Download free e-books of philosophy from

www.gallup.unm.edu/~smarandache/neutrosophy.htm

Neutrosophy is a new branch of philosophy that studies the origin,
nature, and scope of neutralities, as well as their interactions with
different ideational spectra.
The neutrosophics were introduced by Dr. F. Smarandache in 1995.
This theory considers every notion or idea <A> together with its
opposite or negation <Anti-A> and the spectrum of "neutralities" <Neut-A>
(i.e. notions or ideas located between the two extremes, supporting
neither <A> nor <Anti-A>). The <Neut-A> and <Anti-A> ideas together are
referred to as <Non-A>.
According to this theory every idea <A> tends to be neutralized and
balanced by <Anti-A> and <Non-A> ideas - as a state of equilibrium.

Neutrosophy is the base of neutrosophic logic, neutrosophic set,
neutrosophic probability and statistics used in engineering applications
(especially for software and information fusion), medicine, military,
cybernetics.

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+[.

For software engineering proposals the classical unit interval [0, 1]
can be used.
T, I, F are independent components, leaving room for incomplete
information (when their superior sum < 1), paraconsistent and contradictory
information (when the superior sum > 1), or complete information (sum of
components = 1).

As an example: a statement can be between [0.4, 0.6] true, {0.1} or
between (0.15,0.25) indeterminant, and either 0.4 or 0.6 false.

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 <= 1, while in neutrosophic probability
n_sup <= 3+.
In imprecise probability: the probability of an event is a subset T in
[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.