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Ph. D. Dissertations on Neutrosophic Logic/Set/Probability:

E-Books on Neutrosophics:

International Conferences on Neutrosophics:

Short Definitions of Neutrosophics:   

    Neutrosophic Logic is a general framework for unification of many existing logics, such as fuzzy logic (especially intuitionistic fuzzy logic), paraconsistent logic, intuitionistic logic, etc.  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⁺[ with not necessarily any connection between them.   

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) indeterminate, and either 0.4 or 0.6 false.

The distinctions between Neutrosophic Logic and Intuitionistic Fuzzy Logic are here.

    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 Set generalizes the fuzzy set (especially intuitionistic fuzzy set), paraconsistent set, intuitionistic set, etc.

The distinctions between Neutrosophic Set and Intuitionistic Fuzzy Set are here.

    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 indeterminate / unknown probability of value x.

    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 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.

In a classical way <A>, <Neut-A>, <Anti-A> are disjoint two by two.

But, since in many cases the borders between notions are vague, imprecise, Sorites, it is possible that <A>, <Neut-A>, <Anti-A> (and <Non-A> of course) have common parts two by two as well.

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, physics.

For more information on neutrosophics see the below links:

Neutrosophic Subjects for Future Research:

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