konrad scheffler tnqcnlmancalacbiouctacza hmm takers one yet ill rephrase problem way makes sense since original contains words dont know meaning x unknown variables taking values set 1 2 n entries joint probability matrix p unknown form aij aij take values unit interval add unity marginal probability distribution x following cases aij given fixed interval distribution aij uniform inside zero outside interval assume intention width interval known b ill leave translation one fuzzy specialist stated way case unproblematic worth adding using finite interval zero probability density outside interval often bad thing practical problems recommended say problem design instead distribution nonzero throughout unit interval avoid nonsensical results cases correct value aij outside interval replacing hard distribution soft distribution small nonzero outside given interval easily done solution remains unproblematic konrad thu 22 sep 2005 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 two special cases approximately aij interpreted interval centering aij b approximately aij interpreted fuzzy triangular number centering aij warm regards lotfi uai mailing list wed 06 aug 2008 193621 0200 uai test problem involving imprecise probabilities