# Re: Number of terms

Pramit 'Jake' Sarma (psarma@che.iitb.ernet.in)
Fri, 18 Jun 1999 11:51:53 +0200 (MET DST)

It is one of the meta-fuzzy reasons why a fuzzy variable of
cardinality N = 7 terms is often used. From 'lay-psychological' analysis
the human designer will usually agree that 7 partitions are quite 'good' - by
intuition. eg., Fuzzy variables in fuzzy logic control (FLC) are heuristically
and very frequently selected with N = 7 +/- 2: which, assuming good remaining
design, always [almost] produces great FLC's which slam-dunk other
controllers, to the chagrin of the crisp control theorists.

Since the fuzzy variable(s) will feed into a fuzzy rule-base (FRB), that
is where the cost of cardinality will be most evident. Suppose the FRB is
2-dimensional, ie., 2-input 1-output (TISO), and both card{Fuzzy Var} = N
for simplicity: Card{FRB rules} <= N^2. This forces the designer to
optimise on the cardinality - something that the human mind does implicitly.
To obtain an approximation of the overall float-ops (OFLOPS), the
single-rule SFLOPS = fn(Inference model, Implication model, Conjunction
model, ...) and is easy to calculate. Then, Max(OFLOPS) >= N^2 * SFLOPS.

Pramit

On Tue, 15 Jun 1999, Boris Shukhat wrote:

> Hi!
> It is well known that a human being usually uses 7-9 grades or
> linguistic terms to describe an intensity of some feature. As far as I
> know it is an empirical fact received in some psychological studies. It
> reflects some compromise between a loss of information as a result of
> granulation and a cost of manipulating those terms.
> Does anybody know if there is any estimate on how the cost of
> manipulating those linguistic terms depends on their number?
> Thanks,
> Boris Shukhat.

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Pramit "Jake" Sarma
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