Fuzzy probability calculation with confidence intervals in Bayesian networks

详细信息    查看全文

• 作者：Derya Ersel ; Duygu İçen
• 关键词：Bayesian network ; Confidence interval ; Fuzzy probability ; Fuzzy numbers ; \(\alpha \) ; Cuts
• 刊名：Soft Computing - A Fusion of Foundations, Methodologies and Applications
• 出版年：2016
• 出版时间：February 2016
• 年：2016
• 卷：20
• 期：2
• 页码：819-829
• 全文大小：1,220 KB
• 参考文献：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, GermanyMATH CrossRef
  Buckley Fuzzy (2006) Probability and statistics, vol 270. Springer, NetherlandsMATH
  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 YorkMATH
  Gudder S (2000) What is fuzzy probability theory? Found Phys 30(10):1663–1678MathSciNet CrossRef
  Heckerman D (1995) Bayesian networks for data mining. Data Min Knowl Discov 1:79–119CrossRef
  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 177:436–448MATH MathSciNet CrossRef
  Parchami A, Mashinchi M (2007) Fuzzy estimation for process capability indices. Inf Sci 177:1452–1462MATH MathSciNet CrossRef
  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 8:338–353MATH MathSciNet CrossRef
  Zadeh LA (1972) A fuzzy-set-theoretic interpretation of linguistic hedges. J Cybern 2(3):4–34MathSciNet CrossRef
  
• 作者单位：Derya Ersel (1)
  Duygu İçen (1)
  
  1. Department of Statistics, Hacettepe University, Beytepe, 06800, Ankara, Turkey
  
• 刊物类别：Engineering
• 刊物主题：Numerical and Computational Methods in Engineering
  Theory of Computation
  Computing Methodologies
  Mathematical Logic and Foundations
  Control Engineering
  
• 出版者：Springer Berlin / Heidelberg
• ISSN：1433-7479

文摘

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.