed algorithms for online-supervised learning of the fuzzy automaton's event transition matrix using fuzzy states before and after the occurrence of fuzzy events. The post-event state was assumed to be readily available while the pre-event state was either directly available or estimatable through learning. This article is focused on algorithm development for learning the transition matrix in a different setting-when the pre-event state is available but the post-event state is not. We suppose the post-event state is described by a fuzzy set that is linked to a (physical) variable whose value is available. Stochastic-gradient-descent-based algorithms are developed that can learn the transition matrix plus the parameters of the fuzzy sets when the fuzzy sets are of the Gaussian type. Computer simulation results are presented to confirm the theoretical development.

Reliable Decentralized Control of Fuzzy Discrete-Event Systems and a Test Algorithm

A framework for decentralized control of fuzzy discrete-event systems (FDESs) has been recently presented to guarantee the achievement of a given specification under the joint control of all local fuzzy supervisors. As a continuation, this paper addresses the reliable decentralized control of FDESs in face of possible failures of some local fuzzy supervisors. Roughly speaking, for an FDES equipped with n local fuzzy supervisors, a decentralized supervisor is called k-reliable (1 ≤ k ≤ n) provided that the control performance will not be degraded even when n - k local fuzzy supervisors fail. A necessary and sufficient condition for the existence of k-reliable decentralized supervisors of FDESs is proposed by introducing the notions of M̃uc-controllability and k-reliable coobservability of fuzzy language. In particular, a polynomial-time algorithm to test the k-reliable coobservability is developed by a constructive methodology, which indicates that the existence of k-reliable decentralized supervisors of FDESs can be checked with a polynomial complexity.

Behavior coordination of mobile robotics using supervisory control of fuzzy discrete event systems

In order to incorporate the uncertainty and impreciseness present in real-world event-driven asynchronous systems, fuzzy discrete event systems (DESs) (FDESs) have been proposed as an extension to crisp DESs. In this paper, first, we propose an extension to the supervisory control theory of FDES by redefining fuzzy controllable and uncontrollable events. The proposed supervisor is capable of enabling feasible uncontrollable and controllable events with different possibilities. Then, the extended supervisory control framework of FDES is employed to model and control several navigational tasks of a mobile robot using the behavior-based approach. The robot has limited sensory capabilities, and the navigations have been performed in several unmodeled environments. The reactive and deliberative behaviors of the mobile robotic system are weighted through fuzzy uncontrollable and controllable events, respectively. By employing the proposed supervisory controller, a command-fusion-type behavior coordination is achieved. The observability of fuzzy events is incorporated to represent the sensory imprecision. As a systematic analysis of the system, a fuzzy-state-based controllability measure is introduced. The approach is implemented in both simulation and real time. A performance evaluation is performed to quantitatively estimate the validity of the proposed approach over its counterparts.

Estimation of Transitional Probabilities of Discrete Event Systems from Cross-Sectional Survey and its Application in Tobacco Control

In order to find better strategies for tobacco control, it is often critical to know the transitional probabilities among various stages of tobacco use. Traditionally, such probabilities are estimated by analyzing data from longitudinal surveys that are often time-consuming and expensive to conduct. Since cross-sectional surveys are much easier to conduct, it will be much more practical and useful to estimate transitional probabilities from cross-sectional survey data if possible. However, no previous research has attempted to do this. In this paper, we propose a method to estimate transitional probabilities from cross-sectional survey data. The method is novel and is based on a discrete event system framework. In particular, we introduce state probabilities and transitional probabilities to conventional discrete event system models. We derive various equations that can be used to estimate the transitional probabilities. We test the method using cross-sectional data of the National Survey on Drug Use and Health. The estimated transitional probabilities can be used in predicting the future smoking behavior for decision-making, planning and evaluation of various tobacco control programs. The method also allows a sensitivity analysis that can be used to find the most effective way of tobacco control. Since there are much more cross-sectional survey data in existence than longitudinal ones, the impact of this new method is expected to be significant.

State-feedback control of fuzzy discrete-event systems

In a 2002 paper, we combined fuzzy logic with discrete-event systems (DESs) and established an automaton model of fuzzy DESs (FDESs). The model can effectively represent deterministic uncertainties and vagueness, as well as human subjective observation and judgment inherent to many real-world problems, particularly those in biomedicine. We also investigated optimal control of FDESs and applied the results to optimize HIV/AIDS treatments for individual patients. Since then, other researchers have investigated supervisory control problems in FDESs, and several results have been obtained. These results are mostly derived by extending the traditional supervisory control of (crisp) DESs, which are string based. In this paper, we develop state-feedback control of FDESs that is different from the supervisory control extensions. We use state space to describe the system behaviors and use state feedback in control. Both disablement and enforcement are allowed. Furthermore, we study controllability based on the state space and prove that a controller exists if and only if the controlled system behavior is (state-based) controllable. We discuss various properties of the state-based controllability. Aside from novelty, the proposed new framework has the advantages of being able to address a wide range of practical problems that cannot be effectively dealt with by existing approaches. We use the diabetes treatment as an example to illustrate some key aspects of our theoretical results.

Hospital site selection using fuzzy AHP and its derivatives

Environmental managers are commonly faced with sophisticated decisions, such as choosing the location of a new facility subject to multiple conflicting criteria. This paper considers the specific problem of creating a well-distributed network of hospitals that delivers its services to the target population with minimal time, pollution and cost. We develop a Multi-Criteria Decision Analysis process that combines Geographical Information System (GIS) analysis with the Fuzzy Analytical Hierarchy Process (FAHP), and use this process to determine the optimum site for a new hospital in the Tehran urban area. The GIS was used to calculate and classify governing criteria, while FAHP was used to evaluate the decision factors and their impacts on alternative sites. Three methods were used to estimate the total weights and priorities of the candidate sites: fuzzy extent analysis, center-of-area defuzzification, and the alpha-cut method. The three methods yield identical priorities for the five alternatives considered. Fuzzy extent analysis provides less discriminating power, but is simpler to implement and compute than the other two methods. The alpha-cut method is more complicated, but integrates the uncertainty and overall attitude of the decision-maker. The usefulness of the new hospital site is evaluated by computing an accessibility index for each pixel in the GIS, defined as the ratio of population density to travel time. With the addition of a new hospital at the optimum site, this index improved over about 6.5 percent of the geographical area.