When we look at the background of Fuzzy Logic, we find that the first person for its development was Buddha. He lived in India in about 500 BC and founded a religious beliefs called Buddhism. His philosophy was based on the idea that the planet is filled up with contradictions, that almost everything contains some of its opposing, or quite simply, that things could be a and not-A at exactly the same time. Here we can see a clear interconnection between Buddha's idea and modern fuzzy reasoning.

About 200 years later, the Greek scholar Aristotle developed binary logic. In contrary to Buddha, Aristotle thought that the planet was made up of opposites, for example male versus female, hot versus frosty, dry versus wet, dynamic versus passive. Everything must be A or not-A, it can't be both.

Aristotle's binary logic became the base of knowledge; it was demonstrated using logic, and was accepted as scientifically right. Like many others, Russell tried to reduce math to reasoning. When he found out his paradox while working, he got terrified himself. It performed, however, give him the honor of being one of the fathers of fuzzy logic.

In 1965 Lotfi Zadeh at UC Berkeley proposed a reasoning system that backed infinite value logic. Zadeh proposed an aspect can have a account function that describes its membership of your set. For example, the expression mA(x) is the membership function of x inside a.

Zadeh's logic was called "Fuzzy placed theory" which includes proved a little regrettable because some took "fuzzy" to suggest imprecise or inaccurate.

He had the idea that if you may tell an air-conditioner to work a little faster when it gets hotter, or similar problems, it might be much more successful than having to give a rule for each heat.

## WHAT IS FUZZY LOGIC?

The phrase FUZZY fundamentally means: imprecise, not clear, hazy or inexact

Few meanings of fuzzy reasoning:

## "A form of reasoning, derived from fuzzy place theory, whereby a real truth value do not need to be exactly zero (phony) or one (true), but rather can be zero, one, or any value among"

en. wiktionary. org/wiki/fuzzy_logic

"Fuzzy Logic was conceived by Lotfi Zadeh, a professor at the University of California at Berkley as an improved method for sorting and managing data. It mimics real human control reasoning and is currently being applied in the world of trading systems. "

www. sicom. com. sg/index. cfm

"A sub-discipline of mathematics used to quantify subjective linguistic principles, such as glowing, dark, very significantly, quite close, most usually, almost impossible, etc. "

www. fileformat. info/mirror/egff/glossary. htm

"A way used to model linguistic expressions that contain nonbinary truth- values. It's been used with PID algorithms in process control, especially where process relationships are nonlinear. "

www. atlab. com/index. php/LIMS-Glossary-Terms-F-J. html

"A technique used by an expert system to deal with imprecise data by combining the probability that the source information is accurate. "

www. thecomputerfolks. com/f. htm

"Fuzzy reasoning is made for situations where information is inexact and traditional digital on/off decisions are not possible. It divides data into obscure categories such as "hot", "medium" and "cold". "

dereng. com/tlas_glossary. htm

Formal Classification:

## The Basic Idea of Fuzzy Sets

Fuzzy sets are functions that map a value, which might be a member of set, to lots which is placed between zero and one, therefore indicating its genuine amount of membership

A amount of zero means that the value is not in the collection, and a amount of one means that the worthiness is totally representative of the set in place.

## Characteristic Function:

Conventionally we can identify a place C by its characteristic function, Char C(x).

If U is the universal place form which prices of C are considered, then we can symbolize C as

C = x

This is the representation for a crisp or non-fuzzy place. For an ordinary collection C, the characteristic function is of the form

Char C(x): U 0, 1

However for a Fuzzy place A we have

Char F(x): U [0, 1]

That is, for a fuzzy set in place the characteristic function assumes all principles between 0 and 1

## and not only the discrete beliefs 0 or 1.

## For a fuzzy place the characteristic function is categorised as the account function and denoted by mF(x)

## An example:

If we use classic method we can say that a person is "TALL" if his elevation is 7 ft and one is NOT High with height 5 feet. This can be represented that the individual is either "TALL" or "NOT High" in Boolean Reasoning 1 or 0, 1 for "TALL" and 0 for "NOT TALL"

## To show the partnership or amount of precision, we can use FUZZY Collections also:

If S is the group of all people in the World, a amount of membership is given to each individual in set S to get the subset TALL.

The account function is based on the person's elevation.

TALL(x) = 0, if Height(x) < 5'

(Level(x) - 5' )/ 2' if 5'<= Level(x) <= 7

1, if height(x)> 7 feet

Boolean logic vs Fuzzy Logic

## Boolean Logic

## Fuzzy Logic

Boolean or "two-valued" logic is traditional reasoning with all statements either being true or phony.

