Understanding Fuzzy Logic: Concepts, Properties, and Applications, Slides of Robotics

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• be introduced to the topics of: fuzzy sets,

fuzzy operators,

fuzzy logic

and come to terms with the technology

learn how to represent concepts using fuzzy logic

understand how fuzzy logic is used to make

deductions

familiarise yourself with the `fuzzy' terminology

What is fuzzinessWhat is fuzziness

Fuzzy logic is then a

superset^ superset

of

conventional Boolean logic.

In

Boolean logic

propositions take a

completely falsevalue of either completely true or

Fuzzy logicFuzzy logic

handles the concept of

extremes.partial truth, i.e., values between the two

What is fuzzinessWhat is fuzzinessWhat is fuzziness

For example, if pressure takes values between

0 and 50

the universe of discoursethe universe of discourse

one might

label the range 20 to 30 as medium pressure

(the

subset)

Medium is known as a

linguistic^ linguistic

variable.

Therefore, with Boolean logic 15.0 (or even

range.19.99) is not a member of the medium pressure

As soon as the pressure equals 20, then it

becomes a member.

What is fuzzinessWhat is fuzzinessWhat is fuzziness

Contrast with the Figure of the next page which

shows the membership function using fuzzy logic.

Here, a value of 15 is a member of the medium

pressure range with a membership grade of about 0.3.

Measurements of 20, 25, 30, 40 have grade of

memberships of 0.5, 1.0, 0.8, and 0.0 respectively.

Therefore, a membership grade progresses from

non-membership.non-membership to full membership and again to

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Fuzzy Medium PressureFuzzy Medium Pressure

10

20

30

40

50

Membership Grade

Pressure

Not-Member

Not-Member

Member

Fuzziness is not

(^) Vague

Fuzziness is notFuzziness is not

Vague^ Vague

• Dimitris is tall

proposition.The third proposition is a fuzzy

context, i.e., the universe of discourse.It is true to some degree depending in the

It might be

SomeWhat True

if we are

bereferring to basketball players or it might

Very True

if we are referring to horse-

jockeys.

Fuzziness is not

(^) Multi-valued logic

Fuzziness is not

(^) Multi-valued logic

The limitations of two-valued logic were recognised very early.

have been formulated through the years.A number of different logic theories based on multiple values of truth

employed.For example, in three-valued logic three truth values have been

respectively.These are TRUTH, FALSE, and UNKNOWN represented by 1, 0 and 0.

In 1921 the first N-valued logic was introduced.

The set of truth values T

n were assumed to be evenly divided over the

closed interval [0,1].

they are somewhat different.Fuzzy logic may be considered as an extension of multi-valued logic but

approximate reasoning.Multi-valued logic is still based on exact reasoning whereas fuzzy logic is

Fuzziness is not

Probability

Fuzziness is not

Probability

Well, membership of 0.9 means that the contents of A are

fairly similar

(^) to perfectly potable liquids.

(^) If, for example, a perfectly liquid is pure water then bottle

A might contain, say, tonic water. (^) Probability of 0.9 means something completely different.

(^) You have a 90% chance that the contents are potable and

of acid maybe.10% chance that the contents will be unsavoury, some kind Hence, with bottle A you might drink something that is

So choose bottle A.not pure but with bottle B you might drink something deadly.

Fuzziness is not

Probability

Fuzziness is not

Probability

Opening both bottles you observe beer (bottle A) and

hydrochloric acid (bottle B). The outcome of this observation is that the membership stays

the same whereas the probability drops to zero.

• All in all:
• (^) fuzzy logic measures the (^) probability measures the likelihood that a future event will occur,

(^) ambiguity of events that have already

occurred.

In fact, fuzzy sets and probability exist as parts of a greater

GeneralizedGeneralized Information Theory.

Information Theory.

-^ This theory also includes: Demster-Shafer evidence theory,

possibility theory,

and so on.

Where is fuzzy logic used?Where is fuzzy logic used?Where is fuzzy logic used?

implication of the word `fuzzy',their fuzzy development secret because of thewhereas in the West companies might keep

or

because

companies

want

to

preserve

competitive advantage,

or

because

fuzzy

logic

is

embedded

in

products without advertisement.

concealed logic system for expert systems.Most applications of fuzzy logic use it as the

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Where is fuzzy logic used?Where is fuzzy logic used?

The areas of potential fuzzy implementation are

numerous and not just for control:

Speech recognition,Speech recognition,

fault analysis,fault analysis,

decision making,decision making,

image analysis,image analysis,

schedulingscheduling

and many more are areas where fuzzy thinking can help.

Hence, fuzzy logic is not just control but can be

utilized for other problems.

19^
Where is fuzzy logic used?Where is fuzzy logic used? Another interesting application has been reported by Aptronix

Inc., where f (^) Fuzzy logic was used as a means of determining correct focus

distance for cameras with

automatic focusing system.^ automatic focusing system.

(^) Traditionally, such a camera focuses at the middle of the view

finder. (^) This can be inaccurate though when the object of interest is not

at the center. (^) Using fuzzy logic, three distances are measured from the view

finder; left, center and right. (^) For each measurement a plausibility value is calculated and the

where the object of interest is located.measurement with the highest plausibility is deemed as the place

(^20) When to use Fuzzy Logic?When to use Fuzzy Logic?

If the system to be modelled is a linear

system

which

can

be

represented

by

a

rulesmathematical equation or by a series of

then

straightforward

techniques

straightforward

techniques

should be used.

Alternatively, if the system is complex,

complex,

fuzzy

logic

may

be

the

technique

to

follow.

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