Neutrosophic Set
by
Florentin Smarandache
UNM

Definition of Neutrosophic Set:

<logic, mathematics> A set which generalizes many existing classes of sets, especially the fuzzy set.

Let U be a universe of discourse, and M a set included in U. An element x from U is noted, with respect to the set M, as x(T, I, F), and belongs to M in the following way: it is T (membership appurtenance), I set, and F here T, I, F are real standard or non-standard subsets, included in the non-standard unit interval ]-0, 1+[, representing truth, indeterminacy, and falsity percentages respectively.

Generalization of fuzzy set, dialethist set, paraconsistent set, intuitionistic set, paradoxist set, tautological set, etc.

Reference:

Florentin Smarandache, Ä Unifying Field in Logics. Neutrosophy: Neutrosophic Probability, Set, and Logic", American Research Press, Rehoboth, 1999.

http://www.gallup.unm.edu/~smarandache/Definitions-neutrosophics.htm

Date received: October 13, 2001