Fuzzy or "multi-valued" reasoning is a variance of traditional reasoning where there are many (sometimes infinitely many) possible fact beliefs for a statement. True is known as add up to a truth value of just one 1, fake is a truth value of 0, and the real figures between 1 and 0 are intermediate prices.

Here's a good example: Suppose you want to illustrate the group of adults utilizing a binary set, we would get a graph like the main one on the right. In this particular picture the assumption is that a person becomes a grown-up on his / her 18th birthday. It really is that every person is either adult or non-adult, in the graph 1 or 0.

When we graph the fuzzy set of people, we get something like the picture on the left. In this there sits a steady process between being adult and non-adult. Again we can claim or disagree over this saying how the curve should be drawn. Someone might say that a 13 time old is totally non-adult or a 19 time old must be counted in the category of adult. But we can be sure that the fuzzy curve of the group of adults is nearer to the truth then the binary curve; as most of us can concur that there can't be given a particular particular date when people turn into adults. It's not like we go to sleep 1 day as a kid and wake up another as a grown-up. Growing up is a gradual process and continuous procedures can be better detailed using fuzzy pieces where there are no discrete values.

## FEW MORE TYPES OF FUZZINESS AND ITS OWN USAGE

For example, if you ask a question in a school class, "Who is feminine?", all girls will set up their hands up and all the boys will keep them down. We are able to get a answer, since many people are either feminine or is a non-female.

What if the same kids are asked a question like, "Who likes college?" Some kids may set up their hands completely (they definitely like school) and more might keep their hands down (they hate university). A lot of the kids however will put their hand up and take it down again several times and then leave it somewhere in the middle. Maybe they like school generally, but there are some bad things about it that they don't really like for case examinations, or they actually don't like school in general, but sometimes it's fun so within an all they are confused and should be proved in middle way.

If these email address details are represented with binary logic, they have to be reduced to each result to the extremes of either caring college or hating college; A or not-A. Here we are in need of a different kind of logic to notice the answers accurately and exactly; we desire a logic where the kids can both like school and not like school at the same time. For that we use fuzzy logic.

A human characteristic such as healthy.

The classification of patients as despondent.

The bifurcation of certain items as large or small.

The distinguition of men and women by era such as old.

A rule for driving a vehicle such as "if an obstacle is close, then brake immediately".

## FUZZY OPERATIONS

## STEPS OF Execution OF FUZZY LOGIC

Fuzzification - to convert numeric data (for e. g. , $24. 50 ) in real-world domain to fuzzy-numbers in fuzzy domain

Aggregation (guideline firing) - computation of fuzzy volumes (all of which rest between 0. 0 and 1. 0 ) i. e. in fuzzy domain

Defuzzification - convert the obtained fuzzy number back again to the numeric data in the real-world site (e. g. 150. 34% altogether success).

## WHY TO MAKE USE OF FUZZY LOGIC?

## Fuzzy reasoning advantages:

Mimics and translates real human decision making to take care of vague, uncertain and imprecise concepts

Rapid and faster computation anticipated to intrinsic parallel control nature

Ability to cope with imprecise or imperfect and uncertain information

Resolving issues by cooperation and propogation

Improved knowledge and information representation and doubt reasoning

Modeling of intricate and non-linear problems

Natural language handling as well as coding capability

Computers do not reason as brains do. The mind can reason with vague assertions or claims that entail uncertainties or value judgments: The environment is cool, " or "That swiftness is fast" or "She is young. " Unlike pcs, humans have good sense that enables these to reason in a world where things are only partly true. Fuzzy logic is a branch of machine brains that helps computer systems paint gray, commonsense pictures of an uncertain world.

## Fuzzy logic limitations:

Highly abstract and heuristic concept

Need of experts for rule discovery (data human relationships) i. e using fuzzy computation

Lack of self-organizing & self-tuning mechanisms of Neural Nets

Though fuzzy Systems are used world-wide in various applications, it still remains controversial amidst statisticians who choose Bayesian reasoning or two-valued theory.

APPLICATIONS OF FUZZY

## There are many applications for fuzzy reasoning. In fact, some claim that fuzzy logic is the encompassing theory over all types of reasoning. These few items identified below are more common applications which one may encounter in everyday activities.

## Bus Time Desks

How effectively do the schedules of bus timings predict the real travel time or the genuine entrance time of the bus?

