Systems, Man & Cybernetics - July 2015 - 46

the basic problem of how to find
Two years later, when Zadeh
a "best" or even a "good" system
was on the editorial board of IRE
Ideal filters are
under uncertainty. [44]
Transactions on Information
Zadeh mentioned in this editoTheory, he penned his editorial
defined as filters that
rial the names of the mathematifor the March 1958 edition, and he
achieve a perfect
cians and statisticians Lionel
pleaded-as Shannon had done
separation of signal
Weiss (1924-2000), Herman Chertwo years earlier-for a critical
noff ( bor n 1923) a nd Witold
examination of the situation in
and noise, but,
Hurewicz (1904-1956)-he had
his own specialist field. He titled
in reality, no such
apparently become familiar with
his foreword-a s Wiener had
their work when he was a visitdone two years earlier-with the
filters exist.
ing researcher at the Institute for
question "What Is Optimal?" He
Advanced Study (IAS) in Princasked readers how reasonable it
eton, New Jersey. In my opinion,
actually was to insist on optimal
this plea is early evidence of the emerging doubts that
solutions. After all, this approach had only established
Zadeh had about traditional mathematics, which had rareitself since Wiener had publicized his findings on optily been challenged previously as a tool for understanding
mal filters and prediction, and proponents were well on
real systems. However, Zadeh was still reluctant to turn
their way "to make a fetish of optimality. If a system is
his back on mathematics altogether.
not 'best' in one sense or
In subsequent years, Zadeh gradually became aware
another, we do not feel satthat, although the descriptions of real systems using the
isfied. Indeed, we are apt
instruments of ordinary mathematics were becoming
to place too much confimore complicated, they were not appropriate for real sysdence in a system that is,
tems. His attempts to characterize adaptive, linear, and
in effect, optimal by definioptimum systems demonstrated his efforts to find good
tion" [44]. Finding an optidefinitions within the framework of the conventional
mal system would mean
mathematical theory. His attempts to describe real syschoosing a per for mance
tems in a mathematically precise manner failed. There
criterion, then specifying
were questions about the problems of pattern recognition,
a class of acceptable syswhich Zadeh was beginning to consider in terms of the
tems
according
to
various
Figure 8. Herbert
Robbins. (Photo courtesy conditions with respect to
gradual membership of elements to sets.
of Lotfi A. Zadeh.)
Zadeh's renouncement of ordinary mathematics would
design, costs, and so on,
soon lead to a capitulation. He was nearing a crossroads.
and, finally, accepting one
Herbert E. Robbins (1915-2001) (Figure 8) was the chair
of these systems from the specified class as the best
of Columbia University's Department of Mathematical Stawith regard to these criteria. Zadeh now doubted that
tistics at the time. He was a good friend of Zadeh as well as
this method was any more sensible than the "relatively
of Deane Montgomery (1909-2002), a member of the IAS.
unsophisticated approach of the pre-Wiener era" [44].
Robbins and Montgomery campaigned for the approval
The selection of a single performance criterion leaves
of the IAS guest residency for which Zadeh had applied,
all of the other criteria that would likewise contribute to
even though it was rare for requests by scientists who were
performance evaluation unconsidered. When scalar funcneither mathematicians nor theoretical physicists or histions were used, the problem was oversimplified; vectortorians to receive a positive response [28]. Zadeh initially
valued functions might possibly be more suitable but also
took a half-year sabbatical from Columbia University in
more difficult to manage.
1956. He wanted to learn more about logic, an interest he
Zadeh similarly criticized the rational selection of decihad cultivated since 1950, when he had predicted that logic,
sion functions under uncertainty: "What should be done
and particularly multivalued logic, would become increaswhen the probabilities of the 'state of nature' characterizing
ingly more important apropos of the problems of EE in the
a problem are not known?" Here, Zadeh rejected the usual
future [58].
solution methods based on stochastics, or game theory:
The ambiance at the IAS very quickly inspired Zadeh,
At present no completely satisfactory rule for selectwho remarked that it was a "mecca for mathematicians"
ing decision functions is available, and it is not very
[30]. He attended lectures by U.S. mathematician and logilikely that one will be found in the foreseeable future.
cian Stephen Kleene (1909-1994), who had also continued
Perhaps all that we can reasonably expect is a rule
developing the multivalued logic devised by the Polish
which, in a somewhat equivocal manner, would
school of logic. Kleene became Zadeh's friend and mentor
delimit a set of "good" designs for a system. In any
at the IAS. "Steven Kleene was my teacher in logic. Yes, I
case, neither Wiener's theory nor the more sophistilearned logic from Stephen Kleene!" said Zadeh [28].
cated approaches of decision theory have resolved
46

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