Logic Tutorial Part I:
TO FUZZY LOGIC
The idea of fuzzy logic was born in 1965.
Lofti A. Zadeh
published a seminar paper on fuzzy sets which was the birth of fuzzy logic
technology. At the beginning fuzzy logic was strongly resisted, but step
by step more studies had been performed. In the decade after Dr.
Zadeth’s seminal paper many theoretical
developments in fuzzy logic took place in the
United States, Europe
These exploited the fact that for example Fuzzy Logic is tolerant of
imprecise data, can model nonlinear functions and can be blended with
conventional control techniques.
Fuzzy Logic is a technique that allows us to map an
input space to an output space, Similar to a black box which does
‘something’ to compute the solution, the output values. As shown in Figure
Figure 1: Black box model: Input-Output System.
There are many ways in which we can implement the black
box: neural networks, linear systems, expert systems, differential
equations, and so on.
So, why should we use Fuzzy Logic? The basic answer is
because basically it is more understandable, faster and cheaper than other
The main principle of fuzzy logic relates to the use of
fuzzy sets, which are classes with (unsharp)
no crisp boundaries. For instance, to define the set of tall people, we
could proceed as shown in Figure 2 below.
Figure 2: Set of tall
A sharp boundary would consider a ‘tall person’ to be
taller than, for instance, 170cm. And it would consider a ‘short person’
to be shorter than 170cm. Therefore if we have two people, one 169.8cm of
tall and the other one 170.1cm of tall, we would consider the first one to
be a short person and the second one to be a tall person. It has no sense
to consider one person tall and another short if the difference between
them is only 0.3cm.
As regards Figure 2, using a crisp or sharp boundary we
would consider person 2 tall and all the other people short.
The human reasoning doesn’t work in that way. We don’t
say that the person number2 is tall and the number 3 isn’t, because it
doesn’t seem sensible. Both number 2 and 3 have, more or less, the same
height so we can’t consider one tall and the other one short. We have
degrees between tall and short. Likewise we can’t consider the number 1
short and the number four also short, because we consider number four not
really tall, but in no way as short as number 1.
Human reasoning has “degrees” between different
concepts; we don’t always have crisp boundaries. Fuzzy logic allows us to
work like we think, so it’s conceptually easy to understand. The
mathematical concepts behind fuzzy reasoning are very simple, which makes
Fuzzy Logic very natural. It is based on both on natural reasoning and on
Fuzzy logic generalizes the binary distribution between
possible and impossible to a matter of degree called the possibility.
Nowadays Fuzzy Logic affects many disciplines:
videography (Sanyo), air-conditioning (Mitsubishi), and washing-machines
(combining smart sensors with Fuzzy Logic by Matsushita), for cars Nissan
introduced a fuzzy automatic transmission. There are also fuzzy toasters,
fuzzy rice-cookers, and so on.
There are applications of fuzzy system theory to
telecommunications such as channel equalization or call acceptance, signal
processing such as fuzzy filters or fuzzy signal detection, fuzzy systems
in control engineering, such as well working together with neural
networks. As we can see Fuzzy Logic has become widely used and this shows
Section 2 is about linguistic variables, fuzzy
membership functions, that is the basic
elements that allow us to build Fuzzy Logic Systems.