BISC: Zadeh: The Robert Example

From: Masoud Nikravesh (nikravesh@eecs.berkeley.edu)
Date: Thu Mar 08 2001 - 04:21:54 MET

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                      The Robert Example
     
         The Robert example is an instance of a class of
    uncertainty-centered problems which lie beyond the
    reach of classical probability theory and Bayesian
    techniques. However, the questions posed in the Robert
    example fall within the reach of a perception-based
    generalization of probability theory. The Robert
    example relates to everyday commonsense reasoning.

         More specifically, assume that I am considering
    calling Robert at home at 6:30 pm. The question is:
    Should I call him person-to-person or
    station-to-station, given that the calls cost a and b,
    respectively.

         The decision-relevant information is the
    probability that Robert is home at 6:30 pm.

         There are three versions of the information which
    I have -- in order of increasing difficulty of
    analysis.

         Version l. My perception is that usually Robert
    returns from work at about 6:00 pm.

         Version 2. My perceptions are: (a) usually
    Robert leaves his office at about 5:30 pm; and (b) it
    takes him about 30 minutes to get home.

         Version 3. My perceptions are: (a) usually
    Robert leaves his office at about 5:30 pm; and (b) the
    travel time depends on the time when he leaves office.
    More specifically:

         when Robert leaves at about 5:l5 pm, the travel
    time is about 25 minutes.
         when Robert leaves at about 5:30 pm,the travel
    time is about 30 minutes.
         when Robert leaves at about 5:45 pm, the travel
    time is about 35 minutes.

         An additional question: What is the earliest time
    at which the probability that Robert is home is high?

         It is understood that in the Robert example,
    terms such as high, usually, about 6:00 pm, etc., do
    not have a crisp meaning.

    =====
    Lotfi A. Zadeh
    Professor in the Graduate School, Computer Science Division, Department of EECS,
    University of California, Berkeley, CA 94720-1776.
    Director, Berkeley Initiative in Soft Computing (BISC)
    Tel (office): (510) 642-4959, Fax (office): (510) 642-1712
    Tel (home): (510) 526-2569, Fax (home): (510) 526-2433, (510) 526-5181
    zadeh@cs.berkeley.edu,
    http://www.cs.berkeley.edu/People/Faculty/Homepages/zadeh.html
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