Abstract
In this study, we propose to use Buckley’s confidence interval approach which has not been used before in the literature to calculate marginal and conditional fuzzy probabilities in Bayesian networks. We apply this approach to a real life problem and show that Buckley’s confidence interval approach provides to indicate uncertainty better and represents knowledge more explicitly than determining fuzzy probabilities based only on the expert opinion in Bayesian networks.
Access this article
Rent this article via DeepDyve
![](http://media.springernature.com/m312/springer-static/image/art%3A10.1007%2Fs00500-014-1545-9/MediaObjects/500_2014_1545_Fig1_HTML.gif)
![](http://media.springernature.com/m312/springer-static/image/art%3A10.1007%2Fs00500-014-1545-9/MediaObjects/500_2014_1545_Fig2_HTML.gif)
![](http://media.springernature.com/m312/springer-static/image/art%3A10.1007%2Fs00500-014-1545-9/MediaObjects/500_2014_1545_Fig3_HTML.gif)
![](http://media.springernature.com/m312/springer-static/image/art%3A10.1007%2Fs00500-014-1545-9/MediaObjects/500_2014_1545_Fig4_HTML.gif)
![](http://media.springernature.com/m312/springer-static/image/art%3A10.1007%2Fs00500-014-1545-9/MediaObjects/500_2014_1545_Fig5_HTML.gif)
![](http://media.springernature.com/m312/springer-static/image/art%3A10.1007%2Fs00500-014-1545-9/MediaObjects/500_2014_1545_Fig6_HTML.gif)
![](http://media.springernature.com/m312/springer-static/image/art%3A10.1007%2Fs00500-014-1545-9/MediaObjects/500_2014_1545_Fig7_HTML.gif)
![](http://media.springernature.com/m312/springer-static/image/art%3A10.1007%2Fs00500-014-1545-9/MediaObjects/500_2014_1545_Fig8_HTML.gif)
![](http://media.springernature.com/m312/springer-static/image/art%3A10.1007%2Fs00500-014-1545-9/MediaObjects/500_2014_1545_Fig9_HTML.gif)
![](http://media.springernature.com/m312/springer-static/image/art%3A10.1007%2Fs00500-014-1545-9/MediaObjects/500_2014_1545_Fig10_HTML.gif)
Similar content being viewed by others
Explore related subjects
Discover the latest articles, news and stories from top researchers in related subjects.References
Beer M (2010) A summary on fuzzy probability theory. In: Proceedings of 2010 IEEE international conference on granular computing, 14–16 Aug, San Jose, CA, USA, pp 5–6
Beer M, Mingqiang Z, Tong QS, Ferson S (2011) Structural reliability assessment with fuzzy probabilities. In: Proceedings of 7th international symposium on imprecise probability: theories and applications, Innsbruck, Austria
Ben Mrad A, Maalej MA, Abid M (2012) Fuzzy Bayesian network model and inference, sciences of electronics, technologies of information and telecommunication, 21–24 Mar, Tunisia
Ben-Gal I (2007) Bayesian networks. In: Ruggeri F, Faltin F, Kenett R (eds) Encyclopedia of statistics in quality and reliability, vol 1800. Wiley, New York
Buckley JJ (2003) Fuzzy probabilities: new approach and applications, vol 164. Physica, Heidelberg
Buckley JJ (2004) Fuzzy statistics, vol 167. Springer, Germany
Buckley Fuzzy (2006) Probability and statistics, vol 270. Springer, Netherlands
DEAL (2009) Deal package for learning Bayesian networks with mixed variables, the comprehensive R archive network. http://cran.r-project.org/web/packages/deal/index.html
Dubois D, Prade H (1980) Fuzzy sets and systems: theory and applications, vol 411. Academic Press, New York
Gudder S (2000) What is fuzzy probability theory? Found Phys 30(10):1663–1678
Heckerman D (1995) Bayesian networks for data mining. Data Min Knowl Discov 1:79–119
Jensen FV (2001) Bayesian networks and decision graphs, vol 268. Springer, New York
Jowers LJ, Buckley JJ, Reilly KD (2007) Simulating continuous fuzzy systems. Inf Sci 177:436–448
Parchami A, Mashinchi M (2007) Fuzzy estimation for process capability indices. Inf Sci 177:1452–1462
Ren J, Wang J, Jenkinson I (2005) Fuzzy Bayesian modelling in maritime risk analysis. In: Proceedings of GERI annual research symposium, John Moores University, Liverpool, UK
Ren J, Jenkinson I, Wang J, Xu DL, Yang JB (2009) An offshore risk analysis method using fuzzy Bayesian network. J Offshore Mech Arct Eng 131(4):041101
Tang H, Liu S (2007) Basic theory of fuzzy Bayesian networks and its application in machinery fault diagnosis. In: Proceedings of fourth international conference on fuzzy systems and knowledge discovery, 24–27 Aug 2007, Haikou, Hainan, China, pp 132–137
Yu D (1997) Expert opinion elicitation process using a fuzzy probability. J Korean Nucl Soc 29(1):25–34
Zadeh LA (1965) Fuzzy sets. Inf control 8:338–353
Zadeh LA (1972) A fuzzy-set-theoretic interpretation of linguistic hedges. J Cybern 2(3):4–34
Author information
Authors and Affiliations
Corresponding author
Additional information
Communicated by V. Loia.
Rights and permissions
About this article
Cite this article
Ersel, D., İçen, D. Fuzzy probability calculation with confidence intervals in Bayesian networks. Soft Comput 20, 819–829 (2016). https://doi.org/10.1007/s00500-014-1545-9
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00500-014-1545-9