ICVL 2016

History of Neutrosophic Theory and its Applications by Florentin Smarandache


History of neutrosophic set and logic, generalization of intuitionistic fuzzy set and logic

Zadeh introduced the degree of membership/truth (t)in 1965 and defined the fuzzy set.

Atanassov introduced the degree of nonmembership/falsehood (f) in 1986 and defined the intuitionistic fuzzy set.

Smarandache introduced the degree of indeterminacy/neutrality (i) as independent component in 1995 (published in 1998) and defined the neutrosophic set on three components (t, i, f) = (truth, indeterminacy, falsehood). The words “neutrosophy” and “neutrosophic” were coined/invented by F. Smarandache in his 1998 book. Etymologically, “neutro-sophy” (noun) [French neutre <Latin neuter, neutral, and Greek sophia, skill/wisdom] means knowledge of neutralthought.

While “neutrosophic” (adjective), means having the nature of, or having the characteristic of Neutrosophy.

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] may 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).
For software engineering proposals the classical unit interval [0, 1] is used. For single valued neutrosophic logic, the sum of the components is:

0 ≤ t+i+f ≤ 3 when all three components are independent;

0 ≤ t+i+f ≤ 2 when two components are dependent, while the third one is independent from them;

0 ≤ t+i+f ≤ 1 when all three components are dependent.

When three or two of the components T, I, F are independent, one leaves room for incomplete information (sum < 1), paraconsistent and contradictory information (sum > 1), or complete information (sum = 1).

If all three components T, I, F are dependent, then similarly one leaves room for incomplete information (sum < 1), or complete information (sum = 1).

In general, the sum of two components x and y that vary in the unitary interval [0, 1] is: 0 ≤ x + y ≤ 2 -

d°(x, y), where d°(x, y) is the degree of dependence between x and y, while d°(x, y) is the degree of independence between x and y.

In 2013 Smarandache refined the neutrosophic set to n components:

(T1, T2, ...; I1, I2, ...; F1, F2, ...); See http://fs.gallup.unm.edu/n-ValuedNeutrosophicLogic-PiP.pdf

Neutrosophy (From Latin "neuter" - neutral, Greek "sophia" - skill/wisdom) A branch of philosophy, introduced by Florentin Smarandache in 1980, which studies the origin, nature, and scope of neutralities, as well as their interactions with different ideational spectra.

Neutrosophy considers a proposition, theory, event, concept, or entity, "A" in relation to its opposite, "Anti-A" and that which is not A, "Non-A", and that which is neither "A" nor "Anti-A", denoted by "Neut-A".

Neutrosophy is the basis of neutrosophic logic, neutrosophic probability, neutrosophic set, and neutrosophic statistics. {From: The Free Online Dictionary of Computing, edited by Denis Howe from England. Neutrosophy is an extension of the Dialectics.}

The Most Important Books and Papers in the Development of Neutrosophics