Definition of the Neutrosophic Probability Measure

The neutrosophic probability measure is a mapping: \[ NP:X\to \left[ {0,1} \right]^{3} \] where $X$ is a neutrosophic sample space (i.e. $X$ is a sample space that contains some indeterminacy), \[ NP\left( A \right)=\left( {ch\left( A \right),ch\left( {indeterm_{A} } \right),ch\left( {\overline A } \right)} \right), \] where \textit{ch(A)} is the chance that event $A$ occurs$, $\textit{ch(indeterm}$_{A})$ is the indeterminate chance related to occurrence of $A$, and $ch\left( {\overline A } \right)$is the chance that $A$ does not occur, such that: $NP\left( X \right)=\left( {\alpha ,\beta ,\gamma } \right),$ where $^{\mathrm{-}}$0 $\le \quad \alpha \quad + \quad \beta \quad + \quad \gamma \quad \le $ 3$^{\mathrm{+}}$, and $^{\mathrm{-}}$0 $\le \quad \alpha $, $\beta $, $\gamma $ $\le $ 1$^{\mathrm{+}}$. \[ NP\left( {A\cup B} \right)=\left( {ch\left( A \right)+ch\left( B \right),ch\left( {indeterm_{A\cup B} } \right),ch\left( {\overline {A\cup B} } \right)} \right) \] for $A\cap B=\Phi $, and for infinite unions \[ NP\left( {\bigcup\limits_{n\ge 0} {A_{n} } } \right)=\left( {\sum\limits_{n\ge 0} {ch\left( {A_{n} } \right)} ,ch\left( {indeterm} \right)=0.10,ch\left( {\bigcup\limits_{n\ge } {\overline {A_{n} } } } \right)} \right) \] for $A_{n} $ disjoint two by two that lie in the neutrosophic sigma-algebra of events.