CCSB354CCSB354ARTIFICIAL INTELLIGENCEARTIFICIAL INTELLIGENCE

Chapter 9.2Introduction to Fuzzy Logic

Chapter 9.2Introduction to Fuzzy Logic

Instructor: Alicia Tang Y. C.

(Chapter 9, pp. 353-363, Textbook)(Chapter 7, Ref. #1)

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Fuzzy Logic & Fuzzy ThinkingFuzzy Logic & Fuzzy Thinking

Fuzzy logic is used to describe fuzziness.– It is not a logic that is fuzzy

Fuzzy logic is the theory of fuzzy sets– sets that calibrate vagueness

Experts rely on common sense when they solve problems

How can we represent expert knowledge that uses vague and ambiguous terms in a computer?

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What is Fuzzy Logic? What is Fuzzy Logic?

It is a powerful problem-solving methodology

Builds on a set of user-supplied human language rules

Fuzzy systems convert these rules to their mathematical equivalents

Introduced by Lofti Zadeh (1965)

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Fuzzy Logic

It deals with uncertainty It deals with ambiguous criteria or values Example: “ the girl is tall”

– but, how tall is tall?– What do you mean by tall?– is 5’3” tall?

A particular height is tall to one person but is not to another

It depends on one’s relative definition of tall

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Degree of membership of a “tall” man

Height, cm Crisp Fuzzy 208 1 1.00205 1 1.00198 1 0.98181 1 0.82179 0 0.78172 0 0.24167 0 0.15158 0 0.06155 0 0.01152 0 0.00

Just ‘yes’ or ‘no’Numericdata

In termsof probability

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Uncertainty terms and their Uncertainty terms and their interpretationsinterpretations

Uncertainty term CF Definitely not -1.0Almost certainly not -0.8Probably not -0.6Maybe not -0.4Unknown -0.2 to +0.2Maybe +0.4Probably +0.6Almost certainly +0.8Definitely +1.0

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What is not Fuzzy Logic ?

Classical logic or Boolean logic has two values

Example:– true or false– yes or no– on or off– black or white– start or stop

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Differences between Fuzzy Logic and Crisp Logic

Crisp Logic– precise properties

Full membership– YES or NO– TRUE or FALSE– 1 or 0

Crisp Sets– Jane is 18 years old– The man is 1.6m tall

Fuzzy Logic– Imprecise properties

Partial membership– YES ---> NO– TRUE ---> FALSE– 1 ---> 0

Fuzzy Sets– Jane is about 18 years

old– The man is about 1.6m

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Tem

pera

ture

(C

º)

Boolean Logic (for ‘Temperature’)

0.0

100.0 Hot

Cold

Boolean logic s discrete…

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Tem

per

atu

re (

C º

)

Fuzzy Logic (for ‘Temperature’)

0.0

100.0 Extremely Hot

Extremely Cold

Hot

Quite Hot

Quite Cold

Cold

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Why Fuzzy Logic?

Fuzzy Logic can:– represent vague language naturally– enrich not replace crisps sets– allow flexible engineering design– improve model performance– are simple to implement– they often work!

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Brief History of Fuzzy LogicBrief History of Fuzzy Logic

1965 - Fuzzy Sets ( Lofti Zadeh, seminar) 1966 - Fuzzy Logic ( P. Marinos, Bell Labs) 1972 - Fuzzy Measure ( M. Sugeno, TIT) 1974 - Fuzzy Logic Control (E.H. Mamdani) 1980 - Control of Cement Kiln (F.L. Smidt, Denmatk) 1987 - Sendai Subway Train Experiment ( Hitachi) 1988 - Stock Trading Expert System (Yamaichi) 1989 - LIFE ( Lab for International Fuzzy Eng)

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Fuzzy Logic SuccessFuzzy Logic Success

Fuzzy Logic success is mainly due to its introduction into consumer products such as:– temperature controlled in showers– air conditioner– washing machines– refrigerators– television– rice cooker– camcorder– heaters– brake control of vehicles

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Fuzzy logic applied to a subway control system

Fuzzy Control used in the subway in Sendai, Japan– fuzzy control system is used to control the

train's acceleration, deceleration and braking

– has proven to be superior to both human and conventional automated controllers

– reduced the energy consumption been by 10%

– passengers hardly notice when the train is actually changing its velocity

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Fuzzy Rule ExampleFuzzy Rule Example

A fuzzy rule can be defined as a conditional statement in the form:

If x is A Then y is B

where x and y are linguistic variables; A and B are linguistic values determined by fuzzy sets

on the universe of discourses x and y, respectively

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What is the difference between classical and fuzzy rules?

Consider the rules in fuzzy form, as follows:

Rule 1 Rule 2IF speed is fast IF speed is slow

THEN stop_distance long THEN stop_distance short

In fuzzy rules, the linguistic variable speed can have the range between 0 and 220 km/h, but the range includes fuzzy sets,

such as slow, medium, fast. Linguistic variable stop_distance can take either value: long or short. The universe of discourse of the linguistic variable stop_distance can

be between 0 and 300m and may include such fuzzy sets as short, medium, and long.

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More Fuzzy RulesIF project_duration is shortAND project_staffing is mediumAND project_funding is inadequateTHEN risk is high

IF project_duration is longAND project_staffing is largeAND project_funding is adequateTHEN risk is low

IF project_duration is shortAND project_staffing is largeAND project_funding is adequateTHEN risk is medium

IF service is excellentOR food is deliciousTHEN tip is generous

:

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ExampleExample

The temperature of room is too hot/cold…How to designed an automatic air-conditioner

which will be able to set temperature:– Hotter(warm) when it is too cold– Colder(cool) when it is too hot

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Methodology: BooleanMethodology: Boolean

Using Boolean:– Determine 2 discrete values which is

mutually exclusive– E.g. hot or cold– Couldn’t cater for continuous value

Problems: – How if too many students or very few

students in the room ? – How hot or how cold the room should be?

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Membership Function

Cold Cool Warm Hot

0

1

-10 0 10 20 30ºC

Bivalent Sets to Characterize the Temperature of a room

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Fuzzy Logic MethodologyFuzzy Logic Methodology

Set the boundaries between two values(cold and hot) which will show the degrees of temperature– Use fuzzy set operations to solve the

problem:

IF temperature is cold THEN set fan to zero

IF temperature is cool THEN set fan to low

IF temperature is warm THEN set fan to medium

IF temperature is hot THEN set fan to high

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Membership Function

Cold Cool Warm Hot

0

1

-10 0 10 20 30ºC

Fuzzy Sets to Characterize the Temperature of a room

Expresses the shift of temperature more natural and smooth

Exercise: Exercise: A question combiningA question combining

fuzzy rules & truth values and fuzzy rules & truth values and resolution proofresolution proof

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FUZZY RULES AND RESOLUTION PROOF

Given the following fuzzy rules and facts with their Truth Values (TV) indicated in brackets:

Q ( TV = 0.3) TVs for factsW ( TV = 0.65)Q P S (TV = 1.0)S U ( TV = 1.0) TVs for fuzzy rulesW R ( TV = 0.9)W P ( TV = 0.6)

You are required to find (or compute) the Truth Value of U by using the fuzzy refutation and resolution rules.

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Convert facts and rules to clausal forms. [in our case, there are 4 rules that need conversion].

By resolution & refutation proof , we negate the goal. [in our case, this is U. assign a TV = 1.0 for it]

For those fuzzy rules, check to see if there is any Truth Value less than 0.5 (i.e. 50%); invert the clause and compute new TV for inverted clause using formula (1 – TV(old-clause)). [we have the clause Q which is < 0.5, in our example]

Apply resolution proof to reach at NIL (i.e. a direct contradiction).– Each time when two clauses are resolved (combined to yield a resolvent), the

minimum of the TVs is taken & assigned it to the new clause.

Combining resolution proof and Combining resolution proof and fuzzy refutation fuzzy refutation

Steps

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SolutionCONFLICT SET:

Q P S (TV=1.0) …………(1) S U (TV=1.0) …………(2) W R (TV=0.9) …………(3) W P (TV=0.6) …………(4) Q (TV=0.3) Q (1 – TV( Q ) = 0.7) …. (5) W (TV=0.65) …………(6) U (TV=1.0) …………(7)

2 & 7: S TV=1.0 ……(8) 8 & 1: Q P TV=1.0 ……(9) 9 & 5: P TV=0.7 ……(10) 10 & 4: W TV=0.6 ……(11)

11 & 6: NIL TV= 0.6 (ANSWER)

U is true, i.e. proven and it has a truth value of 0.6

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Supplementary slidesSupplementary slides

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Applications in Fuzzy logic Applications in Fuzzy logic decision makingdecision making

The most popular area of applications– fuzzy control– industrial applications in domestic appliances

– process control– automotive systems

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FFuzzy uzzy DDecision ecision MMaking aking in in Medicine - IMedicine - I

Medicine– the increased volume of information

available to physicians from new medical technologies

– the process of classifying different sets of symptoms under a single name and determining appropriate therapeutic actions becomes increasingly difficult

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FFuzzy uzzy DDecision ecision MMaking aking in in Medicine - IIMedicine - II

– The past history offered by the patient may be subjective, exaggerated, underestimated or incomplete

– In order to understand better and teach this difficult and important process of medical diagnosis, it can be modeled with the use of fuzzy sets

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FFuzzy uzzy DDecision ecision MMaking aking in in Medicine - IIIMedicine - III

The models attempt to deal with different complicating aspects of medical diagnosis– the relative importance of symptoms– the varied symptom patterns of different disease

stages– relations between diseases themselves– the stages of hypothesis formation– preliminary diagnosis– final diagnosis within the diagnostic process itself.

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FFuzzy uzzy DDecision ecision MMaking aking in in Medicine - IVMedicine - IV

Its importance emanates from the nature of medical information – highly individualized – often imprecise– context-sensitive

– often based on subjective judgmentTo deal with this kind of information without fuzzy

decision making and approximate reasoning is virtually impossible

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FFuzzy uzzy DDecision ecision MMaking aking in Information Systemsin Information Systems

Information systems– information retrieval and database

management has also benefited from fuzzy set methodology

– expression of soft requests that provide an ordering among the items that more or less satisfy the request

– allow for the presence of imprecise, uncertain, or vague information in the database