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<< Back to: FAQ: Fuzzy Logic and Fuzzy Expert Systems 1/1 [Monthly posting]

Question by vandy
Submitted on 9/24/2003
Related FAQ: FAQ: Fuzzy Logic and Fuzzy Expert Systems 1/1 [Monthly posting]
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what is fuzzy logic

Answer by John Nowakowski
Submitted on 10/1/2003
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I'll give a short and simplified answer.

First, you must understand fuzzy logic is referring to something different than regular, western, formal logic (non-fuzzy logic).  

Formal, western, non-fuzzy logic is the basis for most computer programming.

The key concept is that it is a two-valued logic or "bivalent"

in formal logic a proposition is either True or False.

in computer programming, everything is represented through a 0 or 1.

So, if we take an imaginary set of objects, and designate it the S set, and an imaginary thing, X, we would say that either:
X is a member of the S set
X is not a member of the S set

One of those propositions is True and the other is False by non-fuzzy logic.

Let S be the set of all dogs
Let X be Lassie.

Either Lassie is a dog
Lassie is not a dog

So the statement
Lassie is a dog
is either
and those are the only two choices.

This is the standard approach of western formal logic and, derivatively, computer programming.

You might think of this non-fuzzy approach as "black or white" kind of thinking.  You use 0 or 1, never .242.

Fuzzy logic (following the lead of eastern logic) is an attempt to formalize the recognition of "grayness" in life.

Rather than 0 or 1, it is the interval of [0,1] with intermediary intervals in between.  So a proposition is neither 100% true OR 100% false, but allows for uncertainty, vagueness, and "fuzzy" states in between.

The key is that opposed to the non-fuzzy, bivalent logic, fuzzy logic is multivalent.

Some Buddhists employed a four valued logic.

There is debate by logicians more informed than myself as to what exactly to make of fuzzy logic.  Proponents of fuzzy logic view it as advancement, part of the natural progress to evolve from a two-valued logic to a multivalued logic.  Detractors view fuzzy logic as no real logic at all, but rather an undoing of formal logic.  
On this debate, I express no opinion.


Answer by ritesh
Submitted on 11/16/2004
Rating: Not yet rated Rate this answer: Vote
fuzzy logic works on the uncertentity


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