[lug] Weighting of factors and whatnot (a bit OT)

[Chris Riddoch]

So, this isn't entirely a linux thing, but I figure there are enough
programmers here that I'm likely to get some idea of a good solution
to an interesting problem.  The actual thing I'm trying to solve has
nothing to do with books or genres at all, but this is the closest
metaphor I can think of to the real problem as I've been able to come
up with.

I've got a list of things (call them books) I want to rank.  Each of
the things to rank has six numbers associated with it, one for each
category (genre).  Each of these numbers represents the degree of
membership of the book in a particular category, from 0 (not in the
genre at all) to 1 (unquestionably belonging in the genre).

Now, the "ideal" book belongs mostly to a particular genre, slightly
less so to another particular one, less so to the next, and so on to
being not at all part of the least desirable genre.

I need to distill the factors into a single number that can describe
how close to "ideal" a book is, given a desired ranking of genres.
Note that I don't have any specific desired degree of membership for
each genre - I don't mind any two of them are especially close to each
other, so long as it's not (for example) the most and least desirable
genres.  That final, single number, will be the basis of the ranking.

It seems like a class membership, set theory, perhaps permutation sort
of thing.  I don't have any books on this topic.  I suspect there's
more than one way to do this.  Does this problem remind you of any
similar known problems with known solutions?  What do you suggest?

-- 
epistemological humility
  Chris Riddoch