Abstract
When only incomplete information about the probability distribution of an experiment is available, we may have to admit imprecision in the formulation of an uncertainty model. In this paper Random Set Theory is used to build possibilistic uncertainty models from sampled data. In particular Goodman's one-point coverage function of a class of random sets is estimated from data. Finally, we focus on an example to illustrate how from random sets induced possibility distributions may be used in the detection of changes in time-series data.
This work was supported by thr UK Engineering and Physical Sciences Research Council (EPSRC) under grant GR/KR09410.
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References
Dubois, D. and Prade, H.: Possibility Theory. Plenum Press, New York (1988).
Dubois, D. and Prade, H.: The Mean Value of a Fuzzy Number. Fuzzy Sets and Systems 24 (1987) 279–300.
Dubois, D. and Prade, H.: Combination of Fuzzy Information in the Framework of Possibility Theory. In Abidi, M.A. and Gonzales, R.C (eds), ‘Data Fusion in Robotics and Machine Intelligence', Academic Press (1992) 481–505.
Dempster, A.P.: Upper and lower probabilities generated by a random closed interval. The Annals of Mathematical Statistics 39 (1968) 957–966.
Goodman, I.R.: Fuzzy Sets as Equivalence Classes of Random Sets. In Yager, R.R. (ed.): Fuzzy Set and Possibility Theory: recent developments. John Wiley & Sons (1982) 327–343.
Grabisch, M. et.al.: Fundamentals of Uncertainty Calculi with Applications to Fuzzy Inference. Kluwer Academic Publishers (1995).
Kruse, R. and Meyer, K.D.: Statistics with vague data. D.Reidel Publishing Company, Dordrecht (1987).
Wang, P.-Z.: Knowledge Acquisition by Random Sets. International Journal of Intelligent Systems 11 (1996) 113–147.
Wolkenhauer, O.: Possibilistic Change Detection: Onset of Oscillations. Proc. EU-FIT'96, Vol. 3, (1996) 1610–1613.
Wolkenhauer, O. and Edmunds, J.: Dynamic Systems Reliability Evaluation using Uncertainty Techniques for Performance Monitoring. IEE Proc.-Control Theory Appl. 143 No. 6, November 1996.
Wolkenhauer, O. and Edmunds, J.: Local uncertainty models for the analysis of time series data. Accepted for EUFIT'97, Aachen, September 1997.
Wolkenhauer, O.: On the Combination of Probabilistic and Fuzzy Concepts in Signal-Based Data Analysis. Invited Session on Hybrid Methods in the Development of Intelligent Systems, EUFIT'97, Aachen, September 1997.
Zadeh, L.A.: Fuzzy sets as a basis for a theory of possibility. Fuzzy Sets and Systems 1 (1978) 3–28.
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© 1997 Springer-Verlag
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Wolkenhauer, O. (1997). Qualitative uncertainty models from random set theory. In: Liu, X., Cohen, P., Berthold, M. (eds) Advances in Intelligent Data Analysis Reasoning about Data. IDA 1997. Lecture Notes in Computer Science, vol 1280. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0052875
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DOI: https://doi.org/10.1007/BFb0052875
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