Berkeley Initiative in Soft Computing (BISC)
A Critical View of the Foundations of Control and Decision Analysis
Lotfi A. Zadeh *
Practitioners of classical control and decision analysis can point with pride
to a multitude of brilliant successes, among them the conquest of space and
optimal allocation of resources involving linear programs with tens of thousands
of variables and constraints.
But alongside the brilliant successes stand much less grandiose problems which
so far have eluded solution. We cannot automate driving in city traffic, build
robots which can play basketball or construct programs which can do economic
forecasting without human intervention.
The debut of fuzzy logic was motivated in large measure by a realization that
classical-logic-based theories do not have the capability to solve problems of
this type. What is becoming clearer now is that to deal with such problems it
is necessary to develop theories which are capable of processing
perception-based information. At the center of these theories is the recently
developed methodology of computing with words (CW).
As a methodology, computing with words brings to light some basic flaws in the
foundations of control and decision analysis. One such flaw relates to what may
be called the illusion of crisp definability.
More specifically, almost all concepts in classical control, probability theory
and decision analysis are crisp, that is, are based on Aristotelian logic. For
example, under Lyapounov's definition of stability, a system is either stable or
unstable, with no shades of gray allowed; a process is either random or
unrandom; random variables are either dependent or independent; and causal
relations are categorical rather than a matter of degree.
What can be shown is that crisp definitions lead to counterintuitive
conclusions in much the same way as the ancient Greek sorites paradox - a
paradox which involves successive removal of grains of sand from a heap. As an
illustration, consider Lyapounov's definition of stability in application to a
ball of diameter D which is placed on the mouth of an open bottle of diameter
d. When D is slightly larger than d, the system is clearly stable. As D
increases and eventually becomes much larger that d, the system becomes less and
less stable and eventually becomes unstable. This contradicts Lyapounov's
definition of stability, according to which the system is stable no matter how
large D is. In this example, gradual increase in D is analogous to gradual
decrease in the size of the heap.
A related problem arises in the case of a concept which plays a basic role in
decision analysis - the concept of the expected value of a random variable. It
is well known that the widely used principle of minimization of expected utility
leads to paradoxes such as the Allais paradox. A basic reason is that the
crisply-defined expected value of a random variable is its average value, which
may or may not coincide with our intuitive perception of the value which the
variable is most likely to take. To capture this concept, what is needed is the
fuzzy-logic-based concept of the usual value. Manipulation of usual values
falls outside the scope of classical probability theory; it falls however,
within the methodology of computing with words under the rubric of dispositional
The illusion of crisp definability is not the only basic flaw in classical
control and decision analysis. There are others. In particular, both classical
control and decision analysis founder on the rocks of what may be called the
dilemma of "it is possible but not impossible."
Von Neumann, Morgenstern, Wald and other founders of decision analysis were
driven by a quest for a mathematical theory which is rigorous, precise and
prescriptive. The dilemma of "possible but not probable" is a major obstacle to
the development of theories in this spirit. More specifically, decision
analysis and control rest on the tacit assumption that the worst-case scenario,
though possible, is not probable. The problem is that the probability of a
worst-case scenario does not lend itself to precise assessment. As a
consequence, validity of many basic concepts centering on optimality, stability
and causality is called into question. What is needed to deal with this basic
problem is the methodology of computing with words.
Computing with words is not a panacea. In essence, it opens the door to a
potentially radical enlargement of the role of natural languages in science and,
in particular, in information processing, decision and control.
BISC Homepage: http://www-bisc.cs.berkeley.edu
If you ever want to remove yourself from this mailing list,
you can send mail to <Majordomo@EECS.Berkeley.EDU> with the following
command in the body of your email message:
or from another account,
unsubscribe bisc-group <your_email_adress>
This message was posted through the fuzzy mailing list.
(1) To subscribe to this mailing list, send a message body of
"SUB FUZZY-MAIL myFirstName mySurname" to email@example.com
(2) To unsubscribe from this mailing list, send a message body of
"UNSUB FUZZY-MAIL" or "UNSUB FUZZY-MAIL firstname.lastname@example.org"
(3) To reach the human who maintains the list, send mail to
(4) WWW access and other information on Fuzzy Sets and Logic see
(5) WWW archive: http://www.dbai.tuwien.ac.at/marchives/fuzzy-mail/index.html
This archive was generated by hypermail 2b30 : Fri May 11 2001 - 18:21:10 MET DST