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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 relation 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.”
GEOLOGI FM Peter Österholm disputerar i geologi fredagen den 27 maj på avhandlingen ”Previous, Current and Future Leaching of Sulphur and Metals from Acid Sulphate Soils in W. Finland”. ● Disputationen äger rum kl. 12 i Auditorium I, Geologicum. Opponent är prof. Mike Melville, The University of New South Wales, och som kustos fungerar prof. Mats Åström. Så här sammanfattar Peter Österholm själv sin avhandling: ”På västkusten i Finland fi nns stora områden (1000–3000 km 2 ) med mycket svavelrika sediment som landhöjningen lyft upp ovanför havsytan och som senare utvecklats till så kallade sura sulfatjordar (pH
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