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Fuzzy randomness – a contribution to imprecise probability
Author(s) -
Möller B.
Publication year - 2004
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.200410153
Subject(s) - randomness , fuzzy logic , randomness tests , mathematics , fuzzy number , algorithm , computer science , fuzzy set , mathematical optimization , artificial intelligence , statistics
The formal description of data uncertainty as fuzzy randomness combines randomness and fuzziness in an uncertain model. This generalized uncertainty model permits the simultaneous consideration of randomness, fuzziness and fuzzy randomness. Variables and functions with the property of fuzzy randomness are introduced. The formulation of the latter using α‐levels and fuzzy bunch parameters permits the application of fuzzy randomness in the numerical simulation of engineering problems. The finite element method is extended by the inclusion of fuzzy randomness to yield the fuzzy stochastic finite element method (FSFEM). Examples demonstrate the advantage of the chosen formal description in practical applications.