[117824] in Cypherpunks
Is the Neutrosophic Logic a generalization of the Dempster Shafer Theory? CALL FOR PAPERS
daemon@ATHENA.MIT.EDU (Charles Le)
Sat Sep 11 22:57:23 1999
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Date: Sat, 11 Sep 1999 19:34:14 -0700 (PDT)
From: Charles Le <charlestle@yahoo.com>
To: cypherpunks@toad.com
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Reply-To: Charles Le <charlestle@yahoo.com>
Dear Researchers,
I don't know the Dempster Shafer Theory. Can you, please, define it to
me and give me an example?
It might be a particular case of the Neutrosophic Logic (or Smarandache
Logic)? - see the definition
#4.-----------------------------------------
Papers on neutrosophic logic are welcome and will be published in the
Proceedings of the Neutrosophic Logic and its applications. Deadline:
March 31, 2000.If our manuscript is between 50-100 pages and
cameraready, we'll
publish it as a book, and you receive 100 free copies of it.
The neutrosophic logic is already inluded in Denis Howe's On-Line
Dictionary of Computing,
http://www.instantweb.com/D/dictionary/foldoc.cgi?Smarandache+logic
[The below book review is being published in the "Multiple-Valued
Logic" journal, editor Dr. Ivan Stojmenovic,
UniveristyofOttawa,Canada.]
Charles-------------------------------------------------------
"A Unifying Field In Logics.
Neutrosphy:NeutrosophicProbability,Set,
and Logic", by Florentin Smarandache, American Research Press,
Rehoboth, 1999. (book review by Charles T. Le, American
Research Press,
WindowRock& I 40, Lupton, Box 199, AZ 86508, USA
CharlesTLe@yahoo.com)
Starting from a philosophical point of view in 1990theprofessorand
mathematician Florentin Smarandache has generalized thefuzzylogic,
the multi-valued logic, paraconsistent logic,intuitionisticlogicin
the form of "neutrosophic logic". This new logicarousestheambition
of unifying all logics in one field, similarly to Felix Klein's
unification of geometries and to Albert Einstein's unified field
inphysics.
There are many ways to define the neutrosophic set operationsorthe
neutrosophic logical connectives, and the way they are chosen is
important in the neural networks, artificial intelligence, and
quantum theory. The author defines first the
"neutrosophy",his
philosophicaltheory
which asserts that each idea is t% true, i% indeterminate, and f%
false, where t varies in a real subset T, i varies in
arealsubsetI,
and f varies in a real subset F, with no restrictions on T,I,F,nor
on their superior or inferior sums. For example, apropositionmaybe
between 20-30% true (due to multiple sourcesordifferentanalysers),
40 or 45% indeterminate and 65-70 or75% false. This leaves roomfor
much interpretation. I.e., if we have a paradox, this might be100%
true and 100% false in the same time! Neutrosophy is based on
neutralities (indeterminacies) and overlappings. Aneasierexampleis
that a proposition may be 60% true and 70% false (thecomponentsare
not required to sum up 100 like in fuzzy logic, and
someofthemmight
be even negative or greater than 100 - in tautologies). With this
tool, he spreads out the attribute "neutrosophic" to probability,
statistics, set theory, and of course to logic.
Here the are the definitions, introduced by FlorentinSmarandche,of
the "neutrosophic probability", "neutrosophic statistics",
"neutrosophic set", and "neutrosophic logic" and some explanations
compiled from the above book. 1) NEUTROSOPHIC PROBABILITY:
Let T, I, F be real subsets, with sup T = t_sup, inf T =t_inf,supI
=
i_sup, inf I = i_inf, sup F = f_sup, inf F = f_inf, and
n_sup=t_sup+i_sup+f_sup, n_inf=t_inf+i_inf+f_inf.
The neutrosophic probability is a generalization of the classical
probability in which the chance that an event A occurs is t% true
-where t varies in the subset T, i% indeterminate - whereivariesin
the subset I, and f% false - where f varies in the subset F(withno
restrictions on the real subsets T, I, F, neither
ontheirsuperiorsum
n_sup, nor on their inferior sum n_inf).
