Neutrosophy is a new branch of philosophy, introduced by Dr. Florentin Smarandache in 1995, which studies the origin, nature, and scope of neutralities, as well as their interactions with different ideational spectra.    Neutrosophic Logic is a general framework for unification of many existing logics.  The main idea of NL is to characterize each logical statement in a 3D Neutrosophic Space, where each dimension of the space represents respectively the truth (T), the falsehood (F), and the indeterminacy (I) of the statement under consideration, where T, I, F are standard or non-standard real subsets of ]-0, 1+[.      Neutrosophic 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% true in the set, i% indeterminate (unknown if it is) in the set, and f% false, where t varies in T, i varies in I, f varies in F.   Statically T, I, F are subsets, but dynamically T, I, F are functions/operators depending on many known or unknown parameters.    Neutrosophic Probability is a generalization of the classical probability and imprecise probability in which the chance that an event A occurs is t% true - where t varies in the subset T, i% indeterminate - where i varies in the subset I, and f% false - where f varies in the subset F.    In classical probability n_sup   In imprecise probability: the probability of an event is a subset T of [0, 1], not a number p in [0, 1], what’s left is supposed to be the opposite, subset F (also from the unit interval [0, 1]); there is no indeterminate subset I in imprecise probability.     Neutrosophic Statistics is the analysis of events described by the neutrosophic probability.  The function that models the neutrosophic probability of a random variable x is called neutrosophic distribution: NP(x) = ( T(x), I(x), F(x) ), where T(x) represents the probability that value x occurs, F(x) represents the probability that value x does not occur, and I(x) represents the indeterminant / unknown probability of value x.

A Unifying Field in Logics: Neutrosophic Logic. Neutrosophy, Neutrosophic Set, Neutrosophic Probability (third edition) PDF

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