Abstract
In information management systems in particular, and in science and engineering in general, uncertainty is a norm rather than an exception. Uncertainty can take on various different forms, ranging from randomness to imprecision modeled by probabilities and fuzzy sets, respectively. In view of current interests in using the so-called theory of belief functions in engineering applications, we address here a general unified framework for analyzing uncertainties. The building block of our approach is the concept of random sets.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
A.P. Dempster, Upper and lower probabilities induced by a multivalued mapping. Ann. Probab. 38, 325–339 (1967)
G. Gierz, K.H. Hofmann, K. Keimel, J.D. Lawson, M. Mislove, D.S. Scott, A Compendium of Continuous Lattices (Springer, Heidelberg, 1980)
J.A. Hartigan, Estimation of a convex density contour in two dimensions. J. Am. Statist. Assoc. 82, 267–270 (1987)
G. Matheron, Random Sets and Integral Geometry (Wiley, New York, 1975)
R.B. Nelsen, An Introduction to Copulas. Lecture Notes in Computer Science (Springer, Berlin, 1999)
H.T. Nguyen, On random sets and belief functions. J. Math. Anal. Appl. 65, 531–542 (1978), reprinted in Classical Works of the Dempster-Shafer Theory of belief Functions, ed. by R. Yager, L. Liu. (Springer, Berlin, 2008), pp. 105–116
H.T. Nguyen, An Introduction to Random Sets (Chapman and Hall/CRC, Boca Raton, 2006)
H.T. Nguyen, On belief functions and random sets. In Belief Functions: Theory and Applications, ed. by T. Denoeux, M.H. Masson. (Springer, Berlin, 2012), pp. 1–19
H.T. Nguyen, H. Tran, On a continuous lattice approach to modeling of coarse data in system analysis. J. Uncertain Syst. 1(1), 62–73 (2007)
H.T. Nguyen, E.A. Walker, A First Course in Fuzzy Logic, 3rd edn. (Chapman and Hall/CRC, Boca Raton, 2006)
G. Shafer, A Mathematical Theory of Evidence. Princeton University Press, Princeton, 1976)
A. Sklar, Fonctions de repartition a n dimensions et leur marges. Publ. Inst. Statist. Univ. Paris 8, 229–231 (1959)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2014 Springer Science+Business Media New York
About this paper
Cite this paper
Nguyen, H.T. (2014). On Uncertainty Analysis Using Random Sets in Science and Engineering. In: Watada, J., Xu, B., Wu, B. (eds) Innovative Management in Information and Production. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-4857-0_1
Download citation
DOI: https://doi.org/10.1007/978-1-4614-4857-0_1
Published:
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4614-4856-3
Online ISBN: 978-1-4614-4857-0
eBook Packages: EngineeringEngineering (R0)