Abstract
Besides stochastic variation of real data there is another kind of uncertainty in observations called imprecision and the corresponding measurement results are called non-precise data. Usually this kind of uncertainty is not described in statistics. Especially in environment statistics, where also very small quantities are measured, this imprecision cannot be neglected. Otherwise by extrapolations the precision of results is very misleading. Therefore statistical methods have to be generalized for non-precise data. The mathematical concept to describe non-precise data are so-called non-precise numbers and non-precise vectors. Situations are explained, where the characterizing functions of non-precise numbers can be given explicitly. Using the mathematical concept of non-precise numbers and vectors statistical procedures can be generalized to non-precise data. These generalizations are explained in the contribution.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
H. Bandemer (Ed.): Modelling Uncertain Data, Akademie Verlag, Berlin, 1993.
D. Dubois, H. Prade: Fuzzy sets and statistical data, European Journal of Operational Research 25, 345–356 (1986).
S. Frühwirth-Schnatter: On statistical inference for fuzzy data with applica-tions to descriptive statistics, Fuzzy Sets and Systems 50, 143–165 (1992).
S. Frühwirth-Schnatter: On fuzzy Bayesian inference, Fuzzy Sets and Systems 60 (1993).
M.A. Gil, N. Corral. P. Gil: The minimum inaccuracy estimates in x2 tests for goodness of fit with fuzzy observations, Journal of Statistical Planning and Inference 19, 95–115 (1988).
T. Keresztfalvi: Operations on Fuzzy Numbers Extended by Yager’s Family of t-Norms, in: H. Bandemer (Ed.): Modelling Uncertain Data. Akademie Verlag, Berlin, 1993.
R. Kruse, K.D. Meyer: Statistics with vague data, D. Reidel Publ., Dordrecht, 1987.
S.P. Niculescu, R. Viertl: A comparison between two fuzzy estimators for the mean, Fuzzy Sets and Systems 48, 341–350 (1992).
S.P. Niculescu, R. Viertl: A Fuzzy Extension of Bernoulli’s Law of Large Numbers, Fuzzy Sets and Systems 50, 167–173 (1992).
R. Viertl: Is it necessary to develop a Fuzzy Bayesian Inference, in: R. Viertl (Ed.): Probability and Bayesian Statistics, Plenum Press, New York, 1987.
R. Viertl: Modelling of Fuzzy Measurements in Reliability Estimation, in: V. Colombari (Ed.): Reliability Data Collection and Use in Risk and Availability Assessment, Springer-Verlag, Berlin, 1989.
R. Viertl: Statistical Inference for Fuzzy Data in Environmetrics, Environmetrics 1, 37–42 (1990).
R. Viertl: On Statistical Inference Based on Non-precise Data, in: H. Ban¬derner (Ed.): Modelling Uncertain Data, Akademie-Verlag, Berlin, 1993.
R. Viertl, II. Hule: On Bayes’ theorem for fuzzy data, Statistical Papers 32, 115–122 (1991).
R. Viertl: Statistical Methods for Non-precise Data, Monograph, to appear.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1995 Springer-Verlag Wien
About this paper
Cite this paper
Viertl, R. (1995). Statistics with Fuzzy Data. In: Della Riccia, G., Kruse, R., Viertl, R. (eds) Proceedings of the ISSEK94 Workshop on Mathematical and Statistical Methods in Artificial Intelligence. International Centre for Mechanical Sciences, vol 363. Springer, Vienna. https://doi.org/10.1007/978-3-7091-2690-5_3
Download citation
DOI: https://doi.org/10.1007/978-3-7091-2690-5_3
Publisher Name: Springer, Vienna
Print ISBN: 978-3-211-82713-0
Online ISBN: 978-3-7091-2690-5
eBook Packages: Springer Book Archive