NDLI: Theoretical analysis of crisp-type fuzzy logic controllers using various t-norm sum-gravity inference methods

Content Provider	IEEE Xplore Digital Library
Author	Cheng-Liang Chen Sheng-Nan Wang Chung-Tyan Hsieh Feng-Yuan Chang
Copyright Year	1993
Abstract	The input-output parametric relationship of a class of crisp-type fuzzy logic controllers (FLCs) using various t-norm sum-gravity inference methods is studied. Four most important t-norms are used to calculate the matching level of each control rule and the explicit mathematical forms of reasoning surfaces obtained by using these four t-norms are addressed. Reasoning surfaces of these crisp-type FLCs are proved to be composed of a two-dimensional multilevel relay no matter which t-norm is used and a local position-dependent nonlinear compensator with output pattern influenced by the t-norms is selected. By analyzing the intrinsic operation of the four t-norms, the authors find that both standard intersection and algebraic product are suitable operators to perform the inference of the FLC. However, bounded difference and drastic intersection are disqualified because they cannot satisfy some important criteria. A measure of relative degree-of-nonlinearity is defined to examine the output figures of these crisp-type FLCs. The ultimate behavior of these crisp-type FLCs as the number of linguistic terms approaches infinity is also explored. The local stability criteria for the proportional-integral (PI)-type fuzzy control systems and the natural global stability characteristic for the proportional-derivative (PD)-type fuzzy control systems are also examined.
Sponsorship	IEEE Computational Intelligence Society
Starting Page	122
Ending Page	136
Page Count	15
File Size	778123
File Format	PDF
ISSN	10636706
Volume Number	6
Issue Number	1
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	1998-02-01
Publisher Place	U.S.A.
Access Restriction	One Nation One Subscription (ONOS)
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Fuzzy logic Fuzzy control Automatic control Control systems Stability criteria Mathematical analysis Two dimensional displays Relays Performance analysis H infinity control
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Artificial Intelligence Control and Systems Engineering Computational Theory and Mathematics

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