# Fuzzy Logic

Fuzzy Logic is a term that is used in tow different senses, a narrow sense and a broad sense. The Narrow sense is a logical system that generalizes classic binary, true and false or zero and one, logic into uncertantiy. The borad sense of the term is all the technologies that employ classes with unsharp boundaries, or fuzzy sets.

Fuzzy sets can be best represented as a real world problem. If a person were to mathematically represent what "room temperature" is it would be expressed as an interval between two numbers, say from 68 degrees to 75 degrees. This would result in a hard-edged line between what is room temperature and what is not. However, in the human interpretation of room temperature, there is a gradation between not room temperature and room temperature. So certain tempertaure would be considered to be around room temperature. A fuzzy set allows for this by having gradiated boundaries rather than harsh boundaries. This can be represented on a graph by a line sloping up from the value of 0(false) to 1(true) over a period of time before 68. Remaining at 1(true) from 68 to 75 and the sloping back down from 1(true) to 0(false) for another set of numbers.

Examples of Fuzzy Logic used for movie A.I. includes Massive Software Massive Software which was used in the Lord of the Rings Movies as well as the Chronicles of Narnia

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## Brief History

Theory about Fuzzy Logic can be traced back to ancient times. Before Aristotle came up with the theory of binary logic, Buddha suggested that everything contained some of its opposite. Meaning good contained some evil, dry contained some wetness, hot contained some cold, etc. This is a theory behind fuzzy logic; nothing is completely true or completely false.

In 1964 Dr. Lofti Zadeh, a proffesor of Computer Science and Electical Engineering at University of California Berkely, was attempting to find a new and more efficent method of programming Air Conditioning units over the then used method. Traditional systems were too percise for such complex real world problems. He proposed that it would be simpler to tell the conditioner to work harder when it got warmer and to work less when it was cooler then to set a series of rules for each temperature. In 1965 gis paper on fuzzy sets, a gradient membership, was published and met with sharp criticism.

Even through the resistance to fuzzy logic, many researchers and cholars began to adopt Zadeh's system. Scholars and scientist from fields ranging from psychology to engineering were exploring the uses of this system. In the decade that followed Zadeh himself introduced many new theries atached to his first paper on fuzzy sets including fuzzy multi-stage decision making, fuzzy restrictions and linguistics. Other contributors continued Zadeh's work including R.E Bellman, G. Lakoff, J.A. Goguen and a host of other researchers.Many mathmatic practices were "fuzzified" with fuzzy logic sets over this period of time. These practices ranged from logic and relations to algorithms and programs.

### Industial Applications

The first industrial application of fuzzy logic was devoloped over a decade after Zadeh introduced his system. In 1976 Blue Circle Cement and SIRA in Denmark developed a new cement kiln. It used fuzzy logic to encorporate the knowledge of an experienced operator to enhance efficency of a clinker through a smoother grinder. This system first became operational in 1982.

In the mid 1980s in Japan, fuzzy logic was used to control trains. Trains were programmed to apply breaks at upon reachin carkers set at even distances away from the station. However these trains would apply breaks the same going downhill as they would going uphill. This would result in the trains coming to a jerky stop in certain situations. However by harnessing fuzzy logic engineers at Hitachi were able to make the breaking process much smoother. This and other uses of fuxxy logic to increase the performance of trians in Japan fueled for a boom in the use of fuzzy logic overseas.

## How It Works

Fuzzy Logic is used to determine a conclusion based on vague and noisey information that would be indeterminable by traditional problem solving methods. It is used to mimic human control of an application. By using a descriptive yet impercise language it deals with the data much the way a human controller would. Though it is inpercise it is still forgiving of data input and rarely needs much fine tuning.

Fuzzy Logics core technique is based in 4 concepts:

(1) *fuzzy sets*: sets with smooth boundaries;

(2) *linguistic variables*: variables whose values are both qualitative and quantitatively described by a fuzzy set;

(3) *possibility distributions*: constraints in the value of a linguistic variable imposed by assigning it a fuzzy set; and

(4) *fuzzy if-then rules*: a knowledge representation scheme for describing a functional mapping or a logic fomula that generalizes an implication in two-valued logic

The first 3 concepts are important in all areas of fuzzy logic. The fourth is the basis for most industrial applications of fuzzy logic to date.

If you had a group of 50 individuals and you wanted to classify them as old or young you can see how the two approaches differ. In the Boolean approach anyone over a defined age, lets say 45,would be classified as old and everyone else would be young. So someone with the age 44.9 would be classified as young but at 45.0 they would become old.

Fuzzy Logic works on a sloping line. So it could say that everyone up to 40 would be considered absolutely young but from ages to 40 to 50 they would increasingly be considered more old. This comes out to define people as somewhat old or somewhat young in those years in which thier age/oldness is fuzzy. These sets are known as fuzzt sets.

### Fuzzy Sets

A fuzzy set is a set of values with a smooth boudary that allows for partial membership. THis means that one number can be a member of two or more sets. The classic approach for number sets is black-and-white, allowing an object to either be completely part of the set or not poart of the set at all. Though many sets have sharp boundaries (e.g. the set of schools with graduate programs) even more do not have sharp boundaries (e.g. the set of schools with good graduate programs). These non-sharp sets are addressed by fuzzy set theory and its use of degrees of membership.

## Myths of Fuzzy Logic

* Fuzzy logic is a clever disguise of the probability theory*

Probability theory measures the likelihood of an event happening, fuzzy logic measures the degree to which an outcome belongs to an event that does not have a exact boundary.

*Fuzzy Logic and probability or competing techniques and onlin one can be used to solve a given problem.*

No. Fuzzy logic and probability can be used to compliment eachother.

*The behavior of a fuzzy logic system is nondeterministic.*

This is a confusion caused by the use of the word "fuzzy". The behavior of a fuzzy system is deterministic. There is nothing ambiguous about it.

* Fuzzy logic control is ill-founded, not rigurous and may lead to potential disaster.*

Fuzzy logic control systems so far developed in industry have been subjected to rigorous testing and validation. The control of fuzzy logic has been confirmed with each of these successful systems