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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- 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].


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