Abstract
Non-determinism in structural mechanics is ubiquitious. Whenever a mathematical model of a real world engineering system is developed, simplification techniques are employed which lead to systematic errors in the modeling procedure. The fuzzy arithmetical approach which is presented in this chapter is designed to handle epistemic uncertainties, as those systematic errors are also termed, in numerical simulations by the use of fuzzy numbers. The approach consists of the transformation method which is designed to compute fuzzy-valued output quantities and an inverse fuzzy arithmetical method which additionally determines the fuzzy-valued model parameters on the basis of measurement data in a second step. Additionally, a kind of a sensitivity analysis is provided along with a criterion to assess the quality of different competing mathematical models.
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Haag, T., Hanss, M. (2012). Comprehensive Modeling of Uncertain Systems Using Fuzzy Set Theory. In: Elishakoff, I., Soize, C. (eds) Nondeterministic Mechanics. CISM Courses and Lectures, vol 539. Springer, Vienna. https://doi.org/10.1007/978-3-7091-1306-6_4
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DOI: https://doi.org/10.1007/978-3-7091-1306-6_4
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