Bus schedules are created on information that does not remain constant. Because of this fuzzy logic should be utilized because it is impossible to provide a precise answer as to when the bus will be at a certain stop. Many unforeseen incidents can occur. There can be accidents, abnormal traffic backups, or the bus could breakdown. An observant scheduler would take all these possibilities into consideration, you need to include them in a method for determining the approximate timetable. It really is that method which imposes the fuzziness using fuzzy reasoning.

## Predicting hereditary traits

Genetic qualities or characteristics are a fuzzy situation for more than one reason. There is the fact that lots of traits can't 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 Punnet squares are collections in fuzzy logic. The amount of account in those sets is assessed by the incident of a hereditary characteristic. In clear instances of dominating and recessive genes, the possible levels in the sets are quite tight. Take, for illustration, eyeball color. Two brown-eyed parents produce three blue-eyed children. Looks impossible, right? Brown is prominent, so each mother or father will need to have the recessive gene within them. Their membership in the blue attention set in place must be small, but it remains. So their children possess the potential for high membership in the blue attention set as it's a recesive one, so that characteristic actually comes through. Based on the Punnet square, 25% of the children should have blue eyes, with the other 75% should have brown. But in this example, 100% with their children possess the recessive color. Was the wife being unfaithful get back nice, blue-eyed salesman? Most likely not. It's just fuzzy logic at work.

## Temperature control (heat/cooling)

The main aim in temperatures control is to keep the room at the same temperature consistently. Well, that seems quite easy, right? But how much does a room have to cool off before the high temperature kicks in again? There must be some standard, so the heat (or air-con) isn't in a regular talk about of turning on and off i. e. in regular form of 1's and 0's. Therein lies the fuzzy reasoning. The set depends upon what the temp is actually arranged to. Membership for the reason that place weakens as the room heat range varies from the set in place temperature. Once membership weakens to a certain point, temps control kicks directly into get the room back to the temperature it ought to be.

## Auto-Focus on a camera

How will the camera even really know what to focus on?

Auto-focus surveillance cameras are a great trend for many who spent years fighting "old-fashioned" surveillance cameras. These video cameras somehow find out automatically, predicated on multitudes of inputs, what is meant to be the main object of the photo. It uses fuzzy logic to make these assumptions. Possibly the standard is to focus on the thing closest to the center of the viewers. Maybe it focuses on the object closest to the camera. It is not a precise science, and surveillance cameras err periodically. This margin of mistake is satisfactory for the common camera owner, whose main use is ideal for snapshots. However, the "old-fashioned" and earlier used manual concentration cameras are preferred by most professional photography lovers. For any errors in those images cannot be related to a mechanical glitch. The decision making in concentrating a manual camera is fuzzy as well, but it is not controlled by a machine.

## Medical diagnoses

How a lot of what types of symptoms will yield a prognosis? How often are doctors in error?

There is placed a set of symptoms for a horrible disease that say "if you have at least 5 of these symptoms, you are at risk". It really is a hypochondriac's haven. The question is, how do doctors go through that list of symptoms to a examination? Fuzzy logic. There is no guaranteed system to attain a diagnosis. If there were, we wouldn't notice about situations of medical misdiagnosis. The diagnosis can only be some degree within the fuzzy place.

## Predicting travel time

This is especially difficult for driving a car, since there are many traffic situations that can occur due to slow down travel.

As with bus timetabling, predicting ETA's (estimated time of arrival) is a great exercise in fuzzy logic. A significant player in predicting travel time. Weather, traffic, development, mishaps should all be added in to the fuzzy equation to deliver a true estimate.

## Antilock Braking System

The point of Ab muscles is to keep an eye on the braking system on the automobile and release the brakes right before the wheels lock. Your personal computer is involved with determining when the best time to do this is. Two main factors that go into determining this will be the speed of the automobile when the brakes are applied, and how fast the brakes are frustrated. Usually, when you want the Stomach muscles to essentially work are if you are driving a car fast and slam on the brakes. You can find, of course, a margin for mistake. It's the job of the Abdominal muscles to be "smart" enough never to allow the problem go past the point when the wheels will lock. (Quite simply, it doesn't allow the regular membership in the place to become too fragile. )

## Fuzzy Machines

Fuzzy Washing Macine

Fuzzy Rice-Cooker

Fuzzy Vaccum-cleaners

Fuzzy Refrigerators

## REFRENCES

Fuzzy Units and Fuzzy Reasoning theory and applications, George J. Klir, Bo Yuan

A First Course in Fuzzy Logic by Hung T. Nguyen and Elbert A. Walker

http://www. dementia. org/~julied/logic/index. html

http://mathematica. ludibunda. ch/fuzzy-logic6. html

http://pami. uwaterloo. ca/tizhoosh/fuzzy_logic. htm