Download Coping with Uncertainty: Robust Solutions by Kurt Marti, Yuri Ermoliev, Marek Makowski PDF

By Kurt Marti, Yuri Ermoliev, Marek Makowski

Support for addressing the on-going international alterations wishes suggestions for brand spanking new medical difficulties which in flip require new thoughts and instruments. A key factor matters an unlimited number of irreducible uncertainties, together with severe occasions of excessive multidimensional effects, e.g., the weather switch. The obstacle is worried with huge, immense expenditures as opposed to large uncertainties of utmost affects. conventional medical techniques depend on genuine observations and experiments. but no adequate observations exist for brand spanking new difficulties, and "pure" experiments, and studying by means of doing should be dear, harmful, or most unlikely. additionally, the on hand ancient observations are usually infected through prior activities, and guidelines. hence, instruments are offered for the specific therapy of uncertainties utilizing "synthetic" info composed of accessible "hard" information from ancient observations, the result of attainable experiments, and clinical proof, in addition to "soft" info from specialists' reviews, and scenarios.

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E. t0 / D 1. e. t/g for s; t 2 R and 2 Œ0; 1. t/ > 0g is a compact set. g. Dubois and Prade [15] for a more detailed description). R/. R/ denotes a space of all fuzzy sets on the real line. Fuzzy numbers are completely defined by their ˛-cuts. 2 (Grzegorzewski [37]). Let . ; A; P / be a probability space, where is a set of all possible outcomes of the random experiment, A is a -algebra of subsets of , and P is a probability measure. 2 On Joint Modelling of Random Uncertainty and Fuzzy Imprecision 23 e W !

Wiley, Chichester (1972) 27. : Theory of Probability, vols. 1 and 2. Wiley, Chichester (1974–1975). [English translation of a book published earlier in Italian] 28. : Fuzzy Bayesian inference. Fuzzy Sets Syst. 60, 41–58 (1993) 29. : A mathematical analysis of information – preserving transformations between probabilistic and possibilistic formulation of uncertainty. Int. J. General Syst. 20, 143–176 (1992) 36 O. Hryniewicz 30. : Probabilistic–possibilistic approach to some statistical problems with fuzzy experimental observations.

The works of many authors, who have noticed the deficiency of the theory of probability in dealing with many practical problems have led to more or less independent formalizations of two similar theories of uncertainty: Dempster–Shafer theory of evidence and possibility theory. The concept of possibility can be interpreted in different ways. For example, it can be understood as an objective notion or as an epistemic and subjective one. Zadeh [95] understands possibility as objective feasibility; an objective measure of physical easiness to achieve a certain goal.

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