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APPLICATIONS OF FUZZY LOGIC
SONEY SOMACHAN
MSc. Mathematics

PREFACE
Over the years this books has earned a name for itself because of its
completeness of coverage and simplicity of presentation. Fuzzy logic plays an
important role in mathematics. The book is intended to familiarize the reader with the
fuzzy logic in medicine, in domestic goods, and in engineering. Chapter 1 contains the
fuzzy logic in medicine, and bioinformatics. Chapter 2 contains fuzzy logic in
domestic goods. Chapter 3 contains fuzzy logic in engineering and other applications.

CONTENT
Chapter Title Page No.
Chapter 1 Fuzzy logic in medicine and bioinformatics 1
Chapter 2 Fuzzy logic in domestic goods 5
Chapter 3 Fuzzy logic in engineering &other applications 11

CHAPTER - 1
FUZZY LOGIC IN MEDICINE AND BIOINFORMATICS
1.1 Fuzzy logic in Medicine
The diagnosis of disease involves several levels of uncertainty and imprecision
and it is inherent to medicine. A single disease may manifest itself quite differently,
depending on the patient, and with different intensities. A single symptom may
correspond to different diseases. On the other hand, several diseases present in a
patient may interact and interfere with the usual description of any of the diseases. On
the other hand, several diseases present in a patient may interact and interfere with the
usual description of any of the diseases the best and most precise description of
disease entities uses linguistic terms that are also imprecise and vague. Moreover, the
classical concept of health and disease are mutually exclusive and opposite. However,
same recent approaches consider both concepts as complementary processes in the
same continuum. To read with imprecision and uncertainty, we have at our disposal
fuzzy logic. Fuzzy logic interduces partial truth values, between true and false.
According to Aristotelian logic, for a given proposition or state we only have
two logical values; true-false, black-white, 1-10. Thus, in many practical situations, it
is convenient to consider intermediate logical values. Let us show this with a very
simple medical example. Consider the statement “you are healthy”. It is true if you
have only a broken nail? Is it false if you have terminal cancer? Everybody is healthy
to some degree h and i11 to some degree i. if you are totally healthy, then of course
h=1, i=). Usually everybody has some minor health problems and h<1, but h+i=1.
Since uncertainty is inherent in fields such as medicine and massive data in
bioinformatics, fuzzy logic takes into account such uncertainty, fuzzy set theory can
be considered as a suitable formalism to deal with the imprecision intensic to many
biomedical and bioinformatics problems. Fuzzy logic is a method to center precise

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what is imprecise in the world of medicine. Several examples and illustrations are
made mentioned below.
The complexity of medical practice makes traditional quantitative approaches
of analysis inappropriate. In medicine the lack of information’s and its imprecision
and many times contradictory nature are facts. The sources of uncertainty can be
classified as follows.
1. Information about the patient.
2. Medical history of the patient, which is usually supplied by the patient, which
is usually, supplied by the patient and /or his/her family. This is usually highly
subjective and imprecise.
3. Physical examination- The physician usually obtains objective data, but in
some case the boundary between normal and pathological status is not sharp.
4. Result of laboratory and other diagnostic tests, but they are also subject to
some mistakes and even to improper behavior of the patient prior to the
examination.
5. The patient may include stimulated, exaggerated under stated symptoms, or
may even fail to mention some of them.
6. We stress the paradox of the growing number of mental disorders versus the
absence of a natural classification. The classification is critical (i.e.,
borderline) cases is difficult, particularly when a categorical system of
diagnosis is Fuzzy logic plays an important role in medicine. Some examples
showing that fuzzy logic crosses many disease groups are following.
1. To predict the response to treatment with citalopram in alcohol dependence.
2. To analyze diabetic neuropathy and to detect early diabetic retinopathy.
3. To determine appropriate lithium dosage.
4. To calculate volumes of brain tissue from magnetic resonance imagining and
to analyze MRI data.

