creelman@dalcsug.UUCP (Paul Creelman) (03/01/88)
Subject: Uncertainty and FUZZY LOGIC VS PROBABILITY Newsgroups: comp.ai.digest Keywords: UNCERTAINTY, PROBABILITY There appears to be some discussion about uncertainty by Eric Neufeld and others. According to Spiegelhalter, the use of probability for representing uncertainty in expert systems is the wrong method. He says it is inappropriate because uncertainty in knowledge does not match the chance mechanism of an observable event. It is unnecessary since no meaning must be attached to numbers, but instead the rank order of hypotheses is often all that matters in an expert system. Furthermore probability is somewhat impractical since it requires too many estimates of prior probabilities, fails to distinguish ignorance from uncertainty, and fails to provide an explanation of conclusions. I must agree. Down with probability! Surely what is needed is a simplified version of Shafer's evidence theory which deals with all possible subsets of the possible variable values, the frame of discernment. A number is associated with each subset which measures the certainty that the actual variable value is in that subset. Suppose we coarsen the uncertainty measure by reducing the number of subsets specified. While providing a measure of certainty for all subsets of values may be impractical, a system that uses only a limited number of these subsets could be very useful. If only there was a way of consistently updating certainty for such subsets! I wonder if additivity of the certainty measure is necessary. Perhaps a condition like c(B)> c(C) -> c(A+B) > c(A+C) where A B and C are disjoint subsets and + is set union. Of course, it is desirable to allow A B and C to have common elements as well. I hope this will stimulate discussion. For references, see William Gale,ed.,Artificial Intelligence and Statistics, Addison-Wesley Publishing Company,1986. L.N.Kanal,J.F.Lemmer,eds.,Uncertainty in Artificial Intelligence, North-Holland,1986. Paul Creelman student Dalhousie University ZZ
emneufeld@watdragon.waterloo.EDU (Eric Neufeld) (03/07/88)
In article <8802291913.AA13911@dalcsug.UUCP> creelman@dalcsug.UUCP (Paul Creelman) writes: > >Subject: Uncertainty and FUZZY LOGIC VS PROBABILITY >Newsgroups: comp.ai.digest >Keywords: UNCERTAINTY, PROBABILITY > > There appears to be some discussion about uncertainty by Eric Neufeld > and others. According to Spiegelhalter, the use of probability for > representing uncertainty in expert systems is the wrong method. First favour I would like to ask of the net: Something has happened with our news feed: I have seen nothing of this controversy since my original posting. Would someone, possibly the moderator, be so kind as to mail me the controversy? [Done. -- KIL] To continue the discussion: > it is inappropriate because uncertainty in knowledge does not match the > chance mechanism of an observable event. It is unnecessary since no meaning > must be attached to numbers, but instead the rank order of hypotheses is > often all that matters in an expert system. I have heard Ben-Bassat say that even the rank ordering is unimportant in *applications*. Physicians want to know *possible* diagnoses, relative strengths are what is important. (My apologies to Dr. Ben-Basset if this is incorrect.) But so what? That is an opinion. Suppose rank ordering is important as Spiegelhalter suggests. The use of numbers in probability theory can be viewed merely as a convention. Nothing precludes the use of probability as a way of deriving rank orderings. One of my favourite papers is Koopman's which eliminates the numbers (in the preamble) with the hope of restoring the primal intuition of probability. The numbers are later added for consistency with the mathematical theory. >Furthermore probability is > somewhat impractical since it requires too many estimates of prior > probabilities, fails to distinguish ignorance from uncertainty, and > fails to provide an explanation of conclusions. I must agree. Down with > probability! You contradict yourself! Probability tells us that it is not trivial to distinguish ignorance from uncertainty. Probability tells us that truth is *independent* of explanation (i.e., given our knowledge of your symptoms, the probability of disease X is 0.xx (or rank ordering 3) REGARDLESS OF THE EXPLANATION or ARGUMENT used to get the diagnosis). But that is not what probability is for. It is used to measure (relative) strength in an argument. > Surely what is needed is a simplified version of Shafer's evidence theory > which deals with all possible subsets of the possible variable values, the > frame of discernment. A number is associated with each subset which measures > the certainty that the actual variable value is in that subset. Suppose we > coarsen the uncertainty measure by reducing the number of subsets specified. I would say surely not! Professor Kyburg has, more than a year ago, shown that the theory of Dempster-Shafer is equivalent to an interval-valued theory of probability, with some added statistical assumptions. That is not to say that the D-S model has no useful applications. I will take the liberty of paraphrasing Dr. Kyburg, who concludes his article by saying that there is nothing wrong with variations on the theory of probability containing such statistical assumptions, but these assumptions should be in full view, up-front, for all to criticize constructively. > > Paul Creelman -- . w q