Neutrosophic logic, a generalization of the fuzzy logic

Minh Perez (m_l_perez@yahoo.com)
Tue, 10 Aug 1999 12:08:30 +0200 (MET DST)

The fuzzy logic has been generalized to the "neutrosophic logic" in
the book: NEUTROSOPHY: NEUTROSOPHIC PROBABILITY,
SET, AND LOGIC
by Florentin Smarandache, American Research Press
(Rehoboth, Box 141, NM 87322, USA,
M_L_Perez@yahoo.com), ISBN 1-879585-63-4,
105 pages, 1998, in five chapters:

1. The Neutrosophy is a new branch of philosophy which
studies the origin, nature, and scope of neutralities, as
well as their interactions with different ideational spectra.
Let's note by <A> an idea (or proposition, theory, event,
concept, entity), by <Non-A> what is not <A>, and by <Anti-A>
the opposite of <A>. Also, <Neut-A> means what is neither
<A> nor <Anti-A>, i.e. neutrality in between the two extremes.
The Fundamental Thesis: Any idea <A> is t% true, i%
indeterminate, and f% false, where t+i+f = 100 and f,i,t 0
[0, 100].
The Fundamental Theory: Every idea <A> tends to be
neutralized, diminished, balanced by <Non-A> ideas (not only
<Anti-A> as Hegel asserted) - as a state of equilibrium. In
between <A> and <Anti-A> there are infinitely many <Neut-A>
ideas, which may balance <A> without necessarily <Anti-A>
versions.
To neuter an idea one must discover all its three sides: of
sense (truth), of nonsense (falsity), and of undecidability
(indeterminacy) - then reverse/combine them. Afterwards,
the idea will be classified as neutrality.
http://www.gallup.unm.edu/~smarandache/NeutroSo.txt

2. TransDisciplinarity (Multi-Space, Multi-Structure), a
neutrosophic method.
http://www.gallup.unm.edu/~smarandache/TransDis.txt

3. Neutrosophic Probability (as a generalization of the
classical probability) studies the chance that a particular
event <A> will occur, where that chance is represented by
three coordinates (variables): t% true, i% indeterminate, and
f% false, with t+i+f = 100 and f,i,t 0 [0, 100].
Neutrosophic Statistics is the analysis of such events.
http://www.gallup.unm.edu/~smarandache/NeutProb.txt

4. Neutrosophic Set (as a generalization of the fuzzy set)
is a set such that an element belongs to the set with a
neutrosophic probability, i.e. t% is true that the element is
in the set, f% false, and i% indeterminate.
If a proposition <A> is t% true, doesn't necessarily mean
it is (100-t)% false as in fuzzy logic. There should also be a
percent of indeterminacy on the logical values of <A>.
A better approach is t% true, f% false, and i% indeterminate,
where t+i+f = 100 and t,i,f 0 [0, 100], called neutrosophic
logical value of <A>, and noted by n(A) = (t,i,f).
http://www.gallup.unm.edu/~smarandache/NeutSet.txt

5. Neutrosophic Logic (as a generalization of the fuzzy
logic) means the study of neutrosophic logical values of the
propositions. There exist, for each individual one, PRO
parameters, CONTRA parameters, and NEUTER parameters
which influence the above values.
Indeterminacy results from any hazard which may occur, from
unknown parameters, or from new arising conditions.
This resulted from practice.
http://www.gallup.unm.edu/~smarandache/NeutLog.txt

Applications:
Neutrosophic logic is useful in artificial intelligence,
neural networks, evolutionary programming, neutrosophic
dynamic systems, and quantum theory.

Can be ordered from the University of Microfilm International,
300 North Zeeb Road, P.O.Box 1346, Ann Arbor, Michigan
48106-1346, USA, Tel.: 1-800-521-0600, for $33.50. Papers on
this "neutrosophic logic" are welcome,
and they will be published in a <Proceeding on the Neutrosophic Logic>.
Also, a series of books are being publishing on this subject.
Please send your manuscripts at the address:
<Proceedings on the Nuetrosophic Logic>
John Gilbert, editor
American Research Press
Rehoboth, Box 141, USA

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