aleks jakulin btyqaeaslfdsfriuniljsi lotfi zadeh wrote problem probability theory differentiate fuzziness randomness concomitantly possibility probability simple example meet valentina know old perception 40 instance valentinas age fuzzy variable 40 fuzzy value lotfis case important demonstrates difference value random variable distribution random variable let rephrase example probabilistic terms meet valentina observe values several variables skinslight wrinkles hairstyleformal dressskirt_blouse know old know value variable age previously observed similar women men knowing ages could build probabilistic model pageskinhairstyledress since seen women world started subjective prior model also subjective bayesian perception 40 quickly summarize pageskinslight wrinkleshairstyleformaldressskirt_blouse use mean conditional distribution instance valentinas age fuzzy variable 40 fuzzy value valentinas age subjective probability distribution 40 rounded value mean best regards aleks jakulin department statistics columbia university thu 07 aug 2008 063633 0400 uai determinism versus choice