Information Technology Reference
In-Depth Information
3.3
From the Systems View to the “New View” of Fuzzy
Systems
As we mentioned already, in the 1950s, when
Cybernetics
and
System Theory
were
rising scientific disciplines which concerned the general principles of characteriz-
ing input-output relationships. Engineers in that time were, in general, inadequately
trained to think in abstract terms, but nevertheless, the electrical engineer Lotfi A.
Zadeh (3.4 (a)) had been doing research in the fields of linear and nonlinear systems.
In 1954, when he was an assistant professor at Columbia University in New York,
he wrote an article entitled “System Theory” for the New York student publica-
tion
Columbia Engineering Quarterly
that he wanted to be an easily understandable
introduction to this topic. Here, he described “System Theory” as a scientific disci-
pline “to the study of systems per se, regardless of their physical structure”. [99, p.
16] He believed that it was only a matter of time before system theory attains accep-
tance. He represented systems as block diagrams, i.e. graphical descriptions of the
interrelationships between the variables associated with the system's objects. Thus
block diagrams present in a graphical form the same information about a system as
is conveyed by writing the input-output relationship:
v
1
,...,
v
n
=
f
(
u
1
,...,
u
m
)
(3.6)
with inputs
u
1
,...,
. In the case that these inputs
and outputs are describable as time dependent functions the dynamic behavior of the
system can be studied mathematically.
System theory became a well-known and important methodology in Electrical
Engineering and after Zadeh became professor at the Unversity of California, Berke-
ley, he could describe problems and applications of System Theory and its rela-
tions to Network Theory, Control Theory, and Information Theory. Furthermore,
he pointed out “that the same abstract 'systems' notions are operating in various
guises in many unrelated fields of science is a relatively recent development. It has
been brought about, largely within the past two decades, by the great progress in our
understanding of the behaviour of both inanimate and animate systems—progress
which resulted on the one hand from a vast expansion in the scientific and techno-
logical activities directed toward the development of highly complex systems for
such purposes as automatic control, pattern recognition, data-processing, communi-
cation, and machine computation, and, on the other hand, by attempts at quantitative
analyses of the extremely complex animate and man-machine systems which are en-
countered in biology, neurophysiology, econometrics, operations research and other
fields” [101, p. 856 f.].
This quotation is from Zadeh's article “From Circuit Theory to System Theory”
[101] to mark the 50th year of the Institute of Radio Engineers (IRE) where he
described the successful developments in electrical engineering, and he specifically
mentioned Bertalanffy's General Systems Theory.
Before we will refer to this interesting subject, let us consider an interesting
event, i.e. the
Second Systems Symposium
that took place at the Case Institute of
Technology in Cleveland (Ohio) in the spring of 1963. Entitled “Views on General
u
m
and outputs
v
1
,...,
v
n
,
(
m
,
n
∈
N
)
