The analytic network process (ANP) is a methodology for multi-criteria decision making used to derive priorities of the compared elements in a network hierarchy, where the dependences and feedback within and between the elements can be considered. However, the ANP is limited to the input preferences as crisp judgments, which is often unfavorable in practical applications. As an extension of the ANP, a generalized analytic network process (G-ANP) is developed to allow multiple forms of preferences, such as crisp (fuzzy) judgments, interval (interval fuzzy) judgments, hesitant (hesitant fuzzy) judgments and stochastic (stochastic fuzzy) judgments. In the G-ANP, a concept of complex comparison matrices (CCMs) is developed to collect decision makers’ preferences in the multiple forms. From a stochastic point of view, we develop an eigenvector method based stochastic preference method (EVM-SPM) to derive priorities from CCMs. The main steps of the G-ANP are summarized, and the implementation of the G-ANP in Matlab and Excel environments are given in detail, which is also a prototype for a decision support system. A real-life example of the piracy risk assessment to the energy channels of China is proposed to demonstrate the G-ANP. 
Generalized analytic network process