Seriously this is really WIP!
I'm not a mathematician and this library did not undergo any rigorious inspection by one. More over I wrote this library while learning the subject matter, so there are probably serious mistakes in it. However, at some point, I will collaborate with a mathematician to rectify this situation.
from wikipedia:
A fuzzy set is a pair ( U , m ) where U is a set (often required to be non-empty) and m : U → [ 0 , 1 ] a membership function. The reference set U (sometimes denoted by Ω or X is called universe of discourse, and for each x ∈ U, the value m ( x ) is called the grade of membership of x in ( U , m ). The function m = μ A is called the membership function of the fuzzy set A = ( U , m ).
The classy api will simply save you the trouble of stating μ and U all the time.
TBD: examples and reference
the low level API is implemented as simple functions that will almost always take a μ and a U to operate on.
TBD: examples and reference
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Set is the "natural" choice, since it maintains an important quality of classic mathematical sets which is, the distinctness of it's members.
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Looking at the code though, I noticed that iteration is probably the most used operation. Some quick research on the internet yields that arrays are faster that sets.
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The array api (reduce, filter etc) is much more cleaner than the Set's. Having similar api on a Set will require additional coding.
So for now I choose Array over Set.
- it seems like MU is not a proper subset of MU but is a subset
Using objects as member should work pretty great, as long as you make your MU play nicely with them:
class Member {
gt(something) {}
eq(something) {}
lt(something) {}
... etc
}
const MU = x => {
if (x.gt(5)) return 1
if (x.lt(0)) return 0.5
return 0
}-
Serializing and de-serializing code might be a serious security risk. How to safely serialize fuzzy sets then, without serializing the membership function code?
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perhaps there can be a "static" and "dynamic" versions of a fuzzy set. The dynamic one will have a user provided function and can only be created at run time. The static one will serialize the fuzzy set array
[[x, MU(x)...]]and when loaded will have an internal membership function that outputs from that array (practically this should be an object with a map from x => alpha)
when I started to write this the code was very nice, small and clean, but pretty quickly stuff got verbose and icky. Membership filtering from the crisp in low level api is one example but not the only one. Need to deal with that at some point, but in a way that's not going to double or triple the amount of iterations.
When no member of the crisp set has an alpha of one
- fuzzy numbers
- intervals?
- fuzzy analysis