2. Introduction What is Fuzzy Logic? HOW DOES FL WORK? Differences between Classical set (crisps) and Fuzzy set theory Example 1 Example 2 Classifying Houses Why Use Fuzzy Logic? The Fuzzy Logic Method

3.  The concept of Fuzzy Logic (FL) was conceived by Lotfi Zadeh, a professor at the University of California at Berkley.  way of processing data by allowing partial set membership rather than crisp set membership or non-membership. This approach to set theory was not applied to control systems until the 70's due to insufficient small-computer capability prior to that time.  Professor Zadeh reasoned that people do not require precise, numerical information input, and yet they are capable of highly adaptive control. If feedback controllers could be programmed to accept noisy, imprecise input, they would be much more effective and perhaps easier to implement. Unfortunately, U.S. manufacturers have not been so quick to embrace this technology while the Europeans and Japanese have been aggressively building real products around it. INTRODUCTION BACK

4. WHAT IS FUZZY LOGIC? FL is a problem-solving control system methodology that lends itself to implementation in systems ranging from simple, small, embedded micro-controllers to large, networked, multi- channel PC or workstation-based data acquisition and control systems. It can be implemented in hardware, software, or a combination of both. FL provides a simple way to arrive at a definite conclusion based upon vague, ambiguous, imprecise, noisy, or missing input information. FL's approach to control problems mimics how a person would make decisions, only much faster. BACK

5. HOW DOES FL WORK?  FL requires some numerical parameters in order to operate such as what is considered significant error and significant rate- of-change-of-error, but exact values of these numbers are usually not critical unless very responsive performance is required in which case empirical tuning would determine them.  For example, a simple temperature control system could use a single temperature feedback sensor whose data is subtracted from the command signal to compute "error" and then time- differentiated to yield the error slope or rate-of-change-of-error, hereafter called "error-dot". Error might have units of degs F and a small error considered to be 2F while a large error is 5F. BACK

6. Differences between Classical set (crisps) and Fuzzy set theory  Classical set theory is governed by two-valued logic, whereas Fuzzy set theory governed by many- valued logic. e.g. HOT _ City( Abu Dhabi) have a value which is a real number between 0 and 1.  but in Classical set have value 0 OR 1 Zero : Abu Dhabi belong to Hot _ City One : Abu Dhabi Not belong to Hot _ City

7. Cont …  domain of HOT _ city, f hot (35) = 0, f hot (40) = 1 In the fuzzy logic Ordered pairs of the form (make, degree) HOT _ city = {(Jakarta,0.9), (Abu Dhabi, 0.5),(Amman, 0.1)} Elements of a fuzzy set are members of that set to a degree. In the Classical set we consider all cities which is hot ( top temperature is in average 40 (1) and not consider otherwise (0)) But, what about a city with top-temperature 39C? A city with 35C is still a better choice rather than one with 30C.

8. CONT …. Conjunction & disjunction “Jakarta is a Hot and Tropical city.” In classical logic: Hot _ City( Jakarta) ^ Tropical _ City (Jakarta) is True if both conjuncts are true. In fuzzy logic: if F and G are fuzzy predicates then, F(F^G)(X) = min(fF(X), fG(X)), Thus if Hot _ City (Jakarta) = 0.9 Tropical _ City (Jakarta) = 0.7 Then fuzzy conjunction Hot _ City (Jakarta) and Tropical _ city (Jakarta) = 0.7

9. CONT …. Conjunction & disjunction “Jakarta is a Hot and Tropical city.” In classical logic: Hot _ City( Jakarta) v Tropical _ City (Jakarta) is False if both disjoints are false. In fuzzy logic: if F and G are fuzzy predicates then, F(F^G)(X) = max(fF(X), fG(X)), Thus if Hot _ City (Jakarta) = 0.9 Tropical _ City (Jakarta) = 0.7 Then fuzzy conjunction Hot _ City (Jakarta) and Tropical _ city (Jakarta) = 0.9 BACK

10. Example 1  A simple temperature regulator that uses a fan might look like this: IF temperature IS very cold THEN stop fan. IF temperature IS cold THEN turn down fan. IF temperature IS normal THEN maintain level. IF temperature IS hot THEN speed up fan.

11. Example 2 Classifying Houses Problem. A realtor wants to classify the houses he offers to his clients. One indicator of comfort of these houses is the number of bedrooms in them. Let the available types of houses be represented by the following set. U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} The houses in this set are described by u number of bedrooms in a house. The realtor wants to describe a "comfortable house for a 4-person family," using a fuzzy set. Solution. The fuzzy set "comfortable type of house for a 4-person family" may be described using a fuzzy set in the following manner

12. CONT …. BACK

13. Why Use Fuzzy Logic? 1.An Alternative Design Methodology Which Is Simpler, And Faster 2.Fuzzy Logic reduces the design development cycle 3.Fuzzy Logic simplifies design complexity 4.Fuzzy Logic improves time to market 5.A Better Alternative Solution To Non-Linear Control 6.Fuzzy Logic improves control performance 7.Fuzzy Logic simplifies implementation

14. 8. Fuzzy Logic reduces hardware costs e.g. Using a lookup table the two-input temperature controller requires 64Kb of memory, while the fuzzy approach is accomplished with less than 0.5Kb of memory for labels and object code combined. Cont … BACK

15. The Fuzzy Logic Method The fuzzy logic analysis and control method is, therefore: 1.Receiving of one, or a large number, of measurement or other assessment of conditions existing in some system we wish to analyze or control. 2. Processing all these inputs according to human based, fuzzy "If-Then" rules, which can be expressed in plain language words, in combination with traditional non-fuzzy processing. 3. Averaging and weighting the resulting outputs from all the individual rules into one single output decision or signal which decides what to do or tells a controlled system what to do. The output signal eventually arrived at is a precise appearing, defuzzified, "crisp" value. Please see the following Fuzzy Logic Control/Analysis Method diagram: