Modeling Decisions for Artificial Intelligence: 6th by Roman Słowiński (auth.), Vicenç Torra, Yasuo Narukawa,

By Roman Słowiński (auth.), Vicenç Torra, Yasuo Narukawa, Masahiro Inuiguchi (eds.)

This publication constitutes the complaints of the sixth foreign convention on Modeling judgements for synthetic Intelligence, MDAI 2009, hung on Awaji Island, Japan, in November/December 2009.

The 28 papers awarded during this booklet including five invited talks have been rigorously reviewed and chosen from sixty one submissions. the themes lined are aggregation operators, fuzzy measures and video game conception; choice making; clustering and similarity; computational intelligence and optimization; and desktop studying.

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Additional info for Modeling Decisions for Artificial Intelligence: 6th International Conference, MDAI 2009, Awaji Island, Japan, November 30–December 2, 2009. Proceedings

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D. We will get 100 dollars if we pick a black or white ball. Many people show the preference (Ellsberg, 1961), a f b, d f c . (29) The probability of picking up a red ball is 1/3. Let pb and pw be the probability of picking up a black ball and a white ball, respectively. Then pb + pw = 2 . 3 (30) The expected utility theory says that afb ⇒ 1 1 u (1M ) > pbu (1M ) ⇒ pb < 3 3 (31) d fc⇒ 1 2 u (1M ) > u (1M ) + pwu (1M ) 3 3 (32a) ⇒ pw < 1 1 ⇒ pb > 3 3 (32b) where u denotes a von Neumann-Morgenstern utility function and 1M = 100 dollars.

P, ∀x ∈ X. 2. equality: A = B ⇔ µjA (x) = µjB (x), j = 1, . . , p, ∀x ∈ X. 3. sum: A + B is defined by the sum operation in X × [0, 1] for crisp bags [32]. 4. union: µjA∪B (x) = µjA (x) ∨ µjB (x), j = 1, . . , p, ∀x ∈ X. 5. intersection: µjA∩B (x) = µjA (x) ∧ µjB (x), j = 1, . . , p, ∀x ∈ X. G-Bags. A further generalization of fuzzy bags is useful from theoretical viewpoint. It has been studied by the author [19] and is called G-bags here (this name is an abbreviation of generalized bags). We introduce a G-bag using a closed region on a first quadrant [0, +∞]2 of a plane.

In prospect theory (PT), the value V for the prospect (5) is evaluated using the evaluation function V= n ∑ π ( p j )v ( x j ) (21) j =1 where the value function v is convex with a gentle curve in the gain domain, while it is concave and its curve is steeper in the loss domain, as shown in Figure 1. This shows that people, in general, are loss averse. The weighting function π is a convex function as shown in Figure 2, so a small probability is weighted higher and middle or large probabilities are weighted lower.

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