The sets T, I, F are not necessarily intervals, but may be anyreal
subsets: discrete or continuous;
single-element,finite,or(countably
or uncountably) infinite; union or intersection of varioussubsets;
formed of positive or negative numbers; etc. They may alsooverlap.
One notes NP(A)=(T,I,F), a triple of sets.
This representation is closer to the human mind reasoning than any
other used logic. In the case when the truth-andfalsity-components
are complementary, i.e. no indeterminacy and their sum is 100, one
falls to the classical probability. As, for example, tossingdiceor
coins, or drawing cards from a well-shuffled
deck,ordrawingballsfrom
an urn. 2) NEUTROSOPHIC STATISTICS:
Analysis of the events described by the neutrosophicprobability.
This is also a generalization of the classical statistics.
3) NEUTROSOPHIC SET:
Let T, I, F be real subsets, with sup T = t_sup, inf T =t_inf,supI
=
i_sup, inf I = i_inf, sup F = f_sup, inf F = f_inf, and
n_sup=t_sup+i_sup+f_sup, n_inf=t_inf+i_inf+f_inf.
An element x(T,I,F) belongs to a set M in the following way:itist%
true in the set, i% indeterminate in the set, and f% false, wheret
varies in T, i varies in I, f varies in F (with
norestrictionsonthe
real subsets T, I, F, neither on their superior sum
n_sup,norontheir
inferior sum n_inf).
One can say, by language abuse, that any element neutrosophically
belongs to any set, due to the percentages of
truth/indeterminacy/falsity involved, which varies between
0and100or
even less than 0 or greater than 100.
For example: x(50,20,30) belongs to A (which
means,withaprobability
of 50% x is in A, with a probability of 30% x is not in
A,andtherest
is undecidable), or y(0,0,100) belongs to A (which
normallymeansyis
not for sure in A), or z(0,100,0) belongs to A
(whichmeansonedoesn't
know absolutely anything about z's affiliation with A).
More general, x( (20-30), (40-45)U[50-51], {20,24,28}
)belongstothe
set A, which means:
- with a probability in between 20-30% x is in A (one cannotfindan
exact appurtenance because of various sources used);
- with a probability of 20% or 24% or 28% x is not in A;
- the indeterminacy related to the appurtenance of x to A is in
between 40-45% or between 50-51% (limits included).
The subsets representing the appurtenance,indeterminacy,andfalsity
may overlap, and n_sup = 30+51+28 > 100 in this case.
4) NEUTROSOPHIC LOGIC (OR SMARANDACHE LOGIC - as
namedinDenisHowe's
On-Line Dictionary of Computing,
http://foldoc.doc.ic.ac.uk/foldoc/foldoc.cgi?Smarandache+logic):
A logic in which each proposition is estimated tohavethepercentage
of truth in a subset T, the percentage of indeterminacy
inasubsetI,
and the percentage of falsity in a subset F, with
norestrictiononthe
subsets T, I, F, neither on
theirsuperiorsumn_sup=t_sup+i_sup+f_sup
nor on their inferior sum n_inf=t_inf+i_inf+f_inf, where
supT=t_sup,
inf T = t_inf; sup I = i_sup, inf I = i_inf; sup F = f_sup, inf F=
f_inf. We use a set of truth/falsity, instead of a number only,
because in many cases we are unable to exactly determine the
percentages of truth and of falsity but to approximate them: for
example a proposition is between 30-40% true
andbetween60-70%false,
even worst: between 30-40% or 45-50% true (according to various
analysers), and 60% or between 66-70% false.
The subsets are not necessary intervals, but any real subsets
(discrete, continuous, open or closed or half-open/half-closed
intervals, intersections or unions of the previous subsets,etc.)in
accordance with the given proposition.
A such subset may have one element only in special cases of this
logic.
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