Casals, M. R.; Gil, M. A.; Gil, P. On the use of Zadeh’s probabilistic definition for testing statistical hypotheses from fuzzy information. (English) Zbl 0611.62018 Fuzzy Sets Syst. 20, 175-190 (1986). This paper deals with the testing of statistical hypotheses when the sample is fuzzy. The authors prove a fuzzy version of the Neyman-Pearson lemma and give a fuzzy Bayes test for testing a simple hypothesis against a simple alternative. A sequel to the paper under review is the authors’ paper in Eur. J. Oper. Res. 27, 371-382 (1986; Zbl 0605.62018)]. Reviewer: O.Kaleva Cited in 1 ReviewCited in 22 Documents MSC: 62F03 Parametric hypothesis testing 62F15 Bayesian inference Keywords:fuzzy information; fuzzy test; fuzzy random sample; fuzzy version of the Neyman-Pearson lemma; fuzzy Bayes test; simple hypothesis Citations:Zbl 0605.62018 × Cite Format Result Cite Review PDF Full Text: DOI References: [1] Corral, N.; Gil, M. A., The minimum inaccuracy fuzzy estimation: An extension of the maximum likelihood principle, Stochastica, 8, 63-81 (1984) · Zbl 0599.62010 [2] Ferguson, T. S., Mathematical Statistics, (A Decision Theoretic Approach (1967), Academic Press: Academic Press New York) · Zbl 0153.47602 [3] Fourgeaud, C.; Fuchs, A., Statistique (1967), Dunod: Dunod Paris · Zbl 0201.51501 [4] Gil, M. A.; Corral, N.; Gil, P., The fuzzy decision problem: An approach to the point estimation problem with fuzzy information, European J. Oper. Res., 22, 26-34 (1985) · Zbl 0576.90003 [5] Goguen, J. A., \(l\)-Fuzzy sets, J. Math. Anal. Appl., 18, 145-174 (1967) · Zbl 0145.24404 [6] Hogg, R. V.; Craig, A. T., Introduction to Mathematical Statistics (1970), Macmillan: Macmillan New York · Zbl 0192.25603 [7] Kwakernaak, H., Fuzzy random variables - I. Definitions and theorems, Inform. Sci., 15, 1-29 (1978) · Zbl 0438.60004 [8] Lehmann, E. L., Testing Statistical Hypotheses (1959), Wiley: Wiley New York · Zbl 0089.14102 [9] Lindley, D. V., Introduction to Probability and Statistics (1970), Cambridge University Press · Zbl 0431.62002 [10] Negoita, C. V.; Ralescu, D. A., Applications of Fuzzy Sets to Systems Analysis (1975), Birkhäuser: Birkhäuser Basel · Zbl 0326.94002 [11] Rohatgi, V. K., An Introduction to Probability Theory and Mathematical Statistics (1976), Wiley: Wiley New York · Zbl 0354.62001 [12] Tanaka, H.; Okuda, T.; Asai, K., Fuzzy information and decision in statistical model, (Advances in Fuzzy Sets Theory and Applications (1979), North-Holland: North-Holland Amsterdam), 303-320 [13] Tanaka, H.; Sommer, G., On posterior probabilities concerning a fuzzy information, Die Betriebswirtschaft (Stuttgart), 1, 166 (1977) [14] Zadeh, L. A., Fuzzy sets, Inform. and Control, 8, 338-353 (1965) · Zbl 0139.24606 [15] Zadeh, L. A., Probability measures of fuzzy events, J. Math. Anal. Appl., 23, 421-427 (1968) · Zbl 0174.49002 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. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.