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5. To characterize stroke subtypes and co-existing causes of ischemic stroke.
6. To prove decision-making in eradication therapy.
7. To control hypertension during anesthesia.
8. To determine flexor-tendon repair techniques.
9. To delete breast cancer, lung cancer or prostate cancer.
10. To assist the diagnosis of central nervous systems tumors (astrocytic tumors).
11. To visualize nerve fibers in the human brain.
12. To represent quantitative estimates of drug use.
13. Many other areas of application, to mention a few are
a. To study fuzzy epidemics
b. To make decision in nursing.
1.2 Fuzzy logic in Bioinformatics
Bioinformatics derives knowledge from computer analysis of biological data.
This data can consist of the information stored in the genetic code, and also
experimental result (and hence imprecision) from various sources, patient statistics,
and scientific literature. Bioinformatics combines computer science, biology, physical
and chemical principles, and tools for analysis end modeling of large sets of
biological data the managing of chronic diseases, the study of molecular computing,
cloning and the development of training tools of bio computing system.
Bioinformatics is a very active and attractive research field with a high impact in new
technological development.
Fuzzy logic and fuzzy technology are now frequently used in bioinformatics.
The following are some examples.
1. To increase the flexibility of protein motifs.
2. To study differences between polynucleotide’s.
3. To analysis experimental expression data using fuzzy adaptive resonance
theory.
4. DNA sequencing using genetic fuzzy systems.

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5. To cluster genes from microarray data.
6. To predict proteins sub cellular locations from their dipeptide composition
using fuzzy k-nearest neighbors algorithm.
7. To stimulate complex traits influenced by genes with fuzzy valued effects in
pedigreed populations
8. To attribute cluster membership values to genes applying a fuzzy partitioning
method, fuzzy C-means.
9. To map specific sequence patterns to putative functional classes. Since
evolutionary comparison leads to efficient functional characterization of
hypothetical proteins.
10. To analyze gene expression data.
11. To unravel functional and ancestral relationships between proteins via fuzzy
alignment methods, or using a generalized radial basics functional neural
network architecture that generates fuzzy classification rules.
12. To analyze the relationships between genes and decipher a genetic network.
13. To process complementary deoxyribonucleic acid (CDNA) microarray
images. The procedure should be automated due to the large number of spots
and it is achieved using a fuzzy vector filtering framework.
14. To classify amino acid sequence in to different super amities.
1.3 Fuzzy logic in predicting genetic traits
Genetic traits are a fuzzy situation for more than one reason. There is the fact
that many traits can not be linked to a single gene. So only specific combinations of
genes will create a given trait. Secondly, the dominant and recessive genes that are
frequently illustrated with pun net squares are sets in fuzzy logic. The degree of
membership in those sets is measured by the occurrence of a genetic trait. In clear,
cases of dominant and recessive genes, the possible degree in the sets are pretty strict.
Take, for instant eye color. Two brown eyed parents produce three blue-eyed
children. Brown is dominant, so each parent must have the recessive gene within
them. Their membership in the blue eye set, so that trait actually comes through.

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According to the punnet square, 25% of their children should have blue eyes, with the
other 75% having brown.

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CHAPTER-2
FUZZY LOGIC IN DOMESTIC GOODS
2.1 Fuzzy logic in washing machine
Washing machines are a common feature today in Indian household. The most
important utility a customer can drive from a washing machine is that it saves the
effort to put in brushing, agitating and washing the cloth. Most of the people could not
have noticed that different type of cloth need different amount of washing time which
depends directly on the type of dirt, cloth quality etc. The washing machine that are
used. Today serves all the purpose of washing, but which cloths needs what amount of
agitation time is a business which has not been dealt with properly. In most of the
case either the user is compelled to give all the cloth same agitation or is provided
with a restricted amount of control. The thing is that the washing machines used are
not as automatic as they should be and can be.
When one uses a washing machine, the person generally select the length of
wash time based on the amount of clothes wish to wash and type and degree of dirt
cloths have to automate this process, we use sensors to detect these parameters
volume of clothes, degree and type of dirt. The wash time is then determined from
this data. Unfortunately, there is no easy to formulate a precise mathematical
relationship between volume of clothes and dirt and length of wash time required.
Consequently, this problem has remined unsolved until very recently. Conventionally,
people simply set wash times by hand and form personal trial and error experience.
Washing machines were not as automatic as they could be. The sensor system
provides external input signal into the machine from which decision can be made. It is
the controller’s responsibility to make the decision and to signal the outside world by
some form of output. Because the input/output relationship is not clear, the design of a
washing machine controller has not in the past lent itself to traditional methods of
control designs. We address this design problem using fuzzy logic. Fuzzy logic has
been used because a fuzzy logic controlled washing machine controller gives the
correct wash time even though a precise model of the input/output relationship is not
available.

