By Didier Dubois, Henri Prade (auth.), Dr. Przemysław Grzegorzewski, Prof. Dr. Olgierd Hryniewicz, Professor María Ángeles Gil (eds.)
Classical chance concept and mathematical information look occasionally too inflexible for actual existence difficulties, particularly whereas facing obscure facts or vague specifications. those difficulties have inspired many researchers to "soften" the classical conception. a few "softening" ways make the most of recommendations and methods constructed in theories akin to fuzzy units idea, tough units, hazard conception, idea of trust capabilities and obscure chances, and so forth. considering the fact that fascinating mathematical versions and strategies were proposed within the frameworks of varied theories, this article brings jointly specialists representing diversified methods utilized in tender likelihood, statistics and knowledge analysis.
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Extra resources for Soft Methods in Probability, Statistics and Data Analysis
Information Sciences, 118, 173 -212. 9. Delgado M. and Moral S. (1987). On the concept of possibility-probability consistency, Fuzzy Sets and Systems, 21, 311-318. 10. Dempster A. P. (1967). Upper and lower probabilities induced by a multivalued mapping, Ann. Math. , 38, 325-339. 11. Denneberg D. (1994). Nonadditive Measure and Integral, Kluwer Academic, Dordrecht, The Netherlands. 12. Dubois D. (1986). Belief structures, possibility theory and decomposable confidence measures on finite sets, Computers and Artificial Intelligence (Bratislava), 5, 403-416.
Dubois D. and Prade H. (1997) Bayesian conditioning in possibility theory, Fuzzy Sets and Systems, 92, 223-240. 24 27. Dubois D. and Prade H. (1998). Possibility theory: Qualitative and quantitative aspects, Handbook of Defeasible Reasoning and Uncertainty Management Systems- Vol. M. , Dordrecht, 169-226. 28. , Nguyen H. , Prade H. (2000) Possibility theory, probability and fuzzy sets: misunderstandings, bridges and gaps. In: Fundamentals of Fuzzy Sets, (Dubois, D. , The Handbooks of Fuzzy Sets Series , 343-438.
SwedesjSwedes) is :::; mostn;::: (2most-1). (42) Now S most = [0; 1] (43) ;::: (2most- 1) = 2most- 1, (44) and in virtue of monotonicity of most (Zadeh, 1999). Consequently, L Count( tall n blond . Swedes / Swedes) is 2most - 1 (45) and hence the answer to the question is a: (2most- 1)SwedesT aretalland blond. (46) In a more general setting, the principal elements of the reasoning process are the following. 1. Question (query), q. Q. (47) 2. Premises. The collection of premises expressed in a naturallanguage constitutes the initial data set (IDS).
Soft Methods in Probability, Statistics and Data Analysis by Didier Dubois, Henri Prade (auth.), Dr. Przemysław Grzegorzewski, Prof. Dr. Olgierd Hryniewicz, Professor María Ángeles Gil (eds.)