**Previous message:**Vladik Kreinovich: "Re: Elkan crisis"**Messages sorted by:**[ date ] [ thread ] [ subject ] [ author ]

*********************************************************************

Berkeley Initiative in Soft Computing (BISC)

*********************************************************************

A Critical View of the Foundations of Control and Decision Analysis

Lotfi A. Zadeh *

Abstract

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

logic.

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:

unsubscribe bisc-group

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 listproc@dbai.tuwien.ac.at

(2) To unsubscribe from this mailing list, send a message body of

"UNSUB FUZZY-MAIL" or "UNSUB FUZZY-MAIL yoursubscription@email.address.com"

to listproc@dbai.tuwien.ac.at

(3) To reach the human who maintains the list, send mail to

fuzzy-owner@dbai.tuwien.ac.at

(4) WWW access and other information on Fuzzy Sets and Logic see

http://www.dbai.tuwien.ac.at/ftp/mlowner/fuzzy-mail.info

(5) WWW archive: http://www.dbai.tuwien.ac.at/marchives/fuzzy-mail/index.html

**Next message:**Tcmits1: "Re: Humans think fuzzy?"**Previous message:**Vladik Kreinovich: "Re: Elkan crisis"**Messages sorted by:**[ date ] [ thread ] [ subject ] [ author ]

*
This archive was generated by hypermail 2b30
: Fri May 11 2001 - 18:21:10 MET DST
*