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...

Numerical preference relations (NPRs) consisting of numerical judgments can be considered as a general form of the existing preference relations, such as multiplicative preference relations (MPRs), fuzzy preference relations (FPRs), interval MPRs (IV-MPRs) and interval FPRs (IV-FPRs). On the...