L15 fuzzy logic

Fuzzy LogicFuzzy Logic

1Rushdi Shams, Lecturer, Dept of CSE, KUET, Bangladesh

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

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.


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.


An image that describe fuzzy logic


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".


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 fanIF temperature IS cold THEN turn down fanIF temperature IS normal THEN maintain levelIF temperature IS hot THEN speed up fan


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


Zadeh Operators NOT x = (1 - truth(x)) x AND y = minimum(truth(x), truth(y)) x OR y = maximum(truth(x), truth(y))


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"


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)


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


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.


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).


Reference Wikipedia, “Fuzzy Logic”,

http://en.wikipedia.org/wiki/Fuzzy_logic


Technology

L15 fuzzy logic