Computational Intelligence - August 2012 - 52

over the type-1 system, but in this case
are the two system equivalent? If we
consider the complexity of such systems then the systems are clearly not
equivalent. There are a number ways of
measur ing system complexity, for
example the number of terms, the
number of design parameters or the
level of computational complexity.
Garibaldi advocates an investigation
into an information measure analogous
to Akaike's Infor mation Cr iter ion
(AIC). AIC provides a way of measuring the fitness of a statistical model by
essentially measuring the information
lost when fitting the statistical model.
This allows for fair comparisons of
models of different complexities using
appropr iate qualitative techniques.
Such a methodology would be of great
benefit when comparing fuzzy systems
of different types.
3. Misconceptions
3.1. Performance

The first misconception is that type-2
fuzzy logic systems/controllers will
always outperform their type-1 counterparts. This is not necessarily true and the
type-2 community have sometimes
made claims where there is clearly little
or no difference. As discussed above
great care needs to be taken when comparing type-1 and type-2. Indeed we
would argue that this is probably a waste
of time for a given application. The evidence is that in a very noisy environment or where there are linguistic
uncertainties type-2 fuzzy logic may
assist in providing good solutions. In a
way it is still early days for the type-2
applications as only in the recent few
years have we had the algorithms to use
generalized type-2 fuzzy systems. Applications of type-1 fuzzy logic have been
around for decades.
A related misconception is that real
time type-2 fuzzy systems are not possible. Recent advances using alpha planes
and z slices may well allow for real time
and indeed if we deploy interval valued
type-2 fuzzy systems then "fast enough"
systems can be deployed.

52

3.2. The Role of Type-1

The second misconception is that type2 fuzzy logic will become the norm and
replace type-1 fuzzy systems. This is not
our view. As reiterated a number of
times here we see that type-1 fuzzy
logic will continue to be important and
type-2 should be used if necessary. This
is an open research question.
4. Summary

In this paper we have tried to collate
some thoughts on challenges and misconceptions of type-2 fuzzy systems.
There are many challenges for new
researchers in the field and many interesting avenues to pursue. When considering when to use type-2 the chief
message is that it is not type-1 vs type-2
but, to use an English phrase, "Horses
for Courses." That is we can use type-1
or type-2. Experience to date shows
that type-2 can help in certain cases.
The type-2 applications field is still very
new and we have much with which to
look forward.
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IEEE COMPUTATIONAL INTELLIGENCE MAGAZINE | AUGUST 2012

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