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The 6th International Conference on
Modeling Decisions for Artificial Intelligence

Awaji Island, Japan, November 30 - December 2, 2009
Submission deadline:
(extended) May 21, 2009


Talks by Profs. Roman Slowinski, Hiroyuki Tamura, Weldon A. Lodwick, L. Godo, and Sadaaki Miyamoto will be given in MDAI 2009. Abstracts follow.


Prof. Roman Slowinski
(Poznan University of Technology, Laboratory of Intelligent Decision Support Systems, and Systems Research Institute, Polish Academy of Sciences, Poland)
Interactive Robust Multiobjective Optimization Driven by Decision Rule Preference Model
Interactive procedures for multiobjective optimization (MOO) consist of a sequence of steps alternating calculation of a sample of non-dominated solutions and elicitation of preference information from the Decision Maker (DM). We consider three types of procedures, where in preference elicitation stage, the DM is just asked to indicate which solutions are relatively good in the proposed sample. In all three cases, the preference model is a set of decision rules inferred from the preference information using the Dominance-based Rough Set Approach (DRSA) [1,5]. The main advantage of decision rules is their simplicity and human-interpretable form. Moreover, they are able to model interactions between objectives. The first case is a deterministic MOO problem. Selected decision rules permit to focus progressively on the most interesting region of the Pareto-optimal set [2]. The second case is an optimization problem under uncertainty, exemplified by portfolio selection. Feasible portfolios are evaluated in terms of meaningful quantiles of the distribution of return. Using stochastic dominance on these quantiles, DRSA is producing decision rules guiding convergence to the most interesting region of the Pareto-optimal set [3]. The third optimization problem involves both multiple objectives and uncertainty. Some coefficients in the objective functions and/or constraints of this problem are not precisely known and given as interval values. The proposed interactive procedure is called DARWIN [4]. In the calculation stage, a sample of feasible solutions is generated together with a sample of vectors of possible values of the imprecise coefficients, called scenarios. Each feasible solution from the current sample is characterized by a distribution over generated scenarios. Some representative quantiles of these distributions are presented to the DM in the preference elicitation stage. The DM is indicating relatively good solutions and then DRSA based on first- or second-order stochastic dominance is producing decision rules exploited by an evolutionary search of a better sample of solutions.

[1] Greco, S., Matarazzo, B., Slowinski, R.: Rough sets theory for multicriteria decision analysis, European Journal of Operational Research, 129 (2001) 1-47.
[2] Greco, S., Matarazzo, B., Slowinski, R.: Dominance-based Rough Set Approach to Interactive Multiobjective Optimization, [chapter 5 in]: Branke, J., Deb, K., Miettinen, K., Slowinski, R. (eds.), Multiobjective Optimization: Interactive and Evolutionary Approaches, LNCS 5252, State-of-the-Art Surveys, Springer, Berlin, 2008, pp. 121-155.
[3] Greco, S., Matarazzo, B., Slowinski, R.: Dominance-based Rough Set Approach to decision under uncertainty and time preference, to appear in Annals of Operations Research, 2009.
[4] Greco, S., Matarazzo, B., Slowinski, R.: DARWIN: Dominance-based rough set Approach to handling Robust Winning solutions in INteractive multiobjective optimization, [in]: Proc. 5th International Workshop on Preferences and Decisions, Trento, April 6-8, 2009.
[5] Slowinski, R., Greco, S., Matarazzo, B.: Rough set based decision support, [chapter 16 in]: E.K. Burke and G. Kendall (eds.), Search Methodologies: Introductory Tutorials in Optimization and Decision Support Techniques, Springer, New York, 2005, pp. 475-527.

Prof. Hiroyuki Tamura
(Faculty of Engineering Science, Kansai University, Osaka, Japan)
Modeling Ambiguity Averse Behavior of Individual Decision Making: Prospect Theory under Uncertainty
In this presentation, some behavioral (or descriptive) models of individual decision making under risk and/or uncertainty are discussed. Firstly, a behavioral model based on the "Prospect Theory" developed by Kahneman and Tversky is described to explain the violations of expected utility hypothesis. In this model outcome-dependent, non-additive probabilities are introduced where probability of each event occurring is known. The effective application of this approach to the public sector is shown in modeling risks of extreme events with low probability and high outcome. Next, a behavioral model based on our "Prospect Theory under Uncertainty" is described where basic probability of a set of event is known but occurrence probability of each event is not known. It is shown that this model could properly explain the Elsberg paradox of ambiguity aversion. Potential applicability of this approach to evaluating a global warming problem is mentioned.

Prof. Weldon A. Lodwick
(Department of Mathematical and Statistical Sciences, University of Colorado, Denver, USA)
The Relationship Between Fuzzy/Possibilistic Optimization and Interval Analysis
The relationship between fuzzy set theory (in particular fuzzy arithmetic) and interval analysis is well-known. The interconnections between interval analysis and fuzzy/possibilistic optimization via the computation of the constraint set in the presence of possibilistic and fuzzy uncertainty occurring in the set of constraint (in)equalities will be developed. Moreover, the relationship of the united extension (the way to compute functions of real-valued intervals) and Zadeh's extension principle (the way to compute functions of real-valued fuzzy intervals) as it is applied to optimization will be presented with special emphasis on constraint fuzzy arithmetic and gradual numbers in the computation of constraint sets and optimization algorithms. These ideas will be presented within the context of an historical and taxonomic context.

Prof. Lluis Godo
(IIIA - Artificial Intelligence Research Institute, CSIC - Spanish National Research Council, Bellaterra, Catalonia, Spain)
g-BDI: a graded intensional agent model for practical reasoning
In intentional agents, actions are derived from the mental attitudes and their relationships. In particular, preferences (positive desires) and restrictions (negative desires) are important proactive attitudes which guide agents to intentions and eventually to actions. In this talk we will present joint work with Ana Casali and Carles Sierra about a multi-context based agent architecture g-BDI to represent and reasoning about gradual notions of desires and intentions, including sound and complete logical formalizations. We also show that the framework is expressive enough to describe how desires, together with other information, can lead agents to intentions and finally to actions. As a case-study, we will also describe the design and implementation of recommender system on tourism as well as the results of some experiments concerning the flexibility and performance of the g-BDI model.

Prof. Sadaaki Miyamoto
(Department of Risk Engineering, Faculty of Systems and Information Engineering, University of Tsukuba, Ibaraki, Japan)
Generalized bags, bag relations, and applications to data analysis and decision making
Bags alias multisets are old in computer science but recently more attention is paid on bags. In this paper we consider generalized bags which include real-valued bags, fuzzy bags, and fuzzy number-valued bags. Basic definitions as well as their properties are established; advanced operations such as t-norms, conorms, and their duality are also studied. Moreover bag relations are discussed which has max-plus and max-min algebras as special cases. The reason why generalized bags are useful in applications is described. As two application examples, bag-based data analysis and decision making based on convex function optimization related to bags are discussed.

MDAI 2009

IIIA - Institut d'Investigació en Intel·ligència Artificial

CSIC - Consejo Superior de Investigaciones Científicas

Vicenç Torra, Last modified: 00 : 05 December 08 2014.