neutrosophic set

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<◦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).

{Home (http://www.gallup.unm.edu/~smarandache/NeutSet.txt)}.

["Neutrosophy / Neutrosophic Probability, Set, and Logic",

Florentin Smarandache, American Research Press, 1998].

(1999-12-14)