Modeling Decisions for Artificial Intelligence: 11th by Vicenç Torra, Yasuo Narukawa, Yasunori Endo PDF

By Vicenç Torra, Yasuo Narukawa, Yasunori Endo

ISBN-10: 3319120530

ISBN-13: 9783319120539

ISBN-10: 3319120549

ISBN-13: 9783319120546

This ebook constitutes the complaints of the eleventh overseas convention on Modeling judgements for synthetic Intelligence, MDAI 2014, held in Tokyo, Japan, in October 2014. the nineteen revised complete papers offered including an invited paper have been conscientiously reviewed and chosen from 38 submissions. They take care of the speculation and instruments for modeling judgements, in addition to functions that surround selection making methods and data fusion options and are equipped in topical sections on aggregation operators and determination making, optimization, clustering and similarity, and knowledge mining and information privacy.

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Extra info for Modeling Decisions for Artificial Intelligence: 11th International Conference, MDAI 2014, Tokyo, Japan, October 29-31, 2014. Proceedings

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In the next section we discuss relations between risk measures and deviations to introduce other kinds of aggregation of risk measures. 3 Deviation Measures Risk measure is related to deviation measures ([6]). In this section we introduce deviation measures to investigate indirect approaches which are different from direct methods in the previous section. Denote L2 (Ω) and L1 (Ω) the space of square integrable real random variables on Ω and the space of integrable real random variables on Ω respectively.

P. ) Fuzzy Logic: A Spectrum of Theoretical and Practical Issues. STUDFUZZ, vol. 215, pp. 49–64. Springer, Heidelberg (2007) 23. : Fuzzy Preference Modelling and Multicriteria Decision Support. Kluwer Academic Publishers, Dordrecht (1994) 24. : Structure of uninorms. Int. J. Uncertainty Fuzziness Knowledge-Based Syst. 5, 411–427 (1997) 25. : A method of inference in approximate reasoning based on interval-valued fuzzy sets. Fuzzy Sets and Systems 21, 1–17 (1987) 26. : Rule reduction for efficient inferencing in similarity based reasoning.

Let X be a set of real random variables on Ω. a) D(X) ≥ 0 and D(θ) = 0 for X ∈ X and real numbers θ. b) D(X + θ) = D(X) for X ∈ X and real number θ. c) D(λX) = λ D(X) for X ∈ X and nonnegative real numbers λ. d) D(X + Y ) ≤ D(X) + D(Y ) for X, Y ∈ X . e) limk→∞ D(Xk ) = D(X) for {Xk } ⊂ X and X ∈ X such that limk→∞ Xk = X almost surely. 1. 1. 1. Proof. We have |a + b| ≤ |a| + |b| and (a + b)− ≤ a− + b− for a, b ∈ R. We can easily check this lemma with these inequalities and Schwartz’s inequality.

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Modeling Decisions for Artificial Intelligence: 11th International Conference, MDAI 2014, Tokyo, Japan, October 29-31, 2014. Proceedings by Vicenç Torra, Yasuo Narukawa, Yasunori Endo


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