Fuzzy Data and Imprecise Probabilities in Engineering
MichaelĀ Beer
Civil and Environmental Engineering, National University of Singapore, Singapore

The central issue in computational engineering disciplines is the realistic numerical modeling of physical and mechanical phenomena and processes. This is the basis to derive predictions regarding behavior, performance, and reliability of engineering structures and systems. In engineering practice, however, the available information is frequently quite limited and of poor quality. It appears as imprecise, diffuse, fluctuating, incomplete, fragmentary, vague, ambiguous, dubious, or linguistic. Information from maps, plans, measurements, observations, experience, expert knowledge, and from codes and standards has to be quantified and processed. Undetermined boundary and environmental conditions and changes thereof have to be taken into consideration. These characteristics of the available information impede the specification of certain numerical models and precise parameter values without an artificial introduction of unwarranted information. An appropriate mathematical modeling is required in accordance with the underlying real-world information. Shortcomings, in this regard, may lead to biased computational results with an unrealistic accuracy and, therefore, lead to wrong decisions with the potential for associated serious consequences.

Despite traditional probabilistic models are useful, well-established and recognized largely as applicable to real-world problems in engineering, their limitations are obvious in the light of the problematic available information. It is frequently argued that expert knowledge can compensate for these limitations through the use of Bayesian methods based on subjective probabilities. But this expert knowledge is often not available in the required form, and the available information is of an imprecise nature rather than of a stochastic nature so that the prior distributions may be quite arbitrary.

The solution to this conflict is given with imprecise probabilities, which involve both probabilistic uncertainty and non-probabilistic imprecision. An entire set of plausible probabilistic models is considered in one analysis. This leads to more realistic results and helps to prevent wrong decisions. Engineering applications are demonstrated by means of various examples.

Keywords: Imprecise probabilities; Fuzzy probabilities; Fuzzy data; Structural reliability

Biography: Dr. Beer obtained his doctoral degree (Dr.-Ing.) in Civil Engineering from the Technical University of Dresden, Germany, in 2001. In 2003/2004 Dr. Beer worked as a Visiting Scholar at Rice University, Houston, TX, USA with a Feodor-Lynen Research Fellowship from the Alexander von Humboldt-Foundation. Since 2007 Dr. Beer is affiliated as an Assistant Professor to the Department of Civil and Environmental Engineering at National University of Singapore. His research interest is focused on non-traditional methods for modeling and processing of uncertainty in engineering with emphasis on reliability analysis and on robust design. Dr. Beer's research has been awarded on national and international level. He has published a scientific book on Fuzzy Randomness, an Invited Chapter on Fuzzy Probability Theory in an Encyclopedia, and a number of papers in Journals. Dr. Beer is Member of several renowned engineering societies, and of the Editorial Board of the Journal of Probabilistic Engineering Mechanics.