Problem $2$

Consider $=\{a,b,c\},$ and denote by $2^{}$ the respective powerset.

a$)$ Let the mass assignment $m$:$2^{}[0,1]$ given as follows:

$m(A)=\{\begin{array}{ccc}0\mathrm{.}5,& A=\{a,& b\}\\ 0\mathrm{.}2,& A=\{c\}\\ 0\mathrm{.}3,& A=\{b,& c\}\\ 0,& \text{e}\text{l}\text{s}\text{e}& \end{array}$

Determine the belief function Bel$(*)$ associated with $m.$

b$)$ Now, consider the belief function given by $Be{l}_{***}(A)=\frac{|A|}{3},$ for every Ain$2^{}.$ Determine the mass assignment associated with this belief function.

c$)$ Is the belief function $Be{l}_{***}$ from b$)$ a probability measure on $(,2^{})?$ Provide a formally justified answer.