#
APS April Meeting 2014

## Volume 59, Number 5

##
Saturday–Tuesday, April 5–8, 2014;
Savannah, Georgia

### Session T1: Poster Session III (14:00-17:00)

2:00 PM,
Monday, April 7, 2014

Room: Exhibit Hall

Sponsoring
Unit:
APS

Abstract ID: BAPS.2014.APR.T1.26

### Abstract: T1.00026 : An Introduction to Neutrosophic Measure

Preview Abstract
Abstract

####
Author:

Florentin Smarandache

(University of Mew Mexico)

We introduce for the first time the scientific notion of neutrosophic
measure.
Let $X$be a neutrosophic set, and $\Sigma $ a $\sigma $-neutrosophic algebra
over $X$. A neutrosophic measure $\nu $ is defined by $\nu :X\to {\rm
R}^{2}$, where $\nu $ is a function that satisfies the following properties:
Null empty set:$\nu \left( \Phi \right)=\left( {0,0} \right)$ and
Countable additivity (or $\sigma $-additivity): For all countable
collections $\left\{ {A_{n} } \right\}_{n\in L} $ of disjoint neutrosophic
sets in $\Sigma $, one has:
\[
\nu \left( {\bigcup\limits_{n\in L} {A_{n} } } \right)=\left(
{\sum\limits_{n\in L} {m\left( {determ\left( {A_{n} } \right)} \right)}
,\mbox{\thinspace }\sum\limits_{n\in L} {m\left( {indeterm\left( {A_{n} }
\right)} \right)} } \right)
\]
\[
\nu \left( A \right)=\left( {measure\mbox{\thinspace }\left(
{determ\thinspace part\thinspace of\mbox{\thinspace }A}
\right),\mbox{\thinspace }measure\mbox{\thinspace }\left(
{indeterm\thinspace part\thinspace of\mbox{\thinspace }A} \right)} \right)
\]
The neutrosophic measure is practically a double classical measure: a
classical measure of the determinate part of a neutrosophic object, and
another classical measure of the indeterminate part of the same neutrosophic
object. Of course, if the indeterminate part does not exist (or its measure
is zero), the neutrosophic measure is reduced to the classical measure.
An approximate number $N$ can be interpreted as a neutrosophic measure
$N={d}+{i}$, where ${d}$ is its determinate part and ${i}$ its indeterminate
part.
For example if we don't know exactly a quantity $q$, but only that it is
between let's say $q\in \left[ {0.8,0.9} \right]$, then $q=0.8+i$, where 0.8
is the determinate part of $q$, and its indeterminate part $i\in \left[
{0,0.1} \right]$.

To cite this abstract, use the following reference: http://meetings.aps.org/link/BAPS.2014.APR.T1.26