neutrosophic set

neutrosophic set

(logic)A generalisation of the intuitionistic set,classical set, fuzzy set, paraconsistent set, dialetheist set, paradoxist set, tautological set based onNeutrosophy. An element x(T, I, F) belongs to the set inthe following way: it is t true in the set, i indeterminate inthe set, and f false, where t, i, and f are real numbers takenfrom the sets T, I, and F with no restriction on T, I, F, noron their sum n=t+i+f.

The neutrosophic set generalises:

- the intuitionistic set, which supports incomplete settheories (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 or100);

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

- the dialetheist set, which says that the intersection ofsome disjoint sets is not empty (for t=f=100 and i=0; someparadoxist 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].