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The two inputs are : 1. Degree of dirt
2. Type of dirt
FUZZY CONTROLLER
Linguistic Input
Output
Type of dirt
Wash time
Dirtiness of clothes
Figure 1. Basic Block Diagram of the process
Figure 1 shows the basic approach to the problem. The fuzzy controller takes
two inputs, process the information and output a wash time. How to get these two
inputs can be left to the sensoes. The working of the sensoes is not a matter of concern
in this paper. We assume that we have these input at our hand. Any way the two
stated points need a bit of introduction which follows. The degree of dirt is
determined by transparency of the wash water. The dirtier the clothes, less transparent
the water being analyzed by the sensoes is. On the other hand, type of dirt is
Fuzzy arithematic &
Applying criterion
Defuzzyfication
Fuzzificztion

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determined by the time of saturation, the time it takes to reach saturation. Saturation is
a point, at which there is no more appreciable change in the color of the water. Degree
of dirt determines the quality of dirt. Greasy cloths, for example, take longer for water
transparency because grease is less soluble in water than other forms of dirt. Thus a
fairly straight forward sensoe system can provide us the necessary input for our fuzzy
controller.
The decision which the fuzzy controller makes is derived from the rules which
are stored in the data base. These are stored in a set of rules. Basically the rules are if-
then statements that are intuitive and easy to understand, since they are nothing but
common English statements. Rules used in this paper are derived from common
sense, data taken from typical home use, and experimentation in a controlled
environment.
Before the details of the fuzzy controller are dealt with, the range of possible
values for the input and input variables are determined. These (in language of fuzzy
sets theory) are values to the fuzzy values, so that the operations can be applied on
them. Values of the input variables degree of dirt and type of dirt are normalized over
the domain of optional sensor.
The sets of rules used here to derive the output are
1. IF dirtiness of clothes is large and type of dirt is Greasy then wash time is very
long.
2. IF dirtiness of clothes is medium and type of dirt is Greasy then wash time is
long.
3. IF dirtiness of clothes is small and type of dirt is Greasy then wash time is
long.
4. IF dirtiness of clothes is large and type of dirt is Medium then wash time is
long.
5. IF dirtiness of clothes is medium and type of dirt is medium then wash time is
medium.
6. IF dirtiness of clothes is small and type of dirt is Medium then wash time is
medium.

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7. IF dirtiness of clothes is large and type of dirt is not greasy then wash time is
medium.
8. IF dirtiness of clothes is medium and type of dirt is not greasy is short.
9. IF dirtiness of clothes is small and type of dirt is not greasy then wash time is
very short.
The rules too have been defined in imprecise sense and hence they too are not
crisp but fuzzy values. The two input parameters often being road from the sensors
are fuzzified as per the membership function of the respective variables. These in a
additions with the membership function curve are utilized to come to a solution (using
some criteria). At last the crisp value of the wash time is obtained as an answer.
The sensors sense the input valued and using the above model the inputs are
fuzzified and then by using simple fuzzy set operation the output fuzzy function is
obtained and using the criteria the output value for wash time is obtained.
By the use of fuzzy logic control we have been able to obtain a wash time for
different type of dirt and different degree of dirt. The conventional method required
the human intereption to decide upon what should be the wash time for different
cloths. In other words this situation analysis ability has been incorporated in the
machine which makes the machine much more automatic and represents the decision
taking power of the new arrangement.
2.2 Air Conditioner
The task of dehumidification and temperature decrease goes hand in hand in
case of conventional Ac.once target temperature is reached Ac seizes to function like
a dehumidifier. Also complex interactions between user preference, actual room
temperature and humidity level are very difficult to model mathematically. But in this
work this limitation has been taken in to cogitation and overcome to a great extent
using fuzzy logic to represent the intricate influences of all these parameters. The
optimal limits of control zone, typically marked at the temperature of 250
and dew
point 110
C, are used as the target. Conventional AC system control humidity unlike
in its on way without giving the users any scope for changing the set point for the
target humidity unlike the scope it offers to change the set point for the target
temperature through a thermostat. This causes significant level of flexibility as well as
efficiency loss especially in hot and humid countries like India. For instants of higher

