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Title: Decision-making under uncertainty processed by lattice-valued possibilistic measures (English)
Author: Kramosil, Ivan
Language: English
Journal: Kybernetika
ISSN: 0023-5954
Volume: 42
Issue: 6
Year: 2006
Pages: 629-646
Summary lang: English
Category: math
Summary: The notion and theory of statistical decision functions are re-considered and modified to the case when the uncertainties in question are quantified and processed using lattice-valued possibilistic measures, so emphasizing rather the qualitative than the quantitative properties of the resulting possibilistic decision functions. Possibilistic variants of both the minimax (the worst-case) and the Bayesian optimization principles are introduced and analyzed. (English)
Keyword: decision making under uncertainty
Keyword: complete lattice
Keyword: lattice- valued possibilistic measures
Keyword: possibilistic decision function
Keyword: minimax and Bayesian optimization
MSC: 28E10
MSC: 28E99
MSC: 91B06
idZBL: Zbl 1249.28024
idMR: MR2296505
Date available: 2009-09-24T20:19:30Z
Last updated: 2015-03-29
Stable URL:
Reference: [1] Birkhoff G.: Lattice Theory.Third edition. Amer. Math. Society, Providence, RI 1967 Zbl 0537.06001, MR 0227053
Reference: [2] Blackwell D., Girshick N. A.: Theory of Games and Statistical Decisions.Wiley, New York, 1954 Zbl 0439.62008, MR 0070134
Reference: [3] Cooman G. De: Possibility theory I, II, III.Internat. J. Gen. Systems 25 (1997), 4, 291–323, 325–351, 353–371
Reference: [4] Dubois D., Prade H.: Théorie des Possibilités – Applications à la Représentation des Connaissances en Informatique.Mason, Paris 1985 Zbl 0674.68059
Reference: [5] Dubois D., Nguyen, H., Prade H.: Possibility theory, probability theory and fuzzy sets: misunderstandings, bridges and gaps.In: The Handbook of Fuzzy Sets Series (D. Dubois and H. Prade, eds.), Kluwer Academic Publishers, Boston, 2000, pp. 343–438
Reference: [6] Faure R., Heurgon E.: Structures Ordonnées et Algèbres de Boole.Gauthier-Villars, Paris 1971 Zbl 0219.06001, MR 0277440
Reference: [7] Hájek P.: Metamathematics of Fuzzy Logic.Kluwer Academic Publishers, Boston 1998 Zbl 1007.03022, MR 1900263
Reference: [8] Halmos P. R.: Measure Theory.D. van Nostrand, New York – Toronto – London 1950 Zbl 0283.28001, MR 0033869
Reference: [9] Kramosil I.: Extensions of partial lattice-valued possibility measures.Neural Network World 13 (2003), 4, 361–384
Reference: [10] Loève M.: Probability Theory.D. van Nostrand, New York – Toronto – London 1960 Zbl 0385.60001, MR 0123342
Reference: [11] Sikorski R.: Boolean Algebras.Second edition. Springer-Verlag, Berlin – Göttingen – Heidelberg – New York 1964 Zbl 0191.31505, MR 0242724
Reference: [12] Wald A.: Statistical Decision Functions.Wiley, New York 1950 Zbl 0229.62001, MR 0036976


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