International Journal of Dynamics and Control
https://doi.org/10.1007/s40435-020-00622-1
A survey: fuzzify parameters and membership function in electrical
applications
Mehdi Zangeneh
1
· Ebrahim Aghajari
1
· Mehdi Forouzanfar
1
Received: 25 February 2020 / Revised: 6 March 2020 / Accepted: 10 March 2020
© Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract
The unique simplicity and the needless for a mathematical model of the fuzzy logic controller along with the variety of abilities
such as good respond to complex and high-order systems have made it widely used in electrical engineering. Meanwhile, the
influence of fuzzification and defuzzification parameters selection on the quality of the controller performance improvement
is obvious. The selection of fuzzy controller parameters is based on the nature of the system and the designer’s knowledge and
experience and heretofore no organized method for selecting membership functions has been provided. Given the significance
of the issue, this study provides an extensive overview of the fuzzy parameters selection and presents the experiences of dozens
of designers in the field of electrical systems. Finally, a summary is presented based on researches for the applicable selection
of membership functions in electrical engineering.
Keywords Membership functions · Fuzzy logic · Fuzzy inference · Electrical systems
1 Introduction
The fuzzy set theory was first introduced by Professor Lot-
fizadeh in 1965 [1]. Since the introduction of this theory,
tens of thousands of scientific articles have been published
by various scholars on the subject. These articles illustrate
the widespread theoretical and practical application of this
theory. This theory, furthermore, has been used extensively
for controlling processes in various industries. The reasons
for this include simplicity of execution, high adaptability, low
sensitivity to system fluctuations and no need for mathemati-
cal models [2, 3]. In the studied articles, sometimes a method
based on fuzzy logic is used exclusively. Sometimes, more-
over, this method is used along with other methods, such
as Classic PID controllers, sliding mode, neural networks,
genetic algorithms, Particle swarm optimization algorithm,
and other methods.
B Ebrahim Aghajari
aghajari@iauahvaz.ac.ir; ebrahim.aghajar@gmail.com
Mehdi Zangeneh
m.zangeneh.au@gmail.com
Mehdi Forouzanfar
mehdi.forouzanfar@yahoo.com
1
Department of Electrical Engineering, Ahwaz Branch,
Islamic Azad University, Ahwaz, Iran
Since fuzzy logic is mainly used in the systems control
section, researchers have used different control combinations
based on fuzzy logic. Based on the articles reviewed, the
design of the controllers is only done based on fuzzy logic
or by its combination with other control methods, such as
classical controllers, sliding mode, neural networks, or evo-
lutionary optimization algorithms.
Each FIS is essentially composed of five parts. For the
proper function of a FIS, all these five parts must be selected
correctly and accurately. One of the most important parts dis-
cussed in this article, however, is the issue of database type
selection. The database includes information about member-
ship functions, fuzzy sets and their domains. Generally, the
choice of the type of membership functions, the number,
and domain of them are selected by trial and error or by
the designer’s experience and knowledge. Normally, the out-
put responses are improved using conventional optimization
techniques [4]. In the absence of optimization techniques,
the selection of database information is done at two levels. In
the first step, according to the previous experience of control
systems, an initial choice is made for membership functions,
their number and domain. In the next step, by examining the
FIS results in different working conditions, the initial selec-
tion is gradually improved to achieve the desired performance
of the fuzzy control system [5].
Membership functions represent the behavior of a phys-
ical variable, so they must be chosen in a way that is
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