aleks jakulin btyqaeaslfdsfriuniljsi lotfi zadeh wrote x random variables taking values set 1 2 n entries joint probability matrix p form approximately aij aij take values unit interval add unity marginal probability distribution x four special cases approximately aij interpreted interval centering aij b approximately aij interpreted triangular fuzzy number centering aij c approximately aij interpreted uniform probability distribution interval centering aij approximatelt aij interpreted triangular probability density function centering aij let take bayesian stance consider p_ij corresponding probability xi yj random variable probability p defined approximate imprecise matrix bayesian context specified prior likelihood function data fuzzy context given directly notice variable p_ij _not independent_ variables p_kl matrix p namely sum p_ equal 1 therefore reject combinations may consistent a_ result nonnormalized p responsibility allow least one valid combination deal problems ad instead assume nn matrix p normalized random vector furthermore assume bayesian posterior p dirichlet distribution also present walleys approach dirichlet distribution specified terms counts higher counts crisper p lower counts fuzzier p therefore p dirichleta_11a_12a_21a_22a_nn easy prove p_ dirichleta_11a_12a_1n a_n1a_n2a_nn p_ dirichleta_1ia_2ia_ni a_1ia_2ia_ni best regards aleks dr aleks jakulin httpktijssialeks department knowledge technologies jozef stefan institute ljubljana slovenia _______________________________________________ uai mailing list faqengrorstedu httpssecureengroregonstateedumailmanlistinfouai tue 05 aug 2008 222131 0100 uai imprecise probabilitiesa simple yet computationally nontrivial problem