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Towards a logic for a fuzzy logic controller

Authors: Hans Hellendoorn; Dimiter Driankov;

Towards a logic for a fuzzy logic controller

Abstract

Fuzzy control is based on fuzzy logic [3], and the core of a fuzzy logic controller (FLC) is a set of fuzzy conditional statements related by the dual notions of fuzzy implication and the so-called compositional rule of inference[2]. However, despite of the use of the logic-related concepts of fuzzy conditional statements, fuzzy implication, and the compositional rule of inference, all of these are used in a mixed declarative/procedural manner. That is, there is no clear distinction between the "declarative" part of a FLC (the fuzzy conditional statements) and the way this declarative knowledge is used in the inference component of a FLC (the compositional rule of inference). To be more specific, the compositionM rule of inference is defined directly on the extension (meaning) of a fuzzy conditional statement, rather than on its symbolic counterpart. Furthermore, the extension of a fuzzy conditional statement is constructed by applying a fuzzy implication operator on the extensions of its antecedent and consequent. Thus, a fuzzy implication is not any longer defined in terms of a function of the truth-values of the symbolic counterparts of the antecedent and the consequent. In this context, the declarative part of a FLC is nothing else but a collection of "propositions" (fuzzy conditional statements) represented via their extensions and thus yielding a set of equations. Then the inference amounts to "solving" such a system of equations. The clear consequence of all this is the complete lack of any syntactic representation of the declarative part of a FLC and hence, no underlying semantic characterization.

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citations
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
2
Average
Top 10%
Average
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