Modeling of Control Functions by Fuzzy Controllers

Peter Bauer; Erich Klement; Bernhard Moser; Albert Leikermoser

Modeling of Control Functions by Fuzzy Controllers

Peter Bauer
, Erich Klement
, Bernhard Moser
, Albert Leikermoser

Institute for Mathematical Methods in Medicine and Data Based Modeling

Research output: Chapter in Book/Report/Conference proceeding › Chapter › peer-review

Abstract

Mathematical interpretations of the most important types of fuzzy controllers, the Mamdani and the Sugeno controller (under some hypotheses, the latter is shown to be a special case fo the former), are given from three different points of view: The Mamdani controller is interpreted in terms of equality relations and is shown to provide a solution of a certain relational equation (if the rulebase consists of one rule only), and the Sugeno controller is used to reproduce control functions with one-dimensional input or if non-Cartesian inputs are admissable, and to approximate quite general control functions with higher-dimensional input.

Original language	English
Title of host publication	Theoretical Aspects of Fuzzy Control
Number of pages	16
Publication status	Published - 1995

Fields of science

101 Mathematics
101004 Biomathematics
101027 Dynamical systems
101013 Mathematical logic
101028 Mathematical modelling
101014 Numerical mathematics
101020 Technical mathematics
101024 Probability theory
102001 Artificial intelligence
102003 Image processing
102009 Computer simulation
102019 Machine learning
102023 Supercomputing
202027 Mechatronics
206001 Biomedical engineering
206003 Medical physics
102035 Data science

Cite this

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title = "Modeling of Control Functions by Fuzzy Controllers",

abstract = "Mathematical interpretations of the most important types of fuzzy controllers, the Mamdani and the Sugeno controller (under some hypotheses, the latter is shown to be a special case fo the former), are given from three different points of view: The Mamdani controller is interpreted in terms of equality relations and is shown to provide a solution of a certain relational equation (if the rulebase consists of one rule only), and the Sugeno controller is used to reproduce control functions with one-dimensional input or if non-Cartesian inputs are admissable, and to approximate quite general control functions with higher-dimensional input.",

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AU - Klement, Erich

AU - Moser, Bernhard

AU - Leikermoser, Albert

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M3 - Chapter

BT - Theoretical Aspects of Fuzzy Control

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