2021
DOI: 10.3390/app11041793
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Compact Fuzzy Systems Based on Boolean Relations

Abstract: This document presents some considerations and procedures to design a compact fuzzy system based on Boolean relations. In the design process, a Boolean codification of two elements is extended to a Kleene’s of three elements to perform simplifications for obtaining a compact fuzzy system. The design methodology employed a set of considerations producing equivalent expressions when using Boole and Kleene algebras establishing cases where simplification can be carried out, thus obtaining compact forms. In additi… Show more

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Cited by 6 publications
(14 citation statements)
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“…The neuro-fuzzy controller uses the structure of a compact fuzzy system based on Boolean relations such as that presented in [21], which can be used for the identification and control of dynamic systems. Fuzzy systems based on Boolean relations are based on a system design considering possible Boolean regions in the discourse universes; then this system is extended using fuzzy sets for implementation, making it possible to consider the operation of sensors and actuators present in the control system [22].…”
Section: Fuzzy Control Systemmentioning
confidence: 99%
See 2 more Smart Citations
“…The neuro-fuzzy controller uses the structure of a compact fuzzy system based on Boolean relations such as that presented in [21], which can be used for the identification and control of dynamic systems. Fuzzy systems based on Boolean relations are based on a system design considering possible Boolean regions in the discourse universes; then this system is extended using fuzzy sets for implementation, making it possible to consider the operation of sensors and actuators present in the control system [22].…”
Section: Fuzzy Control Systemmentioning
confidence: 99%
“…In this work, the designed neuro-fuzzy controller uses the structure of a compact fuzzy system based on Boolean relations as presented in [21], which can be used for the identification and control of dynamic systems. Neuro-fuzzy systems based on Boolean relations are founded in a system design considering possible Boolean regions in the universe discourse, then being extended using fuzzy sets for implementation [22].…”
Section: Introductionmentioning
confidence: 99%
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“…The fuzzy controller uses the compact structure presented in [24] that allows having an equivalence with a linear controller (in discrete time) using fuzzy sets to model the actions of direct inputs and the controller feedback. The general scheme of the control system can be seen in Figure 4.…”
Section: Fuzzy Controllermentioning
confidence: 99%
“…For the design of compact fuzzy controllers, linear control strategies are considered as a reference: Considering the presented in [24], the compact fuzzy controllers are implemented considering Equation ( 24) associated with Figure 6, having the following expression:…”
Section: Implementation Of Compact Fuzzy Controllersmentioning
confidence: 99%