My example may be overly simplistic intended only for purpose of conceptual understanding, however, based on your response I'm not sure if you understand fuzzy approaches and simply do not agree with them, or if you do not understand fuzzy approaches and are confusing the issue.
In fact, fuzzy approaches are an alternative approach to other kinds of approaches used to deal with uncertainty. It is a very simple approach in application, but really requires a lot of thought is assigning the fuzzy sets. In fact, the fuzzy set would assign a membership value that is a loose estimate of the possiblitity of being correct and is very useful if you have incomplete data sets and/or high degrees of uncertainty. Fuzzy approaches should be viewed as a step in the process of risk assessment (for example) rather than the end all. IN the real world of ecology, the likelihood of a person knowing every variable involved in the system is low. If you can give a probability with a high degree of confidence, I would certainly use a finite number, but you could also use a fuzzy approach. Likewise, if you do have the data to insert into a baeysian approach (as each forthcoming probability is based on the probabilities previously assembled or estimated by observation of previous occurrences) then by all means use a bayesian approach, but you could also use a fuzzy approach. But if you have low confidence in your data and you are not confident in preliminary observations, a fuzzy approach is a very useful tool for understanding what may be going on. Fuzzy approaches do not use probability theory, they use possibility theory. THey are alternative approaches used for similar purposed to infer slightly to very different endpoints. When we use probability we are really trying to assess how likely a single point will happen, typically some mean or median. In possibility theory we are trying to identify what outcomes are definitely possible, what outcomes might be possible, and which outcomes are definitely not possible. The relationship between possiblity and probability could be seen in a similar way to how we view the relationship between Orders and species. For example, all Green Turtles are in Chelonia, but not all Chelonia are Green Turtles, however, All Tuataras are in Sphenodontia, and all extant Sphenodontia are Tuataras because there is only only one species of Tuatara (there may now be 2 species as I recall, but that isn't the point). So, if done correctly what is possible should encompass what is probable, but what is probable will not encompass all that is possible. Is it likely that someone will anonymously send you a million dollars in the mail? No. Is it possible that someone will anonymously send you a million dollars in the mail? yes. Sometimes it is more important to know what is possible and sometimes it is more important to know what is probable. IF you have a large set of outcomes that all have low probability, you may decide that discussing what is possible is more important, however, if you have a small range of variables with very high probability of occurrence, then you may choose to discuss in terms of probability. This is by no means a perfect explanation, but maybe some light bulbs will turn on for some folks? On Fri, Aug 7, 2009 at 8:31 PM, <[email protected]> wrote: > malcolm McCallum wrote: >> >> Maybe this will help... >> >> Imagine you have two people sitting at a table drinking and you are >> the waiter/waitress. >> >> One customer says, "I have 13.21435343234 ml of alchohol in my drink." >> >> The other says, "My drink is low." >> >> Which is more meaningful??? When the first person makes their >> statement, do you really know what it means? You will need a lot more >> information to assess what it means such as: how big is their glass, >> how much ice is in it, was it a mixed drink? >> >> The second person has relayed a very useful statement that tells you >> exactly what is meant, however, you do not know how much it will take >> to fill the drink. >> >> The first example would be a standard estimate such as probability. >> It seeks to get to the exact number of concern. >> >> The second exaple is a fuzzy estimate, and provides a cognitive >> estimate that has obvious meaning but will need further investigation >> to work out the details. >> >> Standard estimates deal with what is probable. >> Fuzzy estimates deal with what is possible. >> >> does that make sense? >> > Not really! > > The first statement is (overly!) precise, and has no probability associated > with it. What it means depends on context, and understanding that is > outside of formal mathematics, of any sort. TBH, I think it's a red herring > that confuses rather than enlightens. > > The second statement is vague. Whether one deals with it as with > probability or fuzzy logic depends on whether you see the vagueness as ontic > or epistemic. > > If one thinks that there is a precise concentration of alcohol, and that > "low" is an estimate of this, then the vagueness is epistemic, so one could > set up a probability model for the concentration. > > Alternatively, one might view "low" as an objective category, where there > are some concentrations that everybody would say are "low", and some where > everybody would say that they are "high". But there are also concentrations > in between where any person is not sure whether to say it is "low" or not. > In this case, we might view "low" as being a vague property, and assign a > non-integer truth value to the statement "the concentration is low", e.g. it > might be "60% true". Note that this would be done even if the concentration > was known exactly. The problem is not one of uncertainty about the actual > concentration (which is what Bayesian probabilities measure), but about > vagueness in the mapping of the exact value to the notion of "low". > > Bob > > -- > Bob O'Hara > Department of Mathematics and Statistics > P.O. Box 68 (Gustaf Hällströmin katu 2b) > FIN-00014 University of Helsinki > Finland > > Telephone: +358-9-191 51479 > Mobile: +358 50 599 0540 > Fax: +358-9-191 51400 > WWW: http://www.RNI.Helsinki.FI/~boh/ > Blog: http://network.nature.com/blogs/user/boboh > Journal of Negative Results - EEB: www.jnr-eeb.org > -- Malcolm L. McCallum Associate Professor of Biology Managing Editor, Herpetological Conservation and Biology Texas A&M University-Texarkana Fall Teaching Schedule: Vertebrate Biology - TR 10-11:40 General Ecology - MW 1-2:40pm Forensic Science - W 6-9:40pm