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humidity level (say at dew point 180
C) an occupant may perceive same comfort level
at 220
C as he would perceive at 260
C at dew point 150
C. this translates to huge
energy and monitory saving in terms of reduced compressor/fan duty cycle. In the
developed scheme, the censor captured temperature, user temperature preference and
humidity reading are fuzzified. These are used to decide fuzzy qualifier, which is
decoded into a crisp value that in turn control different aspect of the AC in the
problem dew point(Td) temperature is used to measure humidity instead of relative
humidity (RH), this is because RH function of both temperature and moisture-content
while Td is a function of moisture content only. Hence it become very easy to model
comfort level on the basis of Td.
Slight modification air circulation method around beat exchanges allow a
conventional AC. To function anywhere between normal AC mode and dehumidifier
only mode. In dehumidifier only mode chilled air is totally passed through hot side of
heat exchange so that AC dehumidifies without any change input in output
temperature. The problem takes three variables into consideration.
1. User temperature preference (180
C ~300
C continues control)
2. Actual room temperature
3. Room dew point temperature
User temperature is subtracted from actual room temperature before being sent
for fuzzyfication. Fuzzy arithmetic and criterion is applied on these variables and final
result is defuzzfied to get following crisp results.
1. Compressors
2. Fan speed
3. Mode of operation
4. Fin direction

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User temperature
setting
Actual Room
Temperature
Room Dewpoint perati
Temperature
Basic block diagram of controller
2.3 Vacuum cleaner
Characteristics of floor and the amount of dust are sensed by an in feared
sensor, and the microprocessor selects the appropriate power by fuzzy control
according to these characteristics. The floor characteristics include the type
[hardwood, cement, tile, carpet, softness carpet, thickness etc]. the changing pattern of
the amount of dust padding through the in feared sensor is established the appropriate
setting of the vacuum head and the power of the motor, using a fuzzy control scheme.
Red and green lamps of the vacuum cleaner shoe the amount of dust left on the floor.
Fuzzificztion
Fuzzyarithematic&
Applyingcriterion
Defuzzificztion
Compressor
Speed
Fan Speed
Operation
mode
Fin Direction

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CHAPTER – 3
FUZZY LOGIC IN ENGINEERING AND OTHER APPLICATION
3.1 Fuzzy logic in civil engineering
Civil engineering, when compaired with other engineering displines is
fundamentally different. This is because each civil engineering project id, by and
large; unique, hence there is almost never a enhance to test a prototype, as in other
engineering displines.
The most fundamental knowledge of the civil engineer concerns the material
employed. How they are made, shaped and assembled; how consistent they are to
stress, weather & use; & how they may fail. Before scientific knowledge regarding
these aspects of materials was available, civil engineering was a craft. Design
decisions were made by subjective judgments based on experience of the designs of
“rules of thumb” derived by accumulating design experience over the continues. In
spite of the scientific knowledge now available, great uncertainty concerning the
application of the knowledge to actual design problems still remains, primarily due to
the uniqueness of each design problem in civil engineering of the use of subjective
judgments and relevant “rules of thumb” is unavoidable. This seems to explain why
civil engineers so quickly found a strong affinity with fuzzy set theory. One important
category of problem in civil engineering for which fuzzy set theory has already
proven useful consists of problems of assigning or evaluating existing constructions.
Typically examples of these problem are the assessment of quality of highway
pavements, and the assessment of damage in building after an earthquake.
Let Ci, Wi denote respectively, the fuzzy no. expressing the structural
significance of component i of let n denote the no of components assessed. Then the
fuzzy set expressing the overall evolution A, is defined by the formula.
1
n
t
wici
=
∑
1
p
n
t
w
=
∑
A=

