A generalisation of the intuitionistic set,
classical set,
fuzzy set, paraconsistent set, dialetheist set, paradoxist set,
tautological set based on
Neutrosophy. An element x(T, I, F) belongs to the set in
the following way: it is t true in the set, i indeterminate in
the set, and f false, where t, i, and f are real numbers taken
from the sets T, I, and F with no restriction on T, I, F, nor
on their sum n=t+i+f.
The neutrosophic set generalises:
- the intuitionistic set, which supports incomplete set
theories (for 0<n<100 and i=0, 0<=t,i,f<=100);
- the
fuzzy set (for n=100 and i=0, and 0<=t,i,f<=100);
- the classical set (for n=100 and i=0, with t,f either 0 or
100);
- the paraconsistent set (for n>100 and i=0, with both
t,f<100);
- the dialetheist set, which says that the intersection of
some disjoint sets is not empty (for t=f=100 and i=0; some
paradoxist sets can be denoted this way).
http://gallup.unm.edu/~smarandache/NeutSet.txt.
["Neutrosophy / Neutrosophic Probability, Set, and Logic",
Florentin Smarandache, American Research Press, 1998].