FUZZ-IEEE’2013 Panel Presentation
Title: Since one of the main advantages
of fuzzy techniques is easiness-of-use,
why make them more complicated?
Presenter: Vladik Kreinovich
An advantage of fuzzy is easiness-of-use, so
why use more complicated techniques?
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First answer: this leads to a more adequate
description of uncertainty
We need fuzzy in situations when an expert cannot
describe an exact value of x, only “small” or “high”
The usual [0,1]-based fuzzy techniques describe the
expert’s uncertainty by a number d from [0,1]
If an expert cannot describe an exact value of x, she
cannot describe her degree d exactly either
A more adequate description is to say, e.g., that 0.7
is a possible degree, and 0.6 is somewhat possible
This means using type-2 fuzzy sets
An advantage of fuzzy is easiness-of-use, so
why use more complicated techniques?
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Second answer: representation complexity often
leads to faster computations
Example 1: ellipsoids are more complex than boxes,
but optimization over ellipsoids is faster
Example 2: complex numbers are more complex than
reals, but optimization and integration are faster
For this reason, complex numbers are used in
processing real-valued signals (e.g., FFT)
In applications like fuzzy control, complex numbers
are sometimes computationally more efficient
An advantage of fuzzy is easiness-of-use, so
why use more complicated techniques?
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Third answer: representations are complex because
we describe them in computer-usable terms
On the intuitive level, we can easily manipulate
“fuzzy” words like “small” or “large”
We want computers to manipulate these words, but
computers were designed for crisp notions
This is similar to the need to translate from decimal to
binary – since binary is the computer language
Ideally, we should teach computers how to deal with
words directly
This will make seemingly complicated
representations easier – but it’s a great challenge