FUZZY LOGIC INTRODUCTION

INTRODUCTION
Fuzzy Logic was originally developed in the early 1960’s by Professor
Lotfi Zadeh, who claimed for a new kind of computational paradigm capable
of modeling the own uncertainness of human reasoning. In 1965, Zadeh
published the first ideas on fuzzy sets, the key concept in Fuzzy Logic (FL).
The acceptance of this soft-computing technique by the highly
"deterministic" scientific community was not immediate. At the beginning,
the most popular applications of Fuzzy Logic were found in the domain of
Control System. On one hand, many conservative engineers in such area
claim that Fuzzy Control does not convey to better solutions than the
classical ones and that Fuzzy Logic is just a marketing hype. On the other
hand, several non-specialist researchers misinterpret the fact that Fuzzy
Logic deals with uncertainness claiming that ”fuzzy systems reason as
humans do ”, as they use to say. This misunderstanding leads some people to
believe that Fuzzy Logic is a kind of cure-all that can solve any kind of
problem.
Away from any kind of fanaticism however, Fuzzy Logic is a rigorous
mathematical field .Fuzzy reasoning is nothing else than a
straightforward formalism for encoding human knowledge or common sense
in a numerical framework. In a Fuzzy Controller, human experience is
codified by means of linguistic if-then rules that build up a so-called Fuzzy
Inference System, which computes control actions upon given conditions.
Fuzzy Logic has been applied to problems that are either difficult to face
mathematically or applications where the use of Fuzzy Logic provides

improved performance and/or simpler implementations. One of its main
advantages lies in the fact that it offers methods to control non-linear plants,
known difficult to model.
Since the first reported application of Fuzzy Logic ,the number
of industrial and commercial developments, covering a wide range of
technological domains, has grown incessantly. Nowadays, countless
researchers from different areas are hardly working on the subject while
contributing with smart and interesting solutions for engineering. Table 1.1,
which summarizes the historical development of Fuzzy Logic, highlights
some of its most significant milestones as reported .In the last years, the astonishing growth of the Japanese industry in
producing a substantial number of consumer appliances using Fuzzy
Controllers put Fuzzy Logic on the focus of the scientific community. In
1990, the market of Fuzzy Logic based products was estimated nearly equal
to $2 billion . According to an investigation of the Market
Intelligence Research Co. of California, in 1991 Japan captured 80% of the
worldwide market. In 1992, the return in fuzzy products doubled with
respect to the previous year, whereas companies, like OMROM, held about
700 patents at that date. Germany, India, France, Korea, Taiwan and China
follow Japan in Fuzzy Logic R&D projects.

This economical success is said to be mainly due to the short
time-to-market needed by the development of Fuzzy Controllers for these
particular applications. However, this is true if
sufficient expertise coming from skilled designers is available
In early Fuzzy Logic applications, empiricism was the main method for
selecting the parameters of Fuzzy Controllers. Recent methods for automatic
identification of parameters in Fuzzy Systems from training data paved the
road to the application of Fuzzy Logic to systems where human knowledge
is not available.Most of these are inspired
from Artificial Neural Network learning techniques and lead to the
development of the so-called Neuro-Fuzzy Systems. The
integration of fuzzy and neural techniques is nowadays an active area of
research. It brings together the best features of Fuzzy Logic and Neural
Networks. It provides knowledge-based systems that can be adapted or
optimized according to sample data. In summary, a Neuro-Fuzzy System can
codify structured knowledge as a Fuzzy System while preserving the
adapting and learning capabilities of Neural Networks. To be effective, such
a Neuro-Fuzzy System must hold, at least, the following basic aspects

Succinct and appropriate representation of structured knowledge.
Tuning capabilities for parameters adaptation and identification.
Straightforward relationship between the above parameters and the
structured knowledge.
In this way, using a Neuro-Fuzzy System, the extraction of linguistic
rules from the adapted parameters also gives designers the possibility to
verify and/or rectify their prior knowledge . A clever
solution for this purpose was found by who managed the
representation of a Fuzzy System by means of a multi-layer feed-forward
network called ANFIS (Adaptive Network-based Fuzzy Inference System).
ANFIS is able to learn from data by using the gradient descent algorithm. A
remarkable feature of ANFIS is its fast learning rate when compared, for
instance, with feed-forward perceptrons Neural Networks. This is due to the
previous encoded knowledge before learning starts [Mend95].
Finally, let us summarize the major advantages and disadvantages of
Fuzzy Logic reported in the literature. The main features of Fuzzy Logic
encouraging its use are:
Fuzzy Logic provides a systematic framework to incorporate imprecise
information from a human expert. In this way, the control strategy of an

operator can be easily integrated in an automatic control system, for
instanceIn most Fuzzy Control problems, the exact model of the plant is not
needed for designing the controller provided that further adjustment can
be made during operation of the system.
A Fuzzy Inference System is a Universal Approximator. It allows
modeling non-linear functions of arbitrary complexity. One can create a
Fuzzy System to fit any training data set by means of adaptive
Neuro-Fuzzy techniques like ANFIS .Fuzzy Logic can be combined with classical control techniques .
A common trend that illustrates this is to use a Fuzzy Controller to
supervise a conventional adaptive controller, whose adapting strategy is
encoded into the rule base of the Fuzzy Controller.
In spite of its success and popularity, Fuzzy Control has some remarkable
drawbacks too:
In some cases, it is difficult to warrant the consistency of the rule base
.Conflictive rules may appear, specially when the input space
has a considerably large dimension.
There is no generalized criterion to formally demonstrate the system
stability. This has been addressed in particular cases only .
There is a lack of systematic methods to translate human knowledge into
the rule base. Moreover, the expert knowledge is sometimes incomplete
or vaguely defined. There is no clear-cut procedure for choosing the
suitable number of rules as far as the many factors involved .
Nonetheless, many researchers succeeded in automating the modeling
and optimization processes of Fuzzy Systems. A comprehensive work in this
area can be found in . In this, as an extension of the classical
System Identification methodology used for linear systems,a
three-step identification procedure is proposed:
Variables identification: means to identify the input variables, among a
set of candidates, that play an important role in the process to control.
Structure identification: means to identify the appropriate number of
rules and membership functions per input/output and the correct fuzzy
partition type (i.e. grid, tree or scatter partition).
Parameters identification: means to identify the proper shape and position
of the membership functions.