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
- the fuzzy set
(for n=100 and i=0, and 0- 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- 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).
["Neutrosophy / Neutrosophic Probability, Set, and Logic", Florentin Smarandache, American Research Press, 1998].