Hmm, no takers on this one yet? I'll rephrase the problem in a way that makes more sense to me (since the original contains words I don't know the meaning of):
---- X and Y are unknown variables taking values in the set (1, 2, ..., n). The entries in the joint probability matrix, P, are unknown and of the form aij, where the aij take values in the unit interval and add up to unity. What is the marginal probability distribution of X in each of the following cases? a) For each aij we are given a fixed interval, with the distribution of aij being uniform inside and zero outside this interval. (I assume the intention here was that the width of the interval is known?) b) (I'll leave the translation of this one to a fuzzy specialist.) ---- Stated this way, case (a) is unproblematic. It's worth adding that using a finite interval with zero probability density outside the interval will often be a bad thing to do in practical problems and is not recommended if you have any say in the problem design. Instead, a distribution that is nonzero throughout the unit interval will avoid nonsensical results in cases where the correct value of aij is outside the interval. Replacing the hard distribution in (a) with a soft distribution that is small but nonzero outside the given interval is easily done and the solution remains unproblematic. Konrad On Thu, 22 Sep 2005, Lotfi Zadeh wrote: > > X and Y are random variables taking values in the set (1, 2, ..., > n). The entries in the joint probability matrix, P, are of the form > "approximately aij," where the aij take values in the unit interval > and add up to unity. What is the marginal probability distribution of > X? Two special cases: (a) "approximately aij," is interpreted as an > interval centering on aij; and (b) "approximately aij," is interpreted > as a fuzzy triangular number centering on aij. > > Warm regards to all, > > Lotfi > _______________________________________________ > uai mailing list > uai@ENGR.ORST.EDU > https://secure.engr.oregonstate.edu/mailman/listinfo/uai > _______________________________________________ uai mailing list uai@ENGR.ORST.EDU https://secure.engr.oregonstate.edu/mailman/listinfo/uai
