1 / 35

BEE4333 Intelligent Control

BEE4333 Intelligent Control. FUZZY EXPERT SYSTEM : FUZZY LOGIC. Hamzah Ahmad Ext: 2055/2141. Today Lessons. 3.1 Overview of Fuzzy Concepts and Fuzzy Logic Systems 3.2 Definition of Fuzzy Sets. LO1 : Able to understand basic concept of fuzzy sets which is the basis of fuzzy logic system.

crescent
Download Presentation

BEE4333 Intelligent Control

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. BEE4333 Intelligent Control FUZZY EXPERT SYSTEM : FUZZY LOGIC Hamzah Ahmad Ext: 2055/2141

  2. Today Lessons 3.1 Overview of Fuzzy Concepts and Fuzzy Logic Systems 3.2 Definition of Fuzzy Sets LO1 : Able to understand basic concept of fuzzy sets which is the basis of fuzzy logic system Achievements : CO2

  3. FUZZY EXPERT SYSTEM : FUZZY LOGIC • Introduction, or what is fuzzy thinking? • Fuzzy sets • Linguistic variables and hedges • Operations of fuzzy sets • Fuzzy rules • Summary

  4. Which one comes first? Fuzzy Logic Bicycle tyre pressure : Expert knows how to measure and human may understand on when to re-pump the pressure. But how about computer interpretation? IC supply voltage : Expert knows a considerable average of voltage stability and range to be supplied, but can system or software define properly as we expect? ExistenceofDegree or Level

  5. . System Paradigm Degree of confidence, multi-valued, humanistic Vagueness

  6. Definition of Fuzzy Logic • A set of mathematical principles for knowledge representation based on degree of membership rather than on crisp membership of classical binary logic.[LotfiZadeh, 1965] • Technology proposed to move from probability theory to mathematical logic. • Fuzzy sets : a set with fuzzy boundaries.

  7. Example: Washing Machine http://www.control-systems-principles.co.uk/whitepapers/fuzzy-logic-systems.pdf

  8. Traffic light fuzzy control[1] Fuzzified Rule evaluation Depends on the criteria of what the designer would like the system to decide e.gIf cycle time is short(15s) And cars behind red density is medium (7s) And cars behind green density is medium (6s) Then the change is probably not Defuzzification Depends on the criteria of what the designer would like the system to decide e.g calculating the probability to optimize the solution. If more than 50% then the colour will change. [1]Kaur, D., Konga, E., Fuzzy traffic light controller, Proceedings of the 37th Midwest Symposium on circuit and system, pp. 1507 - 1510 vol.2, 1994.

  9. Differences between Fuzzy Logic and Probability Sanjaa, B., Tsoozol, P., Fuzzy and Probability, International Forum on Strategic Technology, 2007. IFOST 2007, pp141 – 143, 2007

  10. Crisp set vs Fuzzy set A B Fuzzy set Crisp set Fuzzy set Crisp set mA(x): X ® [0, 1], where mA(x) = 1 if x is totally in A;mA(x) = 0 if x is not in A; 0 < mA(x) < 1 if x is partly in A. fA(x): X ® {0, 1}, where

  11. Crisp and fuzzy sets of short, average and tall men

  12. Consider a situation… Reference super set : BEE4333 Course after this defined as B B = {EA00007, EA00008,….,EA00060} of 54 students Crisp Subset of X : Excellent Student after this defined as E E : EA00007, EA00020, EA00060 Subset of E,E = { (EA00007, 1), (EA00008, 0),.., (EA00020,1), ….,(EA00021,0), …,(EA00060,1)} E : Fuzzy subset of B if and only if E ={(EAXXXXX, μE(EAXXXXX))} EAXXXXX ϵ B, : B[0,1] Pair Set = { (EAXXXXX, μE (EAXXXXX)} Only two values of fuzziness are considered.

  13. Computer Representation A = { (x1,μA(x1)), (x2,μA(x2)),…., (xn,μA(xn)) } Membership association A = { μA(x1)/x1), μA(x2)/x2), ….,μA(xn)/xn)} Linear Fit Function is used to represent real data in fuzzy set instead of sigmoid, gaussian and pi as these three(3) increases the computation time. High voltage = (0/200, 0.5/600, 1/1000) High voltage = (0/200, 1/1000)

  14. Today Lessons 3.1 Overview of Fuzzy Concepts and Fuzzy Logic Systems 3.2 Definition of Fuzzy Sets LO1 : Able to understand basic concept of fuzzy sets which is the basis of fuzzy logic system Achievements : CO2

  15. Today Lessons 3.3 Fuzzy Set Operations 3.4 Fuzzy Relation LO1 : Able to execute fuzzy sets using the common fuzzy operations LO2 : Able to understand and determine the purpose of fuzzy relations Achievements : CO2

  16. Linguistic: Affection in Fuzzy • IF sun is shining, THEN temperature is hot. • IF people is happy, THEN society is at peace. • IF stomach is full, THEN ? Linguistic variablefuzzy variable • Linguistic variable has hedges • Hedges • Act as fuzzy set qualifiers • Expression on adverbs ; little, few, most, extreme, some • Reflects human thinking • Creates sets of individual operation; dilation(expansion), concentration • Continuumfuzzy intervals; from tall, average, short to slightly tall, tall, moderately tall etc.

