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 fuzzy set (for n=100 and i=0, and 0<=t,i,f<=100);
- the paraconsistent set (for n>100 and i=0, with both t,f<100);