lotfi zadeh gzrdaeecsberkeleyedu dear hung thank illuminating analyses valentina exampleand comments regarding theory random fuzzy sets high expertise probability theory fuzzy logic evidence regarding bayesian approach outlined aleks jakulin like add following first conditioning information perceptionbased quantifiable specifically would wrinkles example dealt furthermore perception valentina young would bayesian approach apply subjective probability distribution associated young would probability distribution associated young could apply random sets example fuzzy logic would much simpler use clearly power probabilistic methods enhanced move pointvalued discrete probability distributions setvalued discrete probability distributions random sets power enhanced move random sets random fuzzy sets please note 1979 paper fuzzy sets information granularity advances fuzzy set theory applications gupta r ragade r yager eds 318 amsterdam northholland publishing co 1979 available upon request employed random fuzzy sets generalize dempstershafer framework however moving random sets random fuzzy sets sufficient done moving random fuzzy sets granulevalued distributions described paper generalized theory uncertainty gtuprincipal concepts ideas computational statistics data analysis 51 1546 2006 downloadable httpwwwsciencedirectcom available upon request concept granule general concept fuzzy set granule characterized generalized constraint view level generalization needed enhance power probability theory point deal examples given messages try following swedes much taller italians difference average height swedes average height italians solution given gtu paper theory random fuzzy sets enriches probability theory point said randomness fuzziness coexist framework probability theory many problems remain one pointed jspi paper cited previous message dealing imprecise probabilities deal addition imprecise events imprecise functions imprecise relations imprecise dependencies importantly basic problem almost concepts probability theory bivalent eg events b either independent independent process either stationary nonstationary event either occurs occur shades truth allowed reality concepts bivalentthey matter degree may take long time happen doubt eventually recognized bivalent logic right kind logic serve foundation probability theory made continuing make important contributions probability theory fuzzy logic building bridges please continue warm regards lotfi lotfi zadeh professor graduate school director berkeley initiative soft computing bisc thu 07 aug 2008 035456 0800 uai determinism vs chance