A fuzzy finite state machine implementation based on a neural fuzzy system

Abstract

The outputs of a feedforward neural network depend on the present inputs only. Difficulties arise when a solution requires memory in such applications as speech processing, seismic signal processing, language processing, and spatiotemporal signal processing. For such applications, the outputs are not only the functions of the present inputs but the present states (or the past inputs and the outputs) as well. The fuzzy finite state machines can be effectively used in these applications. The aim of this study is to show that a fuzzy finite state machine can be realized using our neural fuzzy system. In a fuzzy finite state machine, the output and the next state depend on the input and the present state which in turn is a function of the previous inputs. To accommodate the memory requirement, the feedfonvard structure of the neural fuzzy system is changed to a recurrent architecture by adding a feedback loop from the output layer to the input layer during the recall mode. The validity of the approach is verified with a temporal pattern matching experiment. and govem the transitions of the FFSM between the fuzzy states. The fuzzification of FSM results in data reduction (less memory to implement the FFSM) as well as more robust operation (less susceptible to system parameter changes or to noise) as stated in [5].Also, with this approach, writing a new program is not required since the ANN of NeuFuz is trained with the state transition table and implementation of a new FFSM is achieved directly with the training data. This increases the reliability. Furthermore, the suggested approach facilitates the design and implementation of a FFSM using a microcontroller.The FFSM concept is introduced in the next section. In Section 3, a brief description of NeuFuz is given. An illustrative temporal pattem matching experiment is carried out in Section 4 to verify the validity of our approach. Section 5 contains the conclusions. A Fuzzy Finite State Machine 1. IntroductionIn our previous works, it has been shown that the artificial neural networks (ANN) can be combined with fuzzy logic systems to achieve high performance and low cost solutions [ll- [3]. In this work, the feedfonvard structure of our neural fuzzy system (NeuFuz) is changed to a recurrent architecture by adding a feedback loop from the output layer to the input layer during the recall mode. With this modification, we demonstrate that NeuFuz can be used to implement a Fuzzy Finite State Machine (FFSM).A FFSM is an extension of a conventional FSM. The difference is that the inputs, the present states and the next states are represented using fuzzy sets in contrast with the crisp inputs and the states of a traditional crisp FSM. The output function and the state transition function of the FSM are replaced by the recurrent fuzzy rules which determine the outputs A FFSM is a synchronous sequential machine and it can be defined as a quintuple following the crisp FSM definition in [4]:where I, 0, and S are finite, nonempty sets of fuzzy inputs, fuzzy outputs, and fuzzy sta...

Fuzzy finite-state automata can be deterministically encoded into recurrent neural networks

“…The synthesis method proposed in [20] uses digital design technology to implement fuzzy representations of states and outputs. In [59], the implementation of a Moore machine with fuzzy inputs and states is realized by training a feedforward network explicitly on the state transition table using a modified backpropagation algorithm. The fuzzification of inputs and states reduces the memory size that is required to implement the automaton with a microcontroller (e.g., antilock braking systems).…”

“…The fundamentals of FFA's have been in discussed in [16], [48], [64] without presenting a systematic method for machine synthesis. Neural network implementations of fuzzy automata have been proposed in the literature [20], [21], [29], [59]. The synthesis method proposed in [20] uses digital design technology to implement fuzzy representations of states and outputs.…”

Supervisory Control of Fuzzy Discrete Event Systems: A Formal Approach

“…In practice, fuzzy finite automata and fuzzy languages have been used to solve meaningful problems such as intelligent interface design [5], clinical monitoring [30], neural networks [33,4], and pattern recognition by DePalma and Yau (see [3,21] for the details). As well, fuzzy finite automata can be viewed as a type of formal models for computing with words [37,36] when the inputs are strings of words rather than symbols.…”

A formal model of computing with words

“…In the early of 1990s, the potential of fuzzy automata as design tools for modeling a variety of uncertain dynamic systems has been exploited; for example, see [6]. Furthermore, various methods for synthesis, analysis, specification and implementation of fuzzy automata have been proposed; for examples, see [7], [3], [4], and [11]. Recently, Giles, Omlin, and Thornber [2], [8] presented a synthesis method for mapping fuzzy automata into recurrent neural networks.…”