An Analytical Approach to Evaluating Bivariate Functions of Fuzzy Numbers with One Local Extremum

Arthur Seibel, Josef Schlattmann

2014

Abstract

This paper presents a novel analytical approach to evaluating continuous, bivariate functions of independent fuzzy numbers with one local extremum. The approach is based on a parametric a-cut representation of fuzzy numbers and allows for the inclusion of parameter uncertainties into mathematical models.

References

  1. Buckley, J. J. and Qu, Y. (1990). On using a-cuts to evaluate fuzzy equations. Fuzzy Sets and Systems, 38(3):309- 312.
  2. Degrauwe, D. (2007). Uncertainty propagation in structural analysis by fuzzy numbers. PhD Thesis, Katholieke Universiteit Leuven, Belgium.
  3. Dong, W. and Shah, H. C. (1987). Vertex method for computing functions of fuzzy variables. Fuzzy Sets and Systems, 24(1):65-78.
  4. Dubois, D. and Prade, H. (1980). Fuzzy Sets and Systems: Theory and Applications. Academic Press, New York, NY, USA.
  5. Fortin, J., Dubois, D., and Fargier, H. (2008). Gradual numbers and their application to fuzzy interval analysis. IEEE Transactions on Fuzzy Systems, 16(2):388-402.
  6. Hanss, M. (2005). Applied Fuzzy Arithmetic: An Introduction with Engineering Applications. Springer, Berlin, Germany.
  7. Klimke, A. (2006). Uncertainty modeling using fuzzy arithmetic and sparse grids. PhD Thesis, University of Stuttgart, Germany.
  8. Moens, D. and Hanss, M. (2011). Non-probabilistic finite element analysis for parametric uncertainty treatment in applied mechanics: Recent advances. Finite Elements in Analysis and Design, 47(1):4-16.
  9. Scheerlinck, K. (2011). Metaheuristic versus tailormade approaches to optimization problems in the biosciences. PhD Thesis, Ghent University, Belgium.
  10. Seibel, A. and Schlattmann, J. (2013). An analytical approach to evaluating monotonic functions of fuzzy numbers. In EUSFLAT Conference Proceedings, pages 289-293, Milano, Italy.
  11. Seibel, A. and Schlattmann, J. (2014). An extended analytical approach to evaluating monotonic functions of fuzzy numbers. Advances in Fuzzy Systems. Article ID 892363, 9 pages.
  12. Wood, K. L., Otto, K. N., and Antonsson, E. K. (1992). Engineering design calculations with fuzzy parameters. Fuzzy Sets and Systems, 52(1):1-20.
  13. Zadeh, L. A. (1965). Fuzzy sets. Information and Control, 8:338-353.
  14. Zadeh, L. A. (1975). The concept of a linguistic variable and its application to approximate reasoning-I. Information Sciences, 8:199-249.
Download


Paper Citation


in Harvard Style

Seibel A. and Schlattmann J. (2014). An Analytical Approach to Evaluating Bivariate Functions of Fuzzy Numbers with One Local Extremum . In Proceedings of the International Conference on Fuzzy Computation Theory and Applications - Volume 1: FCTA, (IJCCI 2014) ISBN 978-989-758-053-6, pages 89-94. DOI: 10.5220/0005026500890094


in Bibtex Style

@conference{fcta14,
author={Arthur Seibel and Josef Schlattmann},
title={An Analytical Approach to Evaluating Bivariate Functions of Fuzzy Numbers with One Local Extremum},
booktitle={Proceedings of the International Conference on Fuzzy Computation Theory and Applications - Volume 1: FCTA, (IJCCI 2014)},
year={2014},
pages={89-94},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0005026500890094},
isbn={978-989-758-053-6},
}


in EndNote Style

TY - CONF
JO - Proceedings of the International Conference on Fuzzy Computation Theory and Applications - Volume 1: FCTA, (IJCCI 2014)
TI - An Analytical Approach to Evaluating Bivariate Functions of Fuzzy Numbers with One Local Extremum
SN - 978-989-758-053-6
AU - Seibel A.
AU - Schlattmann J.
PY - 2014
SP - 89
EP - 94
DO - 10.5220/0005026500890094