BISC: Seminar May 30th: Decision Making under Fuzziness


Subject: BISC: Seminar May 30th: Decision Making under Fuzziness
From: BISC (berthold@cs.berkeley.edu)
Date: Thu May 25 2000 - 10:12:20 MET DST


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Berkeley Initiative in Soft Computing (BISC)
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  BISC Seminar - Tuesday, May 30th, 2000 - 310 Soda Hall - 4:00-5:00pm

     Decision Making under Fuzziness - A new approach to decision
         making based on fuzzy inclusion relations

                     Oliver van Laak
         Gerhard-Mercator-University of Duisburg
                Department of Mathematics
                    Duisburg, Germany
             email: laak@math.uni-duisburg.de

Abstract:
Decision making is one of the subjects to which fuzzy set theory
has been successfully applied to in the recent years. Various
approaches to different aspects of decision problems with vague
data have been published. It has been proved that fuzzy theory
provides a sophisticated framework for describing and processing
uncertain or imprecise information in decision problems.

Undoubtedly, the convenient mathematical description of a decision
problem is closely related to the considered problem itself. For
this reason, various mathematical concepts have been introduced in
fuzzy decision theory. However, due to the heterogeneous nature of
these various mathematical concepts it is difficult, if not even
impossible, to compare these different fuzzy approaches and the
obtained solutions. In fact, most approaches appear to be only
applicable to a highly specialized class of decision problems and
the generalization of these concepts is extremely difficult.
Therefore, these approaches are not suitable for the description
of decision problems with different classes of uncertainty.
Moreover, most of the fuzzy decision models by which imprecise
data can be described and processed cannot be regarded as a
generalization of the symmetric decision model of Bellman and
Zadeh. Undoubtedly, this is the most popular approach for
describing decision problems in a fuzzy environment. Finally,
there is no fuzzy decision model which can be regarded as an
extension of the classical approaches to decision theory.
Especially, there is no sophisticated fuzzy equivalent to the
classical decision models under risk and uncertainty -
nevertheless, these concepts have frequently proved their power in
decision theory.

In this talk we present a new approach to decision making based on
fuzzy inclusion relations. These relations can be regarded as an
extension of the classical inclusion concept. We show that many
known fuzzy measures can be represented by fuzzy inclusion
relations; namely possibility, necessity, and probability measures
can be represented by fuzzy inclusion relations in a unique way.
We outline some general consequences of this result and formulate
a decision model which is based on inclusion relations. This
decision model is an extension of the symmetric decision model. It
is applicable to any (classical) kind of uncertain information. We
present that the decision models of Wald, Hurwicz, and Laplace can
be represented by the formulated model as well as most of the
known classical approaches to decision making under risk. The
model can process both, decisions with a single criterion and
decisions with multi criteria. Therefore, the formulated model
provides a homogeneous theoretical framework for various decision
problems with different classes of uncertainty and opens up this
way new perspectives for decision theory.

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