zbMATH — the first resource for mathematics

Possibilistic decisions and fuzzy statistical tests. (English) Zbl 1099.62008
Summary: The paper deals with the problem of the interpretation of the results of statistical tests in terms of the theory of possibility. The well known concept in statistics of the observed test size \(p\) (also known as \(p\)-value and significance) has been given a new possibilistic interpretation and generalised for the case of imprecisely defined statistical hypotheses and vague statistical data. The proposed approach allows a practitioner to evaluate the test results using intuitive concepts of possibility, necessity or indifference.

62C99 Statistical decision theory
62F03 Parametric hypothesis testing
62F99 Parametric inference
Full Text: DOI
[1] Arnold, B.F., Statistical tests optimally meeting certain fuzzy requirements on the power function and on the sample size, Fuzzy sets and systems, 75, 365-372, (1995) · Zbl 0851.62025
[2] Arnold, B.F., An approach to fuzzy hypothesis testing, Metrika, 44, 119-126, (1996) · Zbl 0862.62019
[3] Casals, R.; Gil, M.A.; Gil, P., The fuzzy decision problem: an approach to the problem of testing statistical hypotheses with fuzzy information, European J. oper. res., 27, 371-382, (1986) · Zbl 0605.62018
[4] Cutello, V.; Montero, J., An extension of the axioms of utility theory based on fuzzy rationality measures, (), 33-50 · Zbl 1008.91028
[5] D. Dubois, L. Foulloy, G. Mauris, H. Prade, Probability – possibility transformations, triangular fuzzy-sets and probabilistic inequalities, Proc. of the Ninth International Conference IPMU, Annecy, 2002, pp. 1077-1083. · Zbl 1043.60003
[6] Dubois, D.; Prade, H., Ranking fuzzy numbers in the setting of possibility theory, Inform. sci., 30, 184-244, (1983)
[7] Dubois, D.; Prade, H., Fuzzy sets and statistical data, European J. oper. res., 25, 345-356, (1986) · Zbl 0588.62002
[8] Grzegorzewski, P., Testing statistical hypotheses with vague data, Fuzzy sets and systems, 112, 501-510, (2000) · Zbl 0948.62010
[9] Grzegorzewski, P.; Hryniewicz, O., Testing hypotheses in fuzzy environment, Mathware and soft comput., 4, 203-217, (1997) · Zbl 0893.68139
[10] Grzegorzewski, P.; Hryniewicz, O., Soft methods in hypotheses testing, (), 55-72
[11] O. Hryniewicz, Possibilistic interpretation of the results of statistical tests, Proc. of the Eight International Conference IPMU, Madrid, Vol. I, 2000, pp. 215-219.
[12] Kruse, R., The strong law of large numbers for fuzzy random variables, Inform. sci., 28, 233-241, (1982) · Zbl 0571.60039
[13] Kruse, R.; Meyer, K.D., Statistics with vague data, (1987), Riedel Dodrecht · Zbl 0663.62010
[14] Kwakernaak, H.; Kwakernaak, H., Fuzzy random variables, part II: algorithms and examples for the discrete case, Inform. sci., Inform. sci., 17, 253-278, (1979) · Zbl 0438.60005
[15] Lehmann, E.L., Testing statistical hypotheses, (1986), Wiley New York · Zbl 0608.62020
[16] Montenegro, M.; Casals, M.R.; Lubiano, M.A.; Gil, M.A., Two-sample hypothesis tests of means of a fuzzy random variable, Inform. sci., 133, 89-100, (2001) · Zbl 1042.62012
[17] Römer, Ch.; Kandel, A., Statistical tests for fuzzy data, Fuzzy sets and systems, 72, 1-26, (1995) · Zbl 0843.62003
[18] Saade, J., Extension of fuzzy hypothesis testing with hybrid data, Fuzzy sets and systems, 63, 57-71, (1994) · Zbl 0843.62004
[19] Saade, J.; Schwarzlander, H., Fuzzy hypothesis testing with hybrid data, Fuzzy sets and systems, 35, 197-212, (1990) · Zbl 0713.62010
[20] Son, J.Ch.; Song, I.; Kim, H.Y., A fuzzy decision problem based on the generalized neyman – pearson criterion, Fuzzy sets and systems, 47, 65-75, (1992) · Zbl 0757.62012
[21] Taheri, S.M.; Behboodian, J., Neyman – pearson lemma for fuzzy hypotheses testing, Metrika, 49, 3-17, (1999) · Zbl 1093.62520
[22] Watanabe, N.; Imaizumi, T., A fuzzy statistical test of fuzzy hypotheses, Fuzzy sets and systems, 53, 167-178, (1993) · Zbl 0795.62025
[23] Zadeh, L.A., Fuzzy sets as a basis for a theory of possibility, Fuzzy sets and systems, 1, 3-28, (1978) · Zbl 0377.04002
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.