Properties and Behaviours of Fuzzy Cellular Automata

Properties and Behaviours of Fuzzy Cellular Automata

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dc.contributor.author Betel, Heather
dc.date.accessioned 2012-05-14T13:19:34Z
dc.date.available 2012-05-14T13:19:34Z
dc.date.created 2012 en_US
dc.date.issued 2012-05-14
dc.identifier.uri http://hdl.handle.net/10393/22858
dc.description.abstract Cellular automata are systems of interconnected cells which are discrete in space, time and state. Cell states are updated synchronously according to a local rule which is dependent upon the current state of the given cell and those of its neighbours in a pre-defined neighbourhood. The local rule is common to all cells. Fuzzy cellular automata extend this notion to systems which are discrete in space and time but not state. In this thesis, we explore fuzzy cellular automata which are created from the extension of Boolean rules in disjunctive normal form to continuous functions. Motivated by recent results on the classification of these rules from empirical evidence, we set out first to show that fuzzy cellular automata can shed some light on classical cellular automata and then to prove that the observed results are mathematically correct. The main results of this thesis can be divided into two categories. We first investigate the links between fuzzy cellular automata and their Boolean counter-parts. We prove that number conservation is preserved by this transformation. We further show that Boolean additive cellular automata have a definable property in their fuzzy form which we call self-oscillation. We then give a probabilistic interpretation of fuzzy cellular automata and show that homogeneous asymptotic states are equivalent to mean field approximations of Boolean cellular automata. We then turn our attention the asymptotic behaviour of fuzzy cellular automata. In the second half of the thesis we investigate the observed behaviours of the fuzzy cellular automata derived from balanced Boolean rules. We show that the empirical results of asymptotic behaviour are correct. In fuzzy form, the balanced rules can be categorized as one of three types: weighted average rules, self-averaging rules, and local majority rules. Each type is analyzed in a variety of ways using a range of tools to explain their behaviours. en_US
dc.language.iso en en_US
dc.subject cellular automata en_US
dc.subject continuous cellular automata en_US
dc.subject fuzzy cellular automata en_US
dc.title Properties and Behaviours of Fuzzy Cellular Automata en_US
dc.type Thèse / Thesis en_US
dc.faculty.department Science informatique et génie électrique / Electrical Engineering and Computer Science en_US
dc.contributor.supervisor Flocchini, Paola
dc.contributor.supervisor Karmouch, Ahmed
dc.embargo.terms immediate en_US
dc.degree.name PhD en_US
dc.degree.level doctorate en_US
dc.degree.discipline Génie / Engineering en_US

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