Equivalence in knowledge representation: automata, recurrent neural networks, and dynamical fuzzy systems

Giles, C. Lee; Omlin, Christian W.; Thornber, K.K.

doi:10.1109/5.784244

Cited by 63 publications

(35 citation statements)

References 52 publications

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“…2 and the FTS S given here. In the literature, there are a large number of formal description tools for dynamic fuzzy systems such as various fuzzy automata [1], [8], [12], [28], [34], [41], fuzzy Petri nets [6], [9], [31], fuzzy control systems [10], [15], [30], fuzzy discrete event systems [7], [13], [25], [33], neuro-fuzzy systems [17], and so on. In general, they are not FTSs, but it is possible to translate a system's description in one of these formalisms into the FTS representing its behavior.…”

Section: Fuzzy Transition Systemsmentioning

confidence: 99%

Bisimulations for Fuzzy-Transition Systems

Cao

Chen

Kerre

2011

IEEE Trans. Fuzzy Syst.

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Abstract-There has been a long history of using fuzzy language equivalence to compare the behavior of fuzzy systems, but the comparison at this level is too coarse. Recently, a finer behavioral measure, bisimulation, has been introduced to fuzzy finite automata. However, the results obtained are applicable only to finite-state systems. In this paper, we consider bisimulation for general fuzzy systems which may be infinite-state or infiniteevent, by modeling them as fuzzy transition systems. To help understand and check bisimulation, we characterize it in three ways by enumerating whole transitions, comparing individual transitions, and using a monotonic function. In addition, we address composition operations, subsystems, quotients, and homomorphisms of fuzzy transition systems and discuss their properties connected with bisimulation. The results presented here are useful for comparing the behavior of general fuzzy systems. In particular, this makes it possible to relate an infinite fuzzy system to a finite one, which is easier to analyze, with the same behavior.

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Section: Fuzzy Transition Systemsmentioning

confidence: 99%

Bisimulations for Fuzzy-Transition Systems

Cao

Chen

Kerre

2011

IEEE Trans. Fuzzy Syst.

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“…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.…”

Section: Introductionmentioning

confidence: 99%

Supervisory Control of Fuzzy Discrete Event Systems: A Formal Approach

Qiu¹

2005

IEEE Trans. Syst., Man, Cybern. B

171

109

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Fuzzy discrete event systems (DESs) were proposed recently by Lin and Ying [19], which may better cope with the real-world problems with fuzziness, impreciseness, and subjectivity such as those in biomedicine. As a continuation of [19], in this paper we further develop fuzzy DESs by dealing with supervisory control of fuzzy DESs. More specifically, (i) we reformulate the parallel composition of crisp DESs, and then define the parallel composition of fuzzy DESs that is equivalent to that in [19]; max-product and max-min automata for modeling fuzzy DESs are considered; (ii) we deal with a number of fundamental problems regarding supervisory control of fuzzy DESs, particularly demonstrate controllability theorem and nonblocking controllability theorem of fuzzy DESs, and thus present the conditions for the existence of supervisors in fuzzy DESs; (iii) we analyze the complexity for presenting a uniform criterion to test the fuzzy controllability condition of fuzzy DESs modeled by max-product automata; in particular, we present in detail a general computing method for checking whether or not the fuzzy controllability condition holds, if max-min automata are used to model fuzzy DESs, and by means of this method we can search for all possible fuzzy states reachable from initial fuzzy state in max-min automata; also, we introduce the fuzzy n-controllability condition for some practical problems; (iv) a number of examples serving to illustrate the applications of the derived results and methods are described; some basic properties related to supervisory control of fuzzy DESs are investigated. To conclude, some related issues are raised for further consideration.

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“…Neural networks are characterized into feedforward and recurrent neural networks. Unlike feedforward neural networks, recurrent neural networks contain feedback connections and have shown to learn and represent dynamical systems (Giles et al, 1999). Neural networks are capable of performing tasks that include pattern classification, function approximation, prediction or forecasting, clustering or categorization, time series prediction, optimization, and control.…”

Section: Artificial Neural Networkmentioning

confidence: 99%

Renosterveld Conservation in South Africa: A Case Study for Handling Uncertainty in Knowledge-Based Neural Networks for Environmental Management

Chandra

Knight²,

Omlin³

2009

J ENV INFORM

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ABSTRACT. This work presents an artificial intelligence method for the development of decision support systems for environmental management and demonstrates its strengths using an example from the domain of biodiversity and conservation biology. The approach takes into account local expert knowledge together with collected field data about plant habitats in order to identify areas which show potential for conserving thriving areas of Renosterveld vegetation and areas that are best suited for agriculture. The available data is limited and cannot be adequately explained by expert knowledge alone. The paradigm combines expert knowledge about the local conditions with the collected ground truth in a knowledge-based neural network. The integration of symbolic knowledge with artificial neural networks is becoming an increasingly popular paradigm for solving real-world applications. The paradigm provides means for using prior knowledge to determine the network architecture, to program a subset of weights to induce a learning bias which guides network training, and to extract knowledge from trained networks; it thus provides a methodology for dealing with uncertainty in the prior knowledge. The role of neural networks then becomes that of knowledge refinement. The open question on how to determine the strength of the inductive bias of programmed weights is addressed by presenting a heuristic which takes the network architecture and training algorithm, the prior knowledge, and the training data into consideration.

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Equivalence in knowledge representation: automata, recurrent neural networks, and dynamical fuzzy systems

Abstract: Neurofuzzy systems-the combination of artificial neural networks with fuzzy logic-have become useful in many application

Cited by 63 publications

References 52 publications

Bisimulations for Fuzzy-Transition Systems

Bisimulations for Fuzzy-Transition Systems

Supervisory Control of Fuzzy Discrete Event Systems: A Formal Approach

Renosterveld Conservation in South Africa: A Case Study for Handling Uncertainty in Knowledge-Based Neural Networks for Environmental Management

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