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# L15 fuzzy logic

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### L15 fuzzy logic

1. 1. Fuzzy LogicFuzzy Logic 1Rushdi Shams, Lecturer, Dept of CSE, KUET, Bangladesh
2. 2. Introduction  Form of multivalued logic  Deals reasoning that is approximate rather than precise  the fuzzy logic variables may have a membership value of not only 0 or 1 – that is, the degree of truth of a statement can range between 0 and 1 and is not constrained to the two truth values of classic propositional logic Rushdi Shams, Lecturer, Dept of CSE, KUET, Bangladesh 2
3. 3. Introduction  Fuzzy logic has been applied to many fields, from control theory to artificial intelligence  it still remains controversial among most statisticians, who prefer Bayesian logic, and  some control engineers, who prefer traditional two-valued logic. Rushdi Shams, Lecturer, Dept of CSE, KUET, Bangladesh 3
4. 4. Degrees of truth  let a 100 ml glass contain 30 ml of water.  Then we may consider two concepts: Empty and Full.  The meaning of each of them can be represented by a certain fuzzy set.  Then one might define the glass as being 0.7 empty and 0.3 full.  The concept of emptiness would be subjective and thus would depend on the observer or designer. Rushdi Shams, Lecturer, Dept of CSE, KUET, Bangladesh 4
5. 5. An image that describe fuzzy logic Rushdi Shams, Lecturer, Dept of CSE, KUET, Bangladesh 5
6. 6. An image that describe fuzzy logic  A point on that scale has three "truth values" — one for each of the three functions.  Since the red arrow points to zero, this temperature may be interpreted as "not hot".  The orange arrow (pointing at 0.2) may describe it as "slightly warm" and  the blue arrow (pointing at 0.8) "fairly cold". Rushdi Shams, Lecturer, Dept of CSE, KUET, Bangladesh 6
7. 7. Fuzzy Rules  fuzzy logic usually uses IF-THEN rules  Rules are usually expressed in the form: IF variable IS property THEN action  For example, 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 Rushdi Shams, Lecturer, Dept of CSE, KUET, Bangladesh 7
8. 8. Fuzzy Rules  There is no "ELSE" – all of the rules are evaluated, because the temperature might be "cold" and "normal" at the same time to different degrees.  The AND, OR, and NOT operators of boolean logic exist in fuzzy logic, usually defined as the minimum, maximum, and complement  when they are defined this way, they are called the Zadeh operators Rushdi Shams, Lecturer, Dept of CSE, KUET, Bangladesh 8
9. 9. Zadeh Operators  NOT x = (1 - truth(x))  x AND y = minimum(truth(x), truth(y))  x OR y = maximum(truth(x), truth(y)) Rushdi Shams, Lecturer, Dept of CSE, KUET, Bangladesh 9
10. 10. Hedges  There are also other operators, more linguistic in nature, called hedges that can be applied.  These are generally adverbs such as "very", or "somewhat" Rushdi Shams, Lecturer, Dept of CSE, KUET, Bangladesh 10
11. 11. Fuzzy Logic Applications  Air conditioning  Washing Machines (LG is the pioneer)  Mono-rails (first used in Tokyo)  Digital image processing (specially in medical imaging)  Elevators (in case of power failure)  Rice cookers  Video game engines (disperse intelligence in prince of Persia)  Special effects (swarm intelligence in Batman Begins, Terminator Salvation, The Lord of the Rings) Rushdi Shams, Lecturer, Dept of CSE, KUET, Bangladesh 11
12. 12. Objections against Fuzzy Logic  The concept of "coldness" cannot be expressed in an equation, because although temperature is a quantity, "coldness" is not  people have an idea of what "cold" is, and agree that there is no sharp cutoff between "cold" and "not cold"  where something is "cold" at N degrees but "not cold" at N+1 degrees — a concept classical logic cannot easily handle Rushdi Shams, Lecturer, Dept of CSE, KUET, Bangladesh 12
13. 13. Objections against Fuzzy Logic  The result has no set answer so it is believed to be a 'fuzzy' answer.  Fuzzy logic simply provides a mathematical model of the vagueness which is manifested in the above example. Rushdi Shams, Lecturer, Dept of CSE, KUET, Bangladesh 13
14. 14. A new way to represent probabilistic logic?  fuzzy set theory uses the concept of fuzzy set membership (i.e., how much a variable is in a set)  probability theory uses the concept of subjective probability (i.e., how probable do I think that a variable is in a set). Rushdi Shams, Lecturer, Dept of CSE, KUET, Bangladesh 14
15. 15. Reference  Wikipedia, “Fuzzy Logic”, http://en.wikipedia.org/wiki/Fuzzy_logic Rushdi Shams, Lecturer, Dept of CSE, KUET, Bangladesh 15