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Statistical Methods for Fuzzy Data by Reinhard Viertl

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14.3 Problems

a. Looking at a fuzzy discrete probability distribution P* on the finite set {x1, … , xk} with fuzzy point probabilities p*(xj), j = 1(1)k explain the validity of the rules for a fuzzy probability distribution given in Section 8.3.

b. Prove the validity of the sequential nature for the upper δ-level curves of the fuzzy a posteriori density π*(·|).

c. Show that the above procedure for fuzzy a posteriori densities gives the classical a posteriori density if the a priori density is a classical density.

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