# Re: fuzzy logic and probability

Warren Sarle (saswss@hotellng.unx.sas.com)
Wed, 24 Jul 1996 15:11:10 +0200

In article <31EDB9C6.565D@hal-pc.org>, "Michael D. Kersey" <mdkersey@hal-pc.org> writes:
|> ...
|> A membership function for say, the variable "height", could be formulated in the
|> following manner:
|> 1) Define or select from the language a set of labels, say the set
|> { short, medium, tall },
|> 2) Using these terms, poll a sample of persons, asking them to
|> classify other persons of measured height as being short, medium, or tall.
|> From this we could infer the probabilities p(x,h) that a person of a given height
|> h be classified as x = {short, medium, or tall} by someone from the general
|> population of persons.
|> 3) Plot p(tall, h). It may not be a monotonically increasing function of height,
|> ( e.g., perhaps wider persons are perceived as being less "tall", and we got
|> a sample including a significant number of wide persons in one height range ).
|>
|> Now p(x,h) are probability functions, but can also be used as membership functions.

p(x|h) is a probability function.
p(h|x) is a likelihood function or a regression function.

|> To me, the most significant thing about fuzzy logic is not that it is associated
|> with probability in any particular way, but that it captures and renders explicit
|> ordinal information sometimes overlooked in qualitative models. In this way, it
|> promotes data from a so-called "nominal" scale to an "ordinal" scale.

In the example above, you are _demoting_ interval data (h) to ordinal data (x).

--

Warren S. Sarle SAS Institute Inc. The opinions expressed here saswss@unx.sas.com SAS Campus Drive are mine and not necessarily (919) 677-8000 Cary, NC 27513, USA those of SAS Institute.