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00663794 Manton, Kenneth G. Woodbury, Max A. Tolley, H.Dennis Statistical applications using fuzzy sets. Wiley Series in Probability and Mathematical Statistics. Probability and Mathematical Statistics. New York, NY: Wiley. xi, 312 p. \sterling\ 49.50 (1994). 1994 New York, NY: Wiley EN crisp set models grade of membership fuzzy partition maximum likelihood estimates aggregate data empirical Bayes model generalized time-dependent model forecasting simulation combined data sets This book presents an approach to model and deal with high dimensional discrete response data. This approach is based on fuzzy set concepts and principles, which are directly reflected in the estimation of parameters of the fuzzy models. The main purpose of the authors has been to show that fuzzy sets can be used in statistical analyses in a computationally appropriate way. The statistical models presented in the book generalize discrete set notions to fuzzy set ones. The basic model, the Grade of Membership (GoM) one, is introduced in Chapter 1 by making use of the concepts of fuzzy partition, the parametrization of the fuzzy partition model, and its probability distribution. Chapter 2 is focussed on the study of the likelihood formulation of the GoM model, and compared with other statistical multivariate methods. Chapter 3 discusses the statistical properties and methods to obtain maximum likelihood estimates of the parameters of the GoM model, as well as their applications in practice. In Chapter 4, the GoM model that has been previously presented is adapted to manage aggregate data by using a proper modification of the likelihood function. In Chapter 5, the GoM model is generalized to represent time by adequately parameterizing the likelihood function. Chapter 6 is devoted to extend the basic GoM model to develop an empirical Bayes model for GoM. Chapter 7 examines the use of parameter estimates from the generalized time-dependent model, stated in Chapter 5, in forecasting and simulation with fuzzy models. Comparisons between crisp and fuzzy set models for these problems are also carried out. In Chapter 8, the authors show how the GoM models can be employed to deal with combined data sets in an integrated analysis. Examples are considered to illustrate this analysis. Finally, Chapter 9 concludes with a short review of properties of GoM models and methods, and differences with respect to other statistical procedures. This review suggests several fields to develop further statistical research similar to what is presented in the book. M.A.Gil (Oviedo)