A Novel Solution for $Z$-Numbers Based on Complex Fuzzy Sets and Its Application in Decision-Making System

$Z$
-numbers have been proven to be advantageous in revealing uncertain information. This article focuses on applying uncertain
$Z$
-numbers to engineering practice. Considering that various uncertain data are inevitable in the process of addressing actual problems, uncertain
$Z$
-numbers are introduced to express information and measure information reliability. Powerful tools are essential when dealing with uncertain information; then, complex fuzzy sets (CFSs) are employed. First, the parameter
$B$
in
$Z$
-numbers is interpreted from the perspective of the phase term, and uncertain
$Z$
-numbers are transformed to interval-valued CFSs. Next, arithmetic operators, aggregation operator, generalized entropy, distance measure, and similarity measure are defined. Besides, a multicriteria group decision-making method is suggested by combining the proposed entropy, distance measure, and aggregation operator. The algorithm is applied to select the brand of the inertial navigation system. The comparison analysis with other widely used methods is conducted to verify the feasibility and validity of
$Z$
-information in the application.