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Part of the book series: Ocean Engineering & Oceanography ((OEO,volume 13))

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Abstract

In 1657, Huygens first studied randomness as a type of uncertainty, and in 1836 referred to the term “uncertainty”.

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References

  • Agarwal H (2004) Reliability based design optimization: formulations and methodologies. PhD thesis, Notre Dame

    Google Scholar 

  • Agarwal H, Renaud JE, Preston EL et al (2004) Uncertainty quantification using evidence theory in multidisciplinary design optimization. Reliab Eng Syst Saf 85(1–3):281–294

    Article  Google Scholar 

  • Bae HR, Grandhi RV, Canfield R (2002) Uncertainty quantification of structural response using evidence theory. In: 43rd AIAA/ASME/ASCE/AHS/ASC structures, structural dynamics, and materials conference. Denver, Colorado

    Google Scholar 

  • Bae HR, Grandhi RV, Canfield RA (2004) Epistemic uncertainty quantification techniques including evidence theory for large-scale structures. Comput Struct 82(13–14):1101–1112

    Google Scholar 

  • Bae HR, Grandhi RV, Canfield R (2006) Sensitivity analysis of structural response uncertainty propagation using evidence theory. Struct Multi Optim 31:270–291

    Article  Google Scholar 

  • Ben-Haim Y, Elishakoff I (1990) Covex methods of uncertainty in applied mechanics. Elsevier, Amsterdam

    Google Scholar 

  • Bifeng S (2006) Aircraft reliability engineering. Northwestern polytechnical university press. (宋笔锋. 飞行器可靠性工程. 西北工业大学出版社, 2006.)

    Google Scholar 

  • Billingsley P (1995) Probability and measure. Wiley-Interscience Publication

    Google Scholar 

  • Chen YH, Wang WJ, Chiu CH (2000) New estimation method for the membership values in fuzzy sets. Fuzzy Set Syst 112:521–525

    Article  MathSciNet  Google Scholar 

  • Cui WC (1990) Uncertainty analysis in structural safety assessment. PhD thesis, Department of Civil Engineering, University of Bristol

    Google Scholar 

  • Cui WC (1993a) Generalized probability theory for handling uncertainty: the foundation. Technical report. China Ship Scientific Research Center

    Google Scholar 

  • Cui WC (1993b) Generalized probability theory for handling uncertainty: the theory. Technical report. China Ship Scientific Research Center

    Google Scholar 

  • Cui WC, Blockley DI (1990) Interval probability theory for evidential support. Int J Intell Syst 5(2):183–190

    Article  Google Scholar 

  • De-Cooman G (1997) Possibility theory I: the measure-and integral-theoretic groundwork. Int J Gen Syst

    Google Scholar 

  • Dempster AP (1967) Upper and lower probabilities induced by a multivalued mapping. Ann Math Stat 38:325–329

    Article  MathSciNet  Google Scholar 

  • Du L (2006) Reliability-based and possibility-based design optimization using inverse analysis methods. PhD thesis of graduate college of the university of Iowa

    Google Scholar 

  • Dubois D, Prade H (1988) Possibility theory: an approach to computerized processing of uncertainty. Plenum Press, New York

    Book  Google Scholar 

  • Durrett R (1996) Probability: theory and examples. Duxbury Press

    Google Scholar 

  • Guo J, Du X (2007) Sensitivity analysis with mixture of epistemic and aleatory uncertainties. AIAA J 45(9):2337–2349

    Article  Google Scholar 

  • Hall J, Lawry J (2001) Imprecise probabilities of engineering system failure from random and fuzzy set reliability analysis. In: 2nd international symposium on imprecise probabilities and their applications. Ithaca, New York

    Google Scholar 

  • Helton J (1997) Uncertainty and sensitivity analysis in the presence of stochastic and subjective uncertainty. J Stat Comput Simul 57:3–76

    Article  Google Scholar 

  • Helton JC, Johnson JD, Oberkampf WL, Storlie CB (2006) A sampling-based computational strategy for the representation of epistemic uncertainty in model predictions with evidence theory. Comput Method Appl Mech Eng 196(37):3980-–998

    Google Scholar 

  • Henrion M (1986) Uncertainty in AI: is probability epistemologically and heuristically adequate. In: Expert systems and expert judgement. Proceedings of the NATO advanced research workshop in Porto. Portugal

    Google Scholar 

  • Huang HZ, Li HB (2005) Perturbation finite element method of structural analysis under fuzzy environment. Eng Appl Artif Intell 18(1):83–91

    Article  MathSciNet  Google Scholar 

  • Jacobsen HS (2002) Representation and calculation of economic uncertainties: intervals, fuzzy numbers, and probabilities. Int J Prod Econ 78:91–98

    Article  Google Scholar 

  • Jensen HA, Sepulveda AE (2000) Use of approximation concept in fuzzy design problem. Adv Eng Softw 31:263–273

    Article  Google Scholar 

  • Klir G (2004) Generalized information theory: aims, results, and open problems. Reliab Eng Syst Saf 85(1–3):21–38

    Article  Google Scholar 

  • Klir G, Wierman M (1999) Uncertainty-based information-elements of generalized information theory. Physica-Verlag, Heidelberg, New York

    Book  Google Scholar 

  • Liu B (2002) Theory and practice of uncertain programming. Physica-Verlag, Heidelberg

    Book  Google Scholar 

  • Liu B (2004) Uncertainty theory: an Introduction to its axiomatic foundations. Springer, Berlin

    Book  Google Scholar 

  • Liu Q, Rao SS (2005) Fuzzy finite element approach for analysis of fiber-reinforced laminated composite beam. AIAA J 43(3):651–661

    Article  Google Scholar 

  • Maglaras G, Nikolaidis E, Haftka RT et al (1997) Analytical-experimental comparison of probabilitic and fuzzy set based methods for designing under uncertainty. Struct Optim 13:69–80

    Article  Google Scholar 

  • Möller B, Graf W, Beer M (2000) Fuzzy structural analysis using α-level optimization. Comput Mech 26:547–565

    Article  Google Scholar 

  • Moore RE (1962) Interval arithmetic and automatic error analysis in digital computing. PhD Dissertation, Stanford University

    Google Scholar 

  • Moore RE (1966) Interval analysis. Prentice-Hall, Englewood Cliffs, NJ

    MATH  Google Scholar 

  • Mourelatos ZP, Zhou J (2005) Reliability estimation and design with insufficient data based on possibility theory. AIAA J 43(8):1696–1705

    Article  Google Scholar 

  • Nahmias S (1978) Fuzzy variable. Fuzzy Sets Syst 1:97–101

    Article  MathSciNet  Google Scholar 

  • Oberkampf W, Helton J (2002) Investigation of evidence theory for engineering applications. AIAA 2002–1569. In: 43th AIAA/ASME/ASCE/AHS/ASC structure, structural dynamics and material conference, 4th non-deterministic approaches forum. Denver, Colorado

    Google Scholar 

  • Oberkampf W, Helton J, Sentz K (2001) Mathematical representation of uncertainty. AIAA 2001–1645. In: 42th AIAA/ASME/ASCE/AHS/ASC structures, structural dynamic and materials conference and exhibit, 2001AIAA non-deterministic approaches forum. Seattle, WA

    Google Scholar 

  • Oberkampf W, Helton J, Joslyn C et al (2004) Challenge problem: uncertainty in system response given uncertain parameters. Reliab Eng Syst Saf 85:11–19

    Article  Google Scholar 

  • Rao SS, Chen L (1998) Numerical solution of fuzzy linear equations in engineering analysis. Int J Numer Meth Eng 43:391–408

    Article  MathSciNet  Google Scholar 

  • Sakawa M (1993) Fuzzy sets and interactive multiobjective optimization. Plenum Press

    Google Scholar 

  • Savoia M (2002) Structural reliability analysis through fuzzy number approach, with application to stability. Comput Struct 80:1087–1102

    Article  MathSciNet  Google Scholar 

  • Shafer G (1976) A mathematical theory of evidence. Princeton University Press, NJ

    MATH  Google Scholar 

  • Shih CJ, Chi CC, Hsiao JH (2003) Alternative α-level-cuts methods for optimum structural design with fuzzy resources. Comput Struct 81:2579–2587

    Article  Google Scholar 

  • Shutie X, Minpin Q, Jun Y (2000) Random mathematics. Higher education press. ISBN 7-04-008990-4. (萧树铁, 钱敏平和叶俊. 随机数学. 高等教育出版社, 2000, ISBN 7-04-008990-4.)

    Google Scholar 

  • Spiegelhalter DJ (1986) A statistical view of uncertainty in expert systems. In: Gale W (ed.) Artificial intelligence and statistics. Addison-Wesley

    Google Scholar 

  • Spiegelhalter DJ (1987) Probabilistic expert systems in medicine: practical issues in handling uncertainty. Stat Sci 2(1):3–44

    Article  MathSciNet  Google Scholar 

  • Stallings W (1977) Fuzzy set theory versus Bayesian statistics. IEEE Trans Syst Man Cybern SMC-7, 216–219

    Google Scholar 

  • Tonon F, Bernardini A (1990) Multiobjective optimization of uncertain structures through fuzzy set and random set theory. Comput-Aided Civil Infrastruct Eng 14:119–140

    Article  Google Scholar 

  • Tribus M (1979) Comment on fuzzy sets, fuzzy algebra and fuzzy statistics. Proc IEEE 67:11–68

    Article  Google Scholar 

  • Weichselberger K (2000) The theory of interval-probability as a unifying concept for uncertainty. Int J Approx Reason 24:149–170

    Article  MathSciNet  Google Scholar 

  • Xiao S, QIAN M, Ye J (2002) Random Mathematics [M]. Beijing: Higher Education Press. (萧树铁, 钱敏平, 叶俊. 随机数学[M]. 北京: 高等教育出版社, 2002.)

    Google Scholar 

  • Zadeh LA (1965) Fuzzy sets. Inf Control 8:338–353

    Article  Google Scholar 

  • Zadeh LA (1978) Fuzzy sets as a basis for a theory of possibility. Fuzzy Sets Syst 1:3–28

    Article  MathSciNet  Google Scholar 

  • Zadeh LA (2006) Generalized theory of uncertainty (GTU)—principal concepts and ideas. Comput Stat Data Anal 51:15–46

    Article  MathSciNet  Google Scholar 

  • Zhentao L (2006) Research on analysis method of uncertain structure. PhD thesis of Xidian university. (梁震涛. 不确定性结构的分析方法研究. 博士学位论文, 西安电子科技大学, 2007.)

    Google Scholar 

  • Zimmermann HJ (1991) Fuzzy set theory and its applications. Kluwer Academic Publishers

    Google Scholar 

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Correspondence to Binbin Pan .

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Pan, B., Cui, W. (2020). Uncertainty Theory. In: Multidisciplinary Design Optimization and Its Application in Deep Manned Submersible Design. Ocean Engineering & Oceanography, vol 13. Springer, Singapore. https://doi.org/10.1007/978-981-15-6455-0_3

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