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Several applied areas of fuzzy set theory are found to be in civil engineering.
They include fuzzy decision making, approximate reasoning and fuzzy control e.g.
(to the control of traffic in cities).
3.2 Fuzzy logic in Mathematical Engineering
Classical mathematics is not equipped to deal with imprecise descriptions. As
a consequence, it has been difficult to provide the designer with computational tools
for the early stages of the design process. It was realized account the mid-19.80,
primarily in the context mechanical engineering design that fuzzy set theory is
eminently suited to facilitate the whole design process, including the early stages. The
basic idea is that fuzzy sets allow. The designer to describe the designed artifact as
approximately as desired at the early stage of the design process. The designer may
express the various dimensions of the design artifact by approximate fuzzy numbers
representing linguistic description such as about 15cm or smaller than but close
to50ky. Triangular fuzzy numbers seem most convenient for this purpose. Assume
that there is a restitution on the dimension to be greater than 10 cm and that the design
wants to keep the dimendion under 22cm. then Fi=<15, 5, 7> id the corresponding
triangular fuzzy number expressed by the triple <s, l, r>
For example, of wide range of materials might be used of the membership
function expressed in terms corrosion, thermal expansion, or some other measurable
material property. A combination of several properties, including the cost of different
materials, may also be used. An example of a membership function constructed from
the cost data for certain steel alloys. It is based on the designer’s preference for
minimum cost.
3.3 Fuzzy logic in computer engineering
Since the mid-1980s, when the utility of fuzzy controllers can became
increasingly visible, the need for computer hardware to implement the various
operations involved in fuzzy logic of approximate reasoning has been recognized.
Initial attempts to develop hardware for fuzzy computing, data from 1985. The
principal reason for using specialized hardware for fuzzy computing is to increase
operational speed via parallel processing. In general, computer hardware for fuzzy
logic is implemented in either digital mode or analog mode. In digital mode, fuzzy
sets are represented as vectors of numbers in [o, i]. operations on vectors. In analog
mode, fuzzy sets are represented in term of continuous electric circuits. The circuits

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play a role similar to function generators in classical analog computers. Either of the
two modes of fuzzy computer hardware has some favorable features. Digital fuzzy
hardware is characterized by flexible program ability of good compatibility with
existing computers, which are predominantly complex schemes of multi stage fuzzy
inference. Analog fuzzy hardware is characterized by high speed and good
compatibility with sensors, it is thus particularly suitable for complex on line fuzzy
controllers.
3.4 Fuzzy logic in Robotics
Robotics is a cross-disciplinary subject area at is concerned with the design
and construction of machines that are capable of human-like behavior. Such machines
are referred to as robots. Intelligent robot must be equipped with atleast three types of
functions: appropriate perceptual functions facilitated by visual auditory and other
sensor to allow the robot to perceive its environment; intelligent information
processing functions that allow the robot to process the incoming information with
respect to a given task; and mechanical functions with appropriate control to allow the
robot to more and act as desired. To achieve human-like behavior an intelligent robot
must have same key capability’s that distinguish human beings from classical non-
intelligent machines. They include the capability of common-sense reasoning in
natural language, that is based on incoming information as well as background
knowledge, high level capability of making decisions in the face of bounded
uncertainly. It is clear that the use of fuzzy set theory is essential for all these
capabilities.
The main subject of fuzzy set theory that are relevant robotics, include
approximate reasoning. Fuzzy controllers, other kind of fuzzy systems, image
processing fuzzy decision making etc… In robotics all these subjects are utilized in
the over all architecture of intelligent robot.

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3.5 Other applications
1. Camcorder (Panasonic, Sanyo, fisher, canon) :- The video camera determines
the best focus and lightening, particularly when several objects are in the
picture. Also it has a digital image stabilizer to remove hand jitter. Fuzzy
decision-making is used in these actions. For example, the following scheme
is used for image stabilization. The present image frame is compared with the
previous frame from memory. A typical stationary object (e.g. house) is
identified and its shift coordinates are computed. This shift is subtracted from
the image to compensate for the hand jitter. A fuzzy algorithm provides a
smooth control/compensation action.
2. Automatic transmission system :- In a conventional automatic transmission
system, electronic sensor measure the vehicle speed and throttle opening, and
gears are shifted based on the predetermined values of these variables.
According to Nissan, this type of system is incapable of uniformly providing
satisfactory control performance to a driver because it provides only about
three different shift patterns. The fuzzy control transmission senses several
variables including vehicle speed and acceleration, throttle opening, the rate of
change of throttle opening, engine load and driving style. Each sensed value is
given a weight, and a fuzzy aggregate is calculated to decide whether to shift
gears. This controller is said to be more flexible, smooth, and efficient,
providing better performance. Also, an integrated system developed by
Mitcubishi uses fuzzy logic for active control of the suspension system, four-
wheeler-derive (traction) streening, and air conditioning.
3. Auto focus on camera :- Auto focus cameras are a great revolution for those
who spent years struggling with “old fashioned” cameras. These cameras
some how figure out, based on multitudes of inputs what is meant to be the
main object of the photo. It takes fuzzy logic to make these assumptions.
Perhaps the standard is to focus on the object closest to the center of the
viewer. May be it focuses on the object closest to the camera. It is not a
precise science, and cameras error periodically. This margin of error is
acceptable for the average cameras owner whose main usage is for snapshots.
However, the “old fashioned” manual focus cameras are preferred by most
professional photographers. For any errors in those photos cannot be attributed

16
to a mechanical glitch. The decision making in focusing a manual camera id
fuzzy as well, but it is mot controlled by a machine.
4. Predicting travel time:- This is especially difficult for driving, since there are
plenty of traffic situations that can occur to slow down travel.
As with bus time tabling, predicting. ETA’s is a great exercise in fuzzy
logic. That’s why it is called an estimated time of arrival. A major player in
predicting travel time is fuzzy logic. Weather, traffic construction, accidents
should all be added in to the fuzzy equation to delive a true estimate.
5. Elevator control (Fujitec, Toshiha) :- A fuzzy scheme evaluates passenger
traffic and the elevator variables (load, speed etc) to determine car
announcement and stopping time. This reduce waiting time and improves the
efficiency and reliability of operation
Hand held computer (Sony):- A fuzzy logic scheme reads the hand written input and
interprets the characters for data entry.
Television (Sony):- A fuzzy logic scheme uses sensed variables such as ambient
lightening, time of day, and users profile and adjust such parameters as screen
brightness, colour contrast, and sound.
Antilock bracking system (Nessan):- The system senses wheel speed, round
comditions and driving patter and fuzzy ABS determine the braking action with skid
control.
Subway train (Sendai):- A fuzzy decision scheme is used by the subway trains in
sendae, Japan to determine the speed and stopping routline. Ride comfort and safety
are used as performance requirements.
6. Other applications of fuzzy logic include a hotwater heater (Matsusbita) a rice
cooker (Hitachi) and a ciment Klin (Denmark). A fuzzy stock- trading
program can manage stock portfolios. A fuzzy golf diagnostic system is able
to select the best golf club based on size, characterstics, and siving of a golfer.
A fuzzy mug search system helps in criminal investigations by analyzing mug
shots (photos of suspects) along with other input data (say, stamets such as
“short, heavy-set, and young-looking…” from witness) to determine the most

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likely criminal. Gift-wrapped chocolates with fuzzy statements available for
valentine’s Day. Even a Yamaha “fuzzy” scooter was spotted in Taipci.
REFERENCE
1. George J Klir / Bo Yuan – Fuzzy sets and Fuzzy logic (Theory and
Application) Published by Asoke K Ghosh, prentice- Hall of India Private
Limited- 1995
2. A. Torres and J.J. Nieto – Biomedicine and Biotechnology published online
2006 March 26
3. L.A Zodeh –Fuzzy Algorithms -1968
4. http://www.mathworks.com
5. http://in .wikipedia.org

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