There are some ideas concerning a generalization of Bayes' theorem to the situation of fuzzy data. Some of them are given in the references , , and . But the proposed methods are not generalizations in the sense of the probability content of Bayes' theorem for precise data. In the present paper a generalization of Bayes' theorem to the case of fuzzy data is described which contains Bayes' theorem for precise data as a special case and allows to use the information in fuzzy data in a coherent way. Moreover a generalization of the concept of HPD-regions is explained which makes it possible to model and analyze the situation of fuzzy data. Also a generalization of the concept of predictive distributions is given in order to calculate predictive densities based on fuzzy sample information.
KeywordsFuzzy Number Precise Data Predictive Distribution Fuzzy Data Predictive Density
Unable to display preview. Download preview PDF.
- M.A. Gil, N. Corral, P. Gil: The Minimum Inaccuracy Estimates inX 2-Tests for Goodness of Fit with Fuzzy Observations, JSPI 19 (1988).Google Scholar
- V.V. Nalimov: Faces of Science, ISI Press, Philadelphia, 1981.Google Scholar
- T. Okuda, H. Tanaka, K. Asai: Discrimination Problems with Fuzzy States and Fuzzy Information. In: TIMS Studies in the Management Sciences 20 (1984).Google Scholar
- R. Viertl: Is it Necessary to Develop a Fuzzy Bayesian Inference? In: Probability and Bayesian Statistics, Plenum, New York, 1987.Google Scholar