New directions in fuzzy automata: A general and more usable formalism

There are many applications in which the whole system can be modeled as a finite number of internal states, each of which can be reached based on a specific sequence of input data and previous states. In fact, a deeper observation into systems and applications we are dealing with daily, shows that almost all of them can be modeled as such, e.g. all logic circuits from a simple AND gate to a supercomputer, diagnosis systems, assembly lines of factories, elevators, controllers, etc. On the other hand, in many such applications including system diagnosis, classification problems, automatic language understanding there is some kind of vagueness in the system, which makes it difficult to make a sharp diagnosis or decision. Today, however, there has been little work in building state system applications that incorporate uncertainty in their operation.; In this dissertation, we present the newly developed paradigm of General Fuzzy Automata (GFA) and show how it can be applied as a useful modeling tool to real-world problems. We will discuss the motivations of GFA development and show the trend of this development, and reveal its capabilities which handle the above requirements elegantly.; Our development of GFA stems from the fact that, in our efforts to use fuzzy automata formalisms as a modeling tool, we discovered some consequential limitations that complicated or prevented their application to real-world problems. This shortage was apparent, in spite of the long history of research in fuzzy automata.; We identified the following limitations of the existing formalisms and proposed the GFA to remedy them: (1) Membership assignment to active states. (2) Handling the multi-membership states conveniently. (3) Output mapping and significance of final states. (4) The lack of methodologies which enable us to define and analyze the continuous operation of fuzzy automata in a reasonable amount of time. (5) The lack of a general paradigm that can represent the existing formalisms. (6) The lack of a formalism that is more easily applicable to real-world problems.; GFA are not only very broad and general, but also can be applied to real-world problems more efficiently and more elegantly. In this dissertation, we will show the generality of GFA, and illustrate how it can model some applications nicely and insightfully. Therefore, another important contribution of this thesis, is to show how the new formalism of GFA can be readily applied to two very different and practical problems: a mechanical control problem (fuzzy control of an inverted pendulum) and protein family identification.