neutrosophic set

logic A generalisation of the intuitionistic set,

classical set, fuzzy set, paraconsistent set, dialetheistset, 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 n100 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 .

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

Florentin Smarandache, American Research Press, 1998].

(1999-12-14)