From: owner-uai@cs.orst.edu on behalf of Lotfi A. Zadeh
[Zadeh@cs.berkeley.edu]
Sent: 2 września 2003 03:13
To: uai@cs.orst.edu
Subject: Re: [UAI] Decision Theories

Dear Konrad:

            Your comment touches upon a basic issue-- the semantics of 
imprecision.  Please note that imprecision is distinct from ambiguity.

    `        The two versions of my problem are intended  to mirror 
decision-making  in realistic settings. Suppose that I have to decide on 
whether to buy stock A or stock B. In large measure, my decision will be 
influenced by my perceptions of how the stocks will perform and with 
what probabilities.  Human perceptions are intrinsically imprecise. 
 Thus, to be able to deal with real-world problems, decision theory must 
address the issue of representation of, and deduction from, 
perception-based information  --   information  which is, for the most 
part, both imprecise and uncertain. Version  2 is a very simple example.

            The issue of how to define " approximately X, " where  X  is 
a real number, came up in earlier comments. In my view, the most natural 
way is to regard  "approximately X" as a label of a fuzzy subset of the 
real line. This fuzzy subset would be characterized by its membership 
function, that is, by specifying the degree  to which a real number, u, 
fits the description " approximately X," for each u.  It is possible, of 
course, but is not realistic, to define "approximately X" as an interval 
centering on X.

            If you do not like this characterization of "approximately 
X,"  use whatever you prefer so long as it is realistic.  What you will 
find is that existing bivalent-logic decision theories are ill-suited to 
deal with the problem of imprecision.   Indeed, given the fact that in 
most realistic settings much of decision-relevant information is 
perception-based  and hence imprecise, it is hard to understand why 
decision theories have lavished so much attention on decision-making 
under uncertainty, and paid so little attention to the basic problem of 
decision-making in an environment of imprecision and partial truth.  

                                                                        
                 Sincerely,

                                                                        
                      Lotfi

 Lotfi A. Zadeh
Professor in the Graduate School, Computer Science Division Department of Electrical Engineering and Computer Sciences University of California Berkeley, CA 94720 -1776 Director, Berkeley Initiative in Soft Computing (BISC)

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