Research

Computing and modelling with fuzzy data and imprecise probabilities

Goals:

• Application of fuzzy and imprecise probability methods for modelling the effects of data uncertainties and fluctuations in civil engineering problems.
• Development of numerical algorithms for computing with fuzzy data and imprecise probabilities.
• Risk and uncertainty analysis in civil engineering by methods of imprecise probability.

Group members:

• Thomas Fetz
• Michael Oberguggenberger
• Bernhard Schmelzer

Former group members:

• Simon Pitschmann
• Diego Alvarez Marin
• Julian King

Research topics:

• imprecise probability methods for sensitivity analysis
• probability measures prameterized by random sets
• random sets, sets of joint probability measures, notionsw of independence
• uncertainty modelling and risk analysis in civil engineering
• finite element methods with imprecise data
• differential equations with fuzzy parameters
• fuzzy project and network analysis

Former events:

• Workshop: Applications of Fuzzy Sets and Fuzzy Logic to Engineering Problems, Pertisau, September 29 - October 1, 2002.

Publications:

1. Th. Fetz, M. Oberguggenberger
   Multivariate Models of Uncertainty: A Local Random Set Approach
   Structural Safety, to appear.
    
2. Th. Fetz
   Multivariate Models and Confidence Intervals: A Local Random Set Approach
   In Proceedings of ISIPTA09 conference, Durham, 2009.
    
3. B. Schmelzer
   On solutions of stochastic dierential equations with parameters modelled by random sets
   In Proceedings of ISIPTA09 conference, Durham, 2009.
    
4. Th. Fetz, F. Tonon
   Probability bounds for series systems with variables constrained by sets of probability measures.
   Int. J. Reliability and Safety, 2(4), 2008, 309-339.
5. W. Fellin, M. Oberguggenberger
   Reliability bounds through random sets: nonparametric methods and geotechnical applications.
   Computers & Structures, 2008, 86, 1093-1101.
6. Th. Fetz
   Multiparameter Models: Probability models parameterized by random sets.
   In: Proceedings ISIPTA'07, 2007. (article, presentation, poster)
7. J. King, M. Oberguggenberger, B. Schmelzer
   Imprecise probability methods for sensitivity analysis in engineering.
   In: Proceedings ISIPTA'07, 2007. (article)
8. D. Alavarez Marin
   On the calculation of the bounds of probability of events using infinite random sets.
   IJAR 3/43, 241 - 267, 2006
9. D. Alavarez Marin
   On the Use of Infinite Random Sets for Bounding the Probability of Failure in the Case of Parameter Unvertainty.
   In: Soares, C. A. et. al. (eds.): Computational Mechanics - Solids, Structures and Coupled Problems, Dordrecht, Springer, 2006.
10. W. Fellin, M. Oberguggenberger
    Assessing the sensitivity of failure probabilities: a random set approach.
    In: G. Augusti, G.I. Schuëller, M. Ciampoli (Eds.), Safety and Reliability of Engineering Systems and Structures. ICOSSAR 2005 - Rome. Millpress, Rotterdam 2005, 1755 - 1760, 2005.
11. W. Fellin, M. Oberguggenberger
    The fuzziness and sensitivity of failure probabilities.
    In: W. Fellin, H. Lessmann, M. Oberguggenberger, R. Vieider (Eds.), Analyzing Uncertainty in Civil Engineering. Springer, 2004.
12. M. Oberguggenberger
    The mathematics of uncertainty: models, methods and interpretations.
    In: W. Fellin, H. Lessmann, M. Oberguggenberger, R. Vieider (Eds.), Analyzing Uncertainty in Civil Engineering. Springer, 2004.
13. M. Oberguggenberger
    Queueing models with fuzzy data in construction management.
    In: W. Fellin, H. Lessmann, M. Oberguggenberger, R. Vieider (Eds.), Analyzing Uncertainty in Civil Engineering. Springer, 2004.
14. M. Oberguggenberger
    Fuzzy and weak solutions to differential equations.
    Proceedings of the Tenth International Conference IPMU 2004, Perugia. Editrice Università La Sapienza, Italy 2004, 517 - 524.
15. Th. Fetz
    Multi-parameter models: rules and computational methods for combining uncertainties.
    In: Analyzing Uncertainty in Civil Engineering. Fellin, Wolfgang, Lessmann, Heimo, Vieider, Robert Oberguggenberger, Michael (Eds.), Springer, 2004
16. Th. Fetz, M. Oberguggenberger
    Propagation of uncertainty trough multivariate functions in the framework of sets of probability measures.
    Reliability Engineering and Systems Safety, Vol. 85, No. 1-3, 73-88, 2004
17. Th. Fetz
    Mengen von gemeinsamen Wahrscheinlichkeitsmaßen erzeugt durch zufällige Mengen.
    Dissertation, Innsbruck 2003
18. W. Fellin, M. Oberguggenberger
    From probability to fuzzy sets: the struggle for meaning in geotechnical risk assessment.
    In: Pöttler, R., Klapperich, H., Schweiger, H. F. editors, Probabilistics in GeoTechnics: Technical and Economic Risk Estimation. United Engineering Foundation, Verlag Glückauf GmbH, Essen, 2002, pages 29 - 38. (.pdf 96k)
19. Th. Fetz
    Sets of joint probability measures generated by marginal focal sets.
    In: de Cooman, G., Fine, T., Seidenfeld, T., editors, ISIPTA '01, Proceedings of the Second International Symposium on Imprecise Probabilities and Their Applications, Shaker Publishing BV, Maastricht 2001, pages 171-178. (.pdf 175k)
20. M. Oberguggenberger, F. Russo
    Fuzzy, probabilistic and stochastic modelling of an elastically bedded beam.
    In: de Cooman, G., Fine, T., Seidenfeld, T., editors, ISIPTA '01, Proceedings of the Second International Symposium on Imprecise Probabilities and Their Applications, Shaker Publishing BV, Maastricht 2001, pages 293-300. (.ps 244k)
21. M. Oberguggenberger, S. Pittschmann
    Differential equations with fuzzy parameters.
    Mathematical and Computer Modelling of Dynamical Systems, 5:181-202, 1999
    (.ps 467k)
22. Th. Fetz, M. Oberguggenberger, S. Pittschmann
    Applicatons of possibility and evidence theory in civil engineering.
    International Journal of Uncertainty, Fuzziness and Knowledge Based System, 8:295-309, 2000. Extended version of contribution in: de Cooman G., Cozman F., Moral S. and Walley P., editors, Proceedings of the First International Symposium on Imprecise Probabilities and Their Applications, pages 146-153, Gent, 1999. (.ps 640k)
23. Th. Fetz, J. Jäger, D. Köll, G. Krenn, H. Lessmann, M. Oberguggenberger, A. Rieser, R. F. Stark
    Fuzzy models in geotechnical engineering and construction management.
    Computer-Aided Civil and Infrastructure Engineering, 14:93-106, 1999.
    (.ps 818k)
24. Th. Fetz
    Finite element method with fuzzy parameters.
    In Troch I. and Breitenecker F., editors, Proceedings IMACS Symposium on Mathematical Modelling, volume 11, pages 81-86, Vienna, 1997, ARGESIM Report.
    (.ps 256k)  

