Previous |  Up |  Next


non-precise data; hypothesis testing
The measurement of continuous quantities is the basis for all mathematical and statistical analysis of phenomena in engineering and science.Therefore a suitable mathematical description of measurement results is basic for realistic analysis methods for such data. Since the result of a measurement of a continuous quantity is not a precise real number but more or less non- precise, it is necessary to use an appropriate mathematical concept to describe measurements. This is possible by the description of a measurement result by a so-called non-precise number. A non-precise number is a generalization of a real number and is defined by a so-called characterizing function. In case of vector valued quantities the concept of so-called non- precise vectors can be used. Based on these concepts more realistic data analysis methods for measurement data are possible.
[1] Bandemer H., Näther W.: Fuzzy Data Analysis. Kluwer, Dordrecht 1992 MR 1175172 | Zbl 0758.62003
[2] Dubois D., Kerre E., Mesiar R., Prade H.: Fuzzy Interval Analysis. In: Fundamentals of Fuzzy Sets (D. Dubois, H. Prade, eds.), Kluwer, Boston 2000 MR 1890240 | Zbl 0988.26020
[3] Klir G., Yuan B.: Fuzzy Sets and Fuzzy Logic – Theory and Applications. Prentice Hall, Upper Saddle River, N.J. 1995 MR 1329731 | Zbl 0915.03001
[4] Menger K.: Ensembles flous et fonctions aléatoires, Comptes Rendus Acad. Sci. 232 (1951), 2001–2003 MR 0042082
[5] Nguyen H.: A note on the extension principle for fuzzy sets, J. Math. Anal. Appl. 64 (1978), 369–380 DOI 10.1016/0022-247X(78)90045-8 | MR 0480044
[6] Viertl R.: Statistical Methods for Non–Precise Data. CRC Press, Boca Raton 1996 MR 1382865 | Zbl 0853.62004
[7] Viertl R.: Non–Precise Data (Encyclopedia Math. Suppl. II). Kluwer, Dordrecht 2000
[8] Viertl R.: Statistical Inference with Non-Precise Data. In: Encyclopedia of Life Support Systems, UNESCO, Paris, to appear on-line
[9] Zadeh L.: Fuzzy sets. Information and Control 8 (1965), 338–353 DOI 10.1016/S0019-9958(65)90241-X | MR 0219427 | Zbl 0139.24606
[10] Zadeh L.: The concept of a linguistic variable and its applications to approximate reasoning. Parts I, II, III. Inform. Sci. 8 (1975), 199–249 MR 0386369
Partner of
EuDML logo