In this paper, the method based on Fuzzy Expectation proposed by Kang et al. (2012) is
employed to transform the theorem of a Z-number to a classical fuzzy number. This theorem is
briefly described in the following paragraphs.
Definition: A fuzzy set (A) is defined as: =
;
))| ∈ , where the membership
function A is shown by : → [0; 1]. The expected value of a fuzzy set can be shown as follows:
) = .
)!
"
(2)
I. Convert the second part of a Z-number (i.e., reliability) to a crisp number using the
following equation:
# =
$ %&
)!
$ %&
)!
(3)
II. Add the weight of the second part of the Z-number to the first component (i.e.,
restriction). Therefore, weighted Z-number can be denoted as:
'&( =
, &*
))|&*
) = +&
); ∈ [0,1]