Diploma theses:

• Simon Pittschmann: Lösungsmethoden für Funktionen und gewöhnliche Differentialgleichungen mit unscharfen Parametern (1995)
• Veronika Sonnweber: Fachdidaktische Aufbereitung der Fuzzy-Methoden in der Mathematik (1996)
• Georg Göbel: Prozessmodellierung mit Fuzzy-Logik (1997)
• Julian King: Stochastic Simulation Methods in Sensitivity Analysis (2007)
• Bernhard Schmelzer: Imprecise Probability Methods for Sensitivity Analysis in Engineering Applications (2007)

In collaboration with the Institute of Hydraulic Engineering:

• Dieter Stolz: Hochwasserabschätzung in unbeobachteten Einzugsgebieten unter Zuhilfenahme von regionalen Extremwertstatistiken (2006)

In collaboration with the Institute of Construction Management:

• Georg Hunger: Verschiedene Problemstellungen der Netzplanberechnung mit der Fuzzy-Methode (1995)
• Robert Zach: Untersuchung über die nicht-deterministische Annahme von Werten in Bauprozessen (Erdbetrieb; Unscharfe Leistung der Geräte) (1995)
• Günther Krenn: Kosten und Bauzeit. Eine Untersuchung über Zusammenhänge mit Fuzzy-Methoden (1996)
• David Köll: Netzplanberechnung mit unscharfen Zahlen (1997)
• Thomas Markt: Komplexe Systeme und Unschärfen: Systemanalyse, Anwendung in der Netzplantechnik (1997)
• Bernd Raderbauer: Entscheidung bei mehrfacher Zielsetzung unter Rsiko und Unschärfe (1998)
• Jochen Bell: Der Einfluß der Warteschlange auf den Erdbetrieb (1998)

In collaboration with the Institute of Geotechnical and Tunnel Engineering:

• Martin Leitgeb: Grundbruchberechnung mit unscharfen Bodenkennwerten (2001)

Dissertations:

• Julius Mühlögger: Netzplantechnik mit unscharfen Methoden (1994)
• Harald Pilser: Fuzzy-Methoden bei der Investitionskostenschätzung im Anlagenbau (1998)
• Rachanee Phuwapathanapun: Network analysis with fuzzy and stochastic data (2000)
• Robert Wachter: Der Einarbeitungseffekt bei mechanischen Tunnelvortrieben (2001)
• Thomas Fetz: Mengen von gemeinsamen Wahrscheinlichkeitsmaßen erzeugt durch zufällige Mengen (2003)
• Simon Pittschmann: Lösungsmethoden für gwöhnliche Differentialgleichungen mit unscharfen Parametern (2003)
• Diego Alvarez Marin: Infinite random sets and applications in uncertainty analysis (2007)