  17. Example

  18. Hedges in fuzzy logic

  19. Hedges in fuzzy logic (cont’d)

  20. Operations of fuzzy sets The classical set theory developed in the late 19th century by Georg Cantor describes how crisp sets can interact. These interactions are called operations.

  21. Complement Crisp Sets:Who does not belong to the set? Fuzzy Sets:How much do elements not belong to the set? The complement of a set is an opposite of this set. For example, if we have the set of tall men, its complement is the set of NOT tall men. When we remove the tall men set from the universe of discourse, we obtain the complement. If A is the fuzzy set, its complement ØA can be found as follows: mØA(x) = 1 -mA(x)

  22. Containment • Crisp Sets:Which sets belong to which other sets? • Fuzzy Sets:Which sets belong to other sets? • Similar to a Chinese box, a set can contain other • sets. The smaller set is called the subset. For • example, the set of tall men contains all tall men; • very tall men is a subset of tall men. However, the • tall men set is just a subset of the set of men. In • crisp sets, all elements of a subset entirely belong to • a larger set. In fuzzy sets, however, each element • can belong less to the subset than to the larger set. • Elements of the fuzzy subset have smaller • memberships in it than in the larger set.

  23. Intersection Crisp Sets:Which element belongs to both sets? Fuzzy Sets:How much of the element is in both sets? In classical set theory, an intersection between two sets contains the elements shared by these sets. For example, the intersection of the set of tall men and the set of fat men is the area where these sets overlap. In fuzzy sets, an element may partly belong to both sets with different memberships. A fuzzy intersection is the lower membership in both sets of each element. The fuzzy intersection of two fuzzy sets A and B on universe of discourse X: mAÇB(x) = min [mA(x), mB(x)] = mA(x) Ç mB(x), where xÎX

  24. Union • Crisp Sets:Which element belongs to either set? • Fuzzy Sets:How much of the element is in either set? • The union of two crisp sets consists of every element • that falls into either set. For example, the union of • tall men and fat men contains all men who are tall • OR fat. In fuzzy sets, the union is the reverse of the • intersection. That is, the union is the largest • membership value of the element in either set. The • fuzzy operation for forming the union of two fuzzy • sets A and B on universe X can be given as: mAÈB(x) = max [mA(x), mB(x)] = mA(x) È mB(x), where xÎX

  25. Operations of fuzzy sets

  26. Fuzzy rules In 1973, LotfiZadehpublished his second most influential paper. This paper outlined a new approach to analysis of complex systems, in which Zadeh suggested capturing human knowledge in fuzzy rules.

  27. What is a 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; and A and B are linguistic values determined by fuzzy sets on the universe of discourses X and Y, respectively.

  28. What is the difference between classical and fuzzy rules? A classical IF-THEN rule uses binary logic, for example, Rule: 1 Rule: 2 IF speed is > 100 IF speed is < 40 THEN stopping_distance is long THEN stopping_distance is short The variable speed can have any numerical value between 0 and 220 km/h, but the linguistic variable stopping_distance can take either value long or short. In other words, classical rules are expressed in the black-and-white language of Boolean logic.

  29. We can also represent the stopping distance rules in a fuzzy form: Rule: 1 Rule: 2 IF speed is fast IF speed is slow THEN stopping_distance is long THEN stopping_distance is short In fuzzy rules, the linguistic variable speed also has the range (the universe of discourse) between 0 and 220 km/h, but this range includes fuzzy sets, such as slow, medium and fast. The universe of discourse of the linguistic variable stopping_distancecan be between 0 and 300 m and may include such fuzzy sets as short, medium andlong.

  30. Fuzzy rules relate fuzzy sets. • In a fuzzy system, all rules fire to some extent, or in other words they fire partially. If the antecedent is true to some degree of membership, then the consequent is also true to that same degree.

  31. Fuzzy sets of tall and heavy men These fuzzy sets provide the basis for a weight estimation model. The model is based on a relationship between a man’s height and his weight: IF height is tall THEN weight is heavy

  32. The value of the output or a truth membership grade of the rule consequent can be estimated directly from a corresponding truth membership grade in the antecedent. This form of fuzzy inference uses a method called monotonic selection.

  33. Afuzzy rule can have multiple antecedents, for example: IF project_duration is long AND project_staffing is large AND project_funding is inadequate THEN risk is high IF service is excellent OR food is delicious THEN tip is generous

  34. The consequent of a fuzzy rule can also include multiple parts, for instance: IF temperature is hot THEN hot_water is reduced; cold_water is increased

  35. Today Lessons 3.3 Fuzzy Set Operations 3.4 Fuzzy Relation LO1 : Able to execute fuzzy sets using the common fuzzy operations LO2 : Able to understand and determine the purpose of fuzzy relations Achievements : CO2

More Related