Sequential bayesian test from fuzzy experimental information
This paper is devoted to the sequential problem of testing hypotheses about an experiment, when its outcomes do not provide exact but rather fuzzy information.
This problem will be formalized as a special fuzzy sequential decision problem and, on assuming the Bayesian framework, we are allowed to extend the notions of risk function, stopping rule and terminal decision rule and the Bayes nonfuzzy decision procedures to the fuzzy case, and particularize them to the sequential problem of testing.
KeywordsZadeh's probabilistic definition fuzzy information system sample fuzzy information Bayes stopping rule Bayes terminal decision rule
Unable to display preview. Download preview PDF.
- 1.J.O. Berger, Statistical Decision Theory and Bayesian Analysis (Springer-Verlag, New York, 1985).Google Scholar
- 2.M.R. Casals, M.A. Gil and P. Gil, On the use of Zadeh's Probabilistic Definition for Testing Statistical Hypotheses from Fuzzy Information, Fuzzy Sets and Systems, 20, (1986), 175–190.Google Scholar
- 3.M.R. Casals, M.A. Gil and P. Gil, The Fuzzy Decision Problem: An Approach to the Problem of Testing Statistical Hipotheses with Fuzzy Information, European J. Oper. Res., 27, (1986), 371–382.Google Scholar
- 4.M.R. Casals, Contraste Secuencial Bayesiano entre Hipótesis Simples con Información Difusa, Actas de las XII Jornadas Luso-Espanholas de Matemática, Braga (Portugal), 1987.Google Scholar
- 5.T.S. Ferguson, Mathematical Statistics. A Decision Theoretic Approach (Academic Press, New York, 1967).Google Scholar
- 6.B.W. Lindgren, Introduction to Probability Statistics (Cambridge University Press, 1970).Google Scholar
- 7.H. Tanaka, T. Okuda and K. Asai, Fuzzy Information and Decision in Statistical Model, Advances in Fuzzy Sets Theory and Applications (North-Holland, 1979), 303–320.Google Scholar
- 8.L.A. Zadeh, Fuzzy Sets, Inform. Contr., 8, (1965), 338–353.Google Scholar
- 9.L.A. Zadeh, Probability Measures of Fuzzy Events, J. Math. Anal. Appl., 23, (1968), 421–427.Google Scholar
- 10.L.A. Zadeh, Fuzzy Sets as a basis for a Theory of Possibility, Fuzzy Sets and Systems, 1,1, (1978), 3–28.Google Scholar