Hela den tryckta tidningen som en pdf-fil (ca 1800 KB) - Åbo Akademi

DISPUTATIONER
INFORMATIONSSYSTEM
M.Sc. Irina Georgescu disputerar i
informationssystem onsdagen den
25 maj på avhandlingen ”Rational
Choice and Revealed Preference:
A Fuzzy Approach”.
● Disputationen äger rum kl.
12 i auditorium 3102, DataCity.
Opponent är prof. Bernard De
Baets, Universiteit Gent, och som
kustos fungerar prof. Christer
Carlsson.
Så här sammanfattar Irina
Georgescu själv sin avhandling:
“Rational choice and revealed
preference are important issues
in social choice theory. A choice
act is said to be rational if it is
based on the optimization of
some preference relation.
The revealed preference
theory of consumers was created
by Samuelson and Houthakker.
Uzawa, Arrow and Sen developed
an axiomatic theory of revealed
preference in an abstract
framework independent of budget
sets and demand functions.
The results of Uzawa, Arrow, Sen
and their followers were proved
under the hypothesis that all
non-empty fi nite sets of alternatives
are included in the domain
of a choice function.
Further on, Richter, Hansson
and Suzumura elaborated a
generalized theory of revealed
16 MEDDELANDEN FRÅN ÅBO AKADEMI
preference with no restriction on
the domain of the choice function.
The contributions of this
thesis are concentrated on a
revealed preference theory for
fuzzy choice functions.
Our concept of fuzzy choice
function includes that of Banerjee.
In Banerjee’s approach, the
range of the fuzzy choice function
consists of fuzzy sets and the
domain consists of crisp sets, in
our approach both the domain
and the range of the fuzzy choice
function consist of fuzzy sets.
Our contributions can be
grouped in fi ve main themes:
1. Revealed preference and
congruence axioms for
fuzzy choice functions;
2. Rationality and normality
of fuzzy choice functions;
3. Consistency conditions for
fuzzy choice functions;
4. Degree of dominance for
fuzzy choice functions;
5. Applications.
Our revealed preference results
are developed in two directions:
– One generalizes the Uzawa-
Arrow-Sen theory
– The second extends the
Richter-Hansson-Suzmura
theory.
The fi rst direction starts from
two hypotheses that extend to
a fuzzy context Uzawa-Arrow-
Sen theory. In this framework
connections between weak
and strong congruence axioms
WFCA, SFCA, weak and strong
revealed preference axioms WA-
FRP, SAFRP and other properties
of rationality and normality
are established.
The main result is a generalization
of the Arrow-Sen theorem.
Further consistency conditions
Fα, Fβ, Fδ which are fuzzy versions
of Sen’s conditions α, β,
δ are studied. We prove that a
fuzzy choice function satisfi es
Fα and Fβ if and only if WFCA
holds. Also, Fδ holds if and only
if the revealed preference rela-
tion R (canonically associated
to the fuzzy choice function) is
quasi-transitive. Other consistency
conditions (Fα2, Fγ2, Fβ(+),
path independence) are also discussed.
In the second direction rationality
and revealed preference
theory for fuzzy choice functions
with arbitrary domains
are investigated. New axioms of
revealed preference WAFRPº,
SAFRPº, HAFRP are introduced
and relations between these axioms
and the previous ones are
established.
We obtain two main theorems:
(1) Axioms WFCA and WAFRPº
are equivalent. (2) Axioms SFCA
and HAFRP are equivalent. We
analyze two concepts of rationality:
G-rationality and M-rationality.
Another result generalizes a
part of a Richter theorem.
We defi ne a notion of the degree
of dominance of an alternative
with respect to an available
fuzzy set of alternatives and we
introduce new axioms of congruence
for fuzzy choice functions.
If we interpret an available set
as a criterion, then we can obtain
a ranking of alternatives (for
each criterion) with respect to
the act of choice.
This ranking is obtained by
using fuzzy choice problems
and the instrument by which it
is established is the degree of
dominance associated with a
fuzzy choice function. In defi ning
this fuzzy choice function
the revealed preference theory is
applied.
The applications describe
concrete economic situations
where partial information or human
subjectivity appears. The
mathematical modelling is done
by formulating some fuzzy choice
problems where criteria are represented
by fuzzy available sets
of alternatives; The degree of
dominance is the mathematical
instrument on which the algorithms
of multicriterial hierarchy
are based.”