Plans in general for fuzzy sets in Maxima/Lisp.
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Detailed Description
Plans in general for fuzzy sets in Maxima/Lisp.
 Todo:
 Basic notions

As abbreviation for a fuzzy set we could use "fys".

A basic problem is that "fuzzy sets" are related to some base set; and this base set in general is infinite (like the natural or the real numbers).

Perhaps this base set is just left unspecified in general, and must be stated for each concrete application.

Then a fys A is a map A: B > [0,1] (where the righthand side denotes the interval from 0 to 1), where B is the base set.

So as a maxima object a fys would just be a function f(x), where all f(b) for b in B can be evaluated and yield a real number from 0 to 1.

We should allow as "number" here precise terms (for integers and rational numbers) as well as floatingpoint numbers (ordinary, or "big
floats").

Should we use for example "fysr" for fuzzysubsets of RR, "fysz" for fuzzy subsets of ZZ, "fysn", "fysn0" for fuzzy subsets of NN resp. NN0, and "fysq" for fuzzy subsets of QQ?

We need then the standard fuzzy setoperations, "fysunion", "fysintersection" and "fyscomplement", for the standard operation (max, min, difference with 1) as well as for arbitrary operations.

Or should we use "union_fys" etc. ? However, since it is not union, but only something similar, we should use "fysunion(A,B)" etc.
 Todo:
 More general notions

What about more general types of "fuzzyfication"?

In a different context, one should also allow arbitrary "truth values", for example elements of a boolean algebra or a hyting lattice, that is, "subsets" of B of the form A: B > P, where P is some quasiordered set.

Perhaps calling such "sets" "Psets" ?

The basic Pset operations would be determined by operations from P^2 to P resp. P to P.

What are general axioms here?
Definition in file general.hpp.