CSNB234 ARTIFICIAL INTELLIGENCE

1. CSNB234ARTIFICIAL INTELLIGENCE Chapter 8.1 Introduction to Fuzzy Logic and Fuzzy Rules Instructor: Alicia Tang Y. C. UNIVERSITI TENAGA NASIONAL

2. Fuzzy Thinking • Fuzzy logic is used to describe fuzziness. • Where fuzzy logic is the theory of fuzzy sets, sets that calibrate vagueness • A fuzzy set can be defined as a set with fuzzy boundaries. • Fuzzy logic is based on the idea that all things admit of “degrees” or “scales”. • Such as: temperature, height, speed, distance, beauty etc. • This is acceptable since experts rely on common sense when they solve problems • How can we represent expert knowledge that uses vague and ambiguous terms in a computer? • By using fuzzy logic in representation!

3. Fuzzy Logic • Introduced by Lofti Zadeh (1965) • It is a powerful problem-solving methodology • Builds on a set of user-supplied human language rules • It deals with uncertainty and ambiguous criteria or values • Example: “the weather outside is cold” • but, how cold is actually the coldness you described? • What do you mean by ‘cold’ here? • As you can see a particular temperature is cold to one person but it is not to another • It depends on one’s relative definition of the said term

4. Most natural language is bounded with vague and imprecise concepts • Example: • “He is quite tall” • “The student is intelligent” • “Today is a very hot day” • These statements are difficult to translate into more precise language • Fuzzy logic was introduced to design systems that can demonstrate human-like reasoning capability to understand such vague terms

5. Degree of membership of a “tall” man Height, cm Crisp value 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 Extremely tall Very tall tall It will just return a ‘yes’ or a ‘no’ In fuzzy, Probability is used When a numeric data is given

6. Relationships between uncertainty terms and certainty factor (CF) CF takes value from -1 to 1 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 So, be careful when you use the term “may be”.. It represents only 40%

7. What is not considered as fuzzy logic ? • Classical logic or Boolean logic that has two values are not fuzzy! • Example: • true or false • yes or no • on or off • black or white • start or stop

8. Differences between Fuzzy Logic and Crisp Logic • CRISP LOGIC • precise properties • Full membership • YES or NO • TRUE or FALSE • 1 or 0 • Crisp Sets • she is 18 years old • man 1.6m tall • FUZZY LOGIC • Imprecise properties • Partial membership • YES ---> NO • TRUE ---> FALSE • 1 ---> 0 • Fuzzy Sets • she is about 18 years old • man about 1.6m tall

9. How does Fuzzy Logic resembles Human intelligence? • It can handle at certain level of imprecision and uncertainty • By clustering & classification • dividing the scenario/problems into parts • focusing on each part with rank of importance and alternatives to solve • combining the parts to as an integrated whole • It reflects some forms of the human reasoning process by • Setting hypothetical rules • Performing inferencing • Performing logic reasoning on the rules

10. Boolean Logic (for ‘Temperature’) to Describe terms such as ‘cold’, ‘hot’ Hot 100.0 Temperature (C º) Cold 0.0 It is discrete, i.e. based on two values

11. Fuzzy Logic (for ‘Temperature’) Extremely Hot 100.0 Hot Quite Hot Temperature (C º) Quite Cold Cold Extremely Cold 0.0 It’s continuous…

12. Fuzzy Logic can • represent vague language naturally • enrich not replace crisps sets • allow flexible engineering design • improve model performance • E.g. save power consumption • E.g. increase lifespan • are simple to implement, and • often work

13. 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)

14. Embedding Fuzzy Logic in Control Systems • Fuzzy Control used in the subway in Sendai, Japan • fuzzy control system is used to control the train'sacceleration, deceleration and braking • & passengers hardly notice when the train is actually changing its velocity • has proven to be superior to both human and conventional automated controllers • reduced the energy consumption been by 10% • The idea of fuzzy controlling technology has been enthusiastically received in Japan

15. Fuzzy Logic Applications • Fuzzy Logic success is mainly due to its introduction into consumer products such as: • temperature controlled electrical shower unit • air conditioner • washing machines • refrigerators • television • rice cooker • brake control of vehicles • Etc.

16. Fuzzy Rule • 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

17. What is the difference between classical and fuzzy rules? Consider the rules in fuzzy form, as follows: Rule 1 Rule 2 IF driving_speed is fast IF driving_speed is slow THEN stop_distance is long THEN stop_distance is 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.

18. Example of 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 One set of 3 fuzzy rules More can be generated IF service is excellent OR food is delicious THEN tip is generous : : Also, look at the linguistic values used here 

19. Example • Problems: • How to handle the temperature of a room so that it is not too hot/cold • How if too many students or very few students are in the room ? • How to designed an automatic air-conditioner which will be able to set temperature: • warmer when it is too cold, and • colder it is too hot?

20. Fuzzy Logic Methodology • Set the boundaries between two values(cold and hot) which will show the degrees of temperature • A sample set of rules IF temperature iscoldTHENset fan_speed tozero IF temperature iscoolTHENset fan_speed tolow IF temperature iswarmTHENset fan_speed to medium IF temperature ishotTHEN setfan_speed tohigh

21. Exercises

22. 2. Design a set of fuzzy rules for an electrical washing machine Or IF Load_Weight is heavy THEN set Water_Amount to maximum IF Load_Weight is medium THEN set Water_Amount to regular IF Load_Weight is light THEN set Water_Amount to minimum

23. 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

24. Exercise: A question combiningfuzzy rules & truth values and resolution proof

25. FUZZY RULES AND RESOLUTION PROOF(WORKED EXAMPLE) • 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.

26. 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.

28. Supplementary slides

29. Applications in Fuzzy logic decision making • The most popular area of applications • fuzzy control • industrial applications in domestic appliances • process control • automotive systems

30. 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

31. 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

32. 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.

33. 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

34. 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

35. Conclusion • Fuzzy Logic Decision Making is used in many applications • Implemented using fuzzy sets operation(if_then_else statements & logical operators) • Resembles human decision making with its ability to work from approximate data and find a precise solutions