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CCSB354 ARTIFICIAL INTELLIGENCE. Chapter 9.2 Introduction to Fuzzy Logic. (Chapter 9, pp. 353-363, Textbook) (Chapter 7, Ref. #1). Instructor: Alicia Tang Y. C. Fuzzy Logic & Fuzzy Thinking. Fuzzy logic is used to describe fuzziness. It is not a logic that is fuzzy
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CCSB354ARTIFICIAL INTELLIGENCE Chapter 9.2 Introduction to Fuzzy Logic (Chapter 9, pp. 353-363, Textbook) (Chapter 7, Ref. #1) Instructor: Alicia Tang Y. C.
Fuzzy 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?
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)
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
Degree of membership of a“tall”man Height, cm Crisp Fuzzy 208 1 1.00 205 1 1.00 198 1 0.98 181 1 0.82 179 0 0.78 172 0 0.24 167 0 0.15 158 0 0.06 155 0 0.01 152 0 0.00 Numeric data Just ‘yes’ or ‘no’ In terms of probability
Uncertainty terms and their interpretations Uncertainty term CF Definitely not -1.0 Almost certainly not -0.8 Probably not -0.6 Maybe not -0.4 Unknown -0.2 to +0.2 Maybe +0.4 Probably +0.6 Almost certainly +0.8 Definitely +1.0
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
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
Boolean Logic (for ‘Temperature’) Boolean logic s discrete… Hot 100.0 Temperature (C º) Cold 0.0
Fuzzy Logic (for ‘Temperature’) Extremely Hot 100.0 Hot Quite Hot Temperature (C º) Quite Cold Cold Extremely Cold 0.0
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!
Brief 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)
Fuzzy 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
Fuzzy logic applied to asubway control system • Fuzzy Control used in the subway in Sendai, Japan • fuzzy control system is used to control the train'sacceleration, 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
Fuzzy 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
What is the difference between classical and fuzzy rules? Consider the rules in fuzzy form, as follows: Rule 1 Rule 2 IF 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.
More Fuzzy Rules IF project_duration is short AND project_staffing is medium AND project_funding is inadequate THEN risk is high IF project_duration is long AND project_staffing is large AND project_funding is adequate THEN risk is low IF project_duration is short AND project_staffing is large AND project_funding is adequate THEN risk is medium IF service is excellent OR food is delicious THEN tip is generous :
Example • 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
Methodology: 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?
Bivalent Sets to Characterize the Temperature of a room Membership Function 1 0 ºC 10 20 30 -10 0 Cold Cool Warm Hot
Fuzzy 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 iscoldTHENset fan tozero IF temperature iscoolTHENset fan tolow IF temperature iswarmTHENset fan to medium IF temperature ishotTHEN setfan tohigh
Fuzzy Sets to Characterize the Temperature of a room Membership Function 1 0 ºC 10 20 30 -10 0 Cold Cool Warm Hot Expresses the shift of temperature more natural and smooth
Exercise: A question combiningfuzzy rules & truth values and resolution proof
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 facts W ( TV = 0.65) Q P S (TV = 1.0) S U ( TV = 1.0) TVs for fuzzy rules W 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.
Combining resolution proof and fuzzy refutation Steps • 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.
Applications in Fuzzy logic decision making • The most popular area of applications • fuzzy control • industrial applications in domestic appliances • process control • automotive systems
Fuzzy Decision Making in Medicine - 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
Fuzzy Decision Making in Medicine - 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
Fuzzy Decision Making in Medicine - 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.
Fuzzy Decision Making in Medicine - IV • Its importance emanates from the nature of medical information • highly individualized • often imprecise • context-sensitive • often based on subjective judgment • To deal with this kind of information without fuzzy decision making and approximate reasoning is virtually impossible
Fuzzy